The ability to control cellular functions can bring about many developments in basic biological research and its applications. The presence of multiple signals, internal as well as externally imposed, introduces several challenges for controlling cellular functions. Additionally the lack of clear understanding of the cellular signaling network limits our ability to infer the responses to a number of signals. This work investigates the control of Kaposi's sarcoma-associated herpesvirus reactivation upon treatment with a combination of multiple signals. We utilize mathematical model-based as well as experiment-based approaches to achieve the desired goals of maximizing virus reactivation. The results show that appropriately selected control signals can induce virus lytic gene expression about ten folds higher than a single drug; these results were validated by comparing the results of the two approaches, and experimentally using multiple assays. Additionally, we have quantitatively analyzed potential interactions between the used combinations of drugs. Some of these interactions were consistent with existing literature, and new interactions emerged and warrant further studies. The work presents a general method that can be used to quantitatively and systematically study multi-signal induced responses. It enables optimization of combinations to achieve desired responses. It also allows identifying critical nodes mediating the multi-signal induced responses. The concept and the approach used in this work will be directly applicable to other diseases such as AIDS and cancer. There is an increasing interest in utilizing and applying systems biological approaches to study a wide range of problems in biology. In this work, we apply different systems biological approaches to investigate the effects of multiple signals on cellular signaling processes with the goals of understanding and controlling these processes. As a model systems, we use the reactivation of Kaposi's Sarcoma-associated herpesvirus (KSHV) to investigate the effects of several drugs on a quantifiable process, virus reactivation. KSHV, also known as human herpesvirus-8 (HHV-8), is a member of the herpesvirus family, which includes simplex viruses, Epstein-Barr virus (EBV) and cytomegalovirus Herpesviruses have two distinct phases in their life cycle: latency and lytic replication. Latency is one strategy for viruses to achieve life-long persistent infection. During latency, the viral genome is replicated by cellular DNA polymerase and only a few gene products are expressed at low levels. A reactivation process causes the virus to enter the lytic replication state from latency and upon replication of the viral genome by a viral DNA polymerase, viral progeny are produced, frequently resulting in cell death. Virus reactivation is controlled by a cellular signaling process in which cellular signals are amplified and can be measured with markers such as Green Fluorescent Protein (GFP) or luciferase. In earlier work, we identified RTA (replication and transcription activator) of KSHV, an immediate-early gene, as the switch in the reactivation process Reactivation, the switch from latency to lytic replication, is an important process for KSHV pathogenesis and a target for the development of therapeutic strategies for the associated tumors. Investigation of the multi-drug regulated reactivation process provides important information for the associated cancer treatment. It should be therapeutically advantageous to intentionally activate the viral lytic cycle in tumor cells in the presence of an anti-herpesviral drug, such as ganciclovir Maximal induction of virus replication is necessary for an effective therapeutic approach. Several studies have looked at inducing KSHV reactivation with a single drug Here, we utilize different approaches to study the problem of multi-signal induced KSHV reactivation. First, we utilized mathematical modeling and learning tools to enable systematic and effective selection of combinations of drugs that can result in high reactivation. This approach is based on using input-output data obtained by testing a relatively small number of signal combinations to create a mathematical model that can predict the responses to the complete space of combinations of considered signals and their respective concentrations. The model, in turn, was used for further analysis of the system and to select combinations that can control the cellular responses in a desired manner. Second, we utilized a stochastic search algorithm to drive a set of experimental trials with the goal of identifying combinations of signals that can yield high reactivation. The results of both approaches were compared and further experimental assays were used to validate the results. Third, we used a combination of linear regression models and subset selection algorithms to identify key factors influencing the multi-signal driven responses. We were able to identify multiple drug interactions that play a dominant role in the response. These interactions represent a subset of the possible connections between the signaling targets.Five drugs were selected to be tested in combination See . Each ofIn order to quantify the viral reactivation response, the RTA binding site in the PAN promoter was identified Measurement of virus reactivation was achieved using flow cytometry where we measured the number of activated cells, i.e., GFP positive, and the total number of cells, i.e., the number of dead and living cells. The reactivation rate (performance) of any given combination was set to be the ratio of GFP positive cells to the total number of cells including dead cells.Investigation of the combinatorial effect of multiple participating pathways on reactivation can be achieved by treating the latently-infected cells with related chemical agents. Single drug dose curves for each chemical agent were obtained to determine the range of effectiveness of each individual chemical agent . Based oUsing a uniform probability distribution over the set of all combinations of concentrations of five drugs, we randomly selected 600 different combinations to be experimentally tested. Six sets of experiments were conducted. In each set, 100 data points along with a positive control, a single drug (TPA) known to reactivate the virus The inputs (drug combinations) and their corresponding measured outputs (reactivation rates) were used to generate a mathematical model, KSHV reactivation model. The predictive reactivation model approximates the KSHV reactivation rate as induced by a combination of drugs within the specified range of drug concentrations. The model can be used to simulate and predict reactivation rates in response to all combinations of the five chemical agents. The combinations are not limited to the 600 tested combinations and include all combinations of the lower order mixtures, i.e., two, three, and four-drug combinations. The use of this relatively small number of combinations is facilitated by the assumption that the response function to these five drugs is reasonably smooth. If the response function is not very smooth then it would require testing of additional combinations to improve the accuracy and prediction power of the model.Several methods can be used to generate a mathematical model. We utilize neural networks, linear regression We trained a multi-layered perceptron with the data and obtained a representative predictive model see the  section.The predictive model generated provides the ability to determine combinations that can lead to high reactivation rates as predicted by the model. The simulated reactivation rates of all termined . The disAn alternate approach to determine the top performing combinations is to utilize a search algorithm, deterministic or stochastic. Examples include gradient descent algorithms The cross entropy algorithm was implemented in silico using the KSHV predictive reactivation model see . The simAn alternate approach to optimizing drug combinations is the use of a search algorithm implemented experimentally rather than on a mathematical model. Recently, several examples of this approach has emerged in biology The experimental cross entropy implementation proceeded in a sequence of experimental iterations. Our results showed that after 12 to 14 iterations, the drug concentrations converged to the ranges leading to consistently high reactivation rates . The conUsing two different approaches, we were able to identify a range of concentrations for which high virus reactivation rates are achievable. The results of the two approaches were consistent. To further validate the findings, we conducted sets of experiments to compare the performance of a selected combination from the identified range to the performances of single drugs.The KSHV early lytic protein K8 is activated by, and expressed after the expression of KSHV RTA (ORF50). It is important for initiating viral DNA replication in the lytic cycle, thus a good marker for viral lytic replication. Western blot analysis of K8 showed that the selected drug combination can cause a much higher induction of K8 than any single drug. The conclusion was consistent 8 hours and 12 hours post treatment .Additionally, we looked at the effect of the selected drug combination on the KSHV lytic transcripts RTA (ORF50) and PAN. RTA plays a central role in regulating the switch from latency to lytic replication in KSHV The signaling network involves complex connections between various molecules that can be perturbed through a large number of external signals. The signals can cause inhibition of certain molecules/pathways and stimulation of others. The interactions amongst these molecules or pathways are very complex and very hard to predict. Alternately, looking at interactions between the input signals and the measured cellular outputs can shed some light on the induced behaviors at the systems level. Particularly, we can uncover some of the interactions of the signaling that are involved in generating the responses upon stimulation with multiple stimuli.Based on the predictive reactivation model, we simulated the interactions generated by the five drugs. The data represents a complex multi-dimensional data set. While some mathematical tools can be useful in reducing this complexity, one might be interested in visually examining the behaviors represented by such a large data set. To that end we created an interactive webpage which displays the KSHV reactivation rates for varying concentrations of the considered drugs Our findings indicate that the dose dependent effect of the individual drugs on reactivation greatly depended on the amounts of the other drugs within the same treatment . The nonThe addition of low concentrations of Bortezomib to combinations of db-cAMP and Prostratin does not result in a significant increase in performance. Higher concentrations of Bortezomib result in a significant decrease in performance. Examining the effect of only adding Valproate to combinations of Bortezomib, db-cAMP, and Prostratin, we notice an increase in performance, indicating that Valproate interacts positively with the three-drug combinations to improve the reactivation. The sole addition of Dexamethasone to combinations of Bortezomib, db-cAMP, and Prostratin results in a smaller increase in performance. The increase becomes less when high concentrations of Bortezomib are used.The above results reflect visual analysis of the responses, in the sequel, we seek to quantitatively analyze these interactions to determine the most significant ones. Such can be achieved using mathematical modeling similar to what is used for optimization. While a drawback of neural networks models is that they are black-box models and do not shed light onto how the different inputs are processed to produce the outputs, other modeling techniques can help in this regard. We fitted a linear regression model to represent the relationship between the drugs and the reactivation see  section.The correlation coefficient between the experimental data and predicted data based on the linear model was 85%, the correlation coefficient for the additional 48 points was 83%. The model provides an insight into which factors play the biggest role in the response . In agreThe residual sum of squares of the best models shows that there is no significant reduction in the residual sum of squares for models with more than 10 variables . This indicates that 10 variables are sufficient to generate a model with comparable prediction and error to the 31-variable model . The 10 Testing a system with five drugs provides advantages over studying mixtures of a smaller set of drugs. A system level study of combinations of multiple drugs enables fast and effective selection of a smaller subset of drugs that is most potent. Although a set of five drugs was used in this study, it is sometimes desirable to use a smaller number of drugs that can interact in a desirable way. We computed the maximum predicted reactivation rate for all possible mixtures of two, three, four, and five drugs, as well as for single drugs . The figFor two-drug mixtures, there is over a six-fold difference between best and worst two-drug combinations. A mixture of Bortezomib and Dexamethasone or Valproate and Dexamethasone perform poorly even compared to a single drug. In contrast, a combination of db-cAMP and Prostratin have a reactivation rate higher than the sum of the individual reactivation rates. Prostratin and Valproate exhibit a similar behavior. This is consistent with our findings of strong positive interaction between Prostratin and Valproate. A mixture of Bortezomib and Prostratin does not improve on the best reactivation rate of Prostratin, suggesting negative or no interaction between the two drugs. This is also consistent with the findings presented above.For three-drug combinations, the best combination is more than twice as effective as the worst mixtures. Furthermore, the best three-drug mixture is about 130% more effective than the best two-drug mixture. Four and five-drug mixture are slightly more effective than the best three-drug mixture. The four-drug mixtures generally perform better than than the three-drug mixtures.Without a study of the combinations of five drugs, evaluating the reactivation rates for combinations of two drugs requires conducting 10 experiments individually to determine the maximum reactivation rate of the 10 possible two-drug combinations out of a set of possible five drugs. Selection of three or four-drug combinations requires similar experiments. Therefore, the combinations of the systems approach, computational tools, and experimental design enabled efficient multi-signal control of cellular/viral processes.Our results indicate that the use of combinations of drugs can have a substantial effect on virus reactivation. In particular, multiple drugs can interact and induce higher levels of virus reactivation. However, the combination needs to be judiciously selected out of a large number of drug concentration combinations. The use of an improperly selected combination can have a drastic effect on the cellular response and on virus reactivation. The low reactivation rates of combinations imply either the ineffectiveness of these combinations in reactivating the virus or the high toxicity of these combinations. The biological relevance of our results was supported by multiple experimental assays that directly measured viral lytic replication products, and demonstrated a synergistic reactivation by a proper drug combination, much higher than by any individual drug, a pattern very consistent with what was obtained in the fluorescent reporter system. The measurement of virion production 48 hours post treatment also confirms our findings and provides additional proof of the validity of our approach. The work presented here, builds upon our recent work in which the approaches used here were introduced to address another problem of multiple signal response quantification and analysis and were applied to study the differential response of cancer and normal cells With the development of genomics and proteomics, more and more cellular components and their physical interactions are identified. However, their dynamic functional interactions have not been studied extensively or quantitatively. Systems biological approaches are emerging with the aim of understanding these functional interactions. In retrospect, a mathematical model-based approach provides means for understanding system level behaviors exhibited by the interacting cellular components in response to one or multiple stimuli.Moreover, the emerging interest and need to develop combination therapies and individualized medicine calls for additional efforts in analyzing multi-signal induced cellular responses. Studies should also involve examining multiple cellular outputs or network signaling intermediates in response to multiple cellular inputs. The approach used in this work is capable of addressing such problems. Additionally, examining the kinetics of cellular responses will allow for more dynamic control.This study using KSHV reactivation as a model system to study multi-signal response quantification, a general issue in cell biology. The concept and the approach used in this work will be directly applicable to other problems such as Epstein-Barr Virus (EBV)-associated malignancies. Moreover, many cancers and HIV associated malignancies can benefit from systematic approaches to studying multi-signal induced responses.The selection of suitable drug combinations was achieved using two different approaches. The experiment-based cross entropy implementation involved iterative testing of combinations in order to search for best performing combinations. The algorithm showed reasonable convergence. The advantages of experiment-based optimization are apparent when the objective function is clearly defined and we are interested in achieving that goal in a reasonably smaller number of tests. Furthermore, when there is no interest in deducing more information regarding the relationship between input signals and output responses, an experiment-based optimization approach can yield satisfactory results without added experimental overhead.On the other hand, a model-based approach was also quite effective in achieving the desired goals. The results were consistent between the two different approaches emphasizing the power of using various mathematical tools to study biological problems. Generating a predictive model required testing a relatively small number of drug combinations. As the combinations are tested over a shorter period of time, the sensitivity of this approach to variations in cell conditions is less prevalent than the experiment-based approach. Another advantage of a model-based approach is that it enables optimizing combinations based on a different number of performance functions with varying sets of parameters without additional experimental measurement. This allows efficient analysis of multiple optimization questions and enables customization of combinations to specific needs, e.g., personalization of treatment based on an individual's characteristics. The model also can be used to study problems beyond the optimization and control of cellular responses such as analyzing the relationships between the various signals in view of the effects of these signals on some measured the cellular outputs.The selected drugs target distinct parts within the signaling network. Yet, there are significant interactions between the targets of these drugs through other molecules within the signaling network. To illustrate this, we have summarized the interactions as predicted by the neural network model and through the regression analysis . These iin vitro and in vivo .5- CACAAAAATGGCGCAAGATGA-3) and ORF50-R (5- TGGTAGAGTTGGGCCTTCAGTT-3); PAN-F (5-GCCGCTTCTGGTTTTCATTG-3) and PAN-R (5-TTGCCAAAAGCGACGCA-3); GAPDH-F (5-GAAGGTGAAGGTCGGAGTC- 3) and GAPDH-R (5-GAAGATGGTGATGGGATTTC-3).The RT-Q-PCR was performed in an Opticon2MJ thermocycler (MJ Research). The primers used for RT-Q-PCR were: ORF50-F  of each neuron is a sigmoidal function. The selection of this neural network structure was a result of trying different structures with a varying number of neurons. The input and output data was pre-processed prior to training by mapping them into the  range. Outputs of the network were post-processed to map them back to the original range. Preprocessing of data allows for better training of the network. A back-propagation Levenberg-Marquardt algorithm was used to train the neural network. The neural network fitting algorithm divides the data into three sets, training (98%), validation (1%), and testing (1%). The training and validation sets are used to train the model and prevent overfitting of data. The testing data is used for post analysis to assess the models predictive capabilities. However, this set is small and no meaningful conclusions can be drawn from it. Instead, we tested an additional set of 48 combinations and used that to test the generalizability of the model (see main text). The low percentages of validation and training set sizes were chosen to maximize the number of points used to fit the model. Training of the model was done using the neural network toolbox of Matlab.We applied the cross entropy combinatorial optimization algorithm both to the predictive reactivation model and experimentally to optimize multi-drug combinations for high KSHV reactivation. The search process evolves in iterations in which the performances of selected points are evaluated. The selected points are randomly chosen using joint Gaussian probability density function over the set of all combinations. The assumption of independence between the different input variables results in a joint density function which is the product of Gaussian distributions, each associated with an input variable. Each Gaussian distribution has a mean and a standard deviation which are continuously updated through the iterations of the algorithm. The means and standard deviations of the distributions reflect the current belief of the values of the maximizing inputs as well as the confidence level. The evolution of the means and standard deviations is based on the convex combination of the current means and standard deviations, and the means and standard deviations of a top performing percentage of model-predicted  performances. The algorithm terminates when the change in the means becomes small and the standard deviations approach zero.In the experimental CE implementation, and similar to the simulated CE implementation, 45 drug combinations were selected in our setup to enable the collection of as many stimuli- response data as enabled by manual measurements. In each iteration, the performances of 45 randomly chosen sample combinations were experimentally evaluated. The top performing 16% of combinations were used to update the means and standard deviations. The choice of 45 combinations was based on a feasible number of combinations to be tested manually in duplicates and based on the previous section. The iterations proceeded for months.The response of the virus is experimentally measured and is denoted by the functionNotice that since the smallest value for the concentrations is zero, taking the log is not possible. Instead, we replace the zero elements in the concentrations with a pseudo element equal to one half of the lowest concentration greater than zero. Whenever the random outcome of a sample element is the pseudo element, it is replaced with zero in the testing stage.Therefore, the elements of the samples, i.e., To make sure that all data points lie within the allowable input range, any point lying outside the allowable input range was dropped and a new point was generated using the same probability density function. Furthermore, the random outcomes are rounded off or discretized to the nearest possible concentration value in the following manner. First, let The discretized It is important to note that implementation of the CE method to the mathematical model is not necessary unless the number of drugs and concentration is very large, in which case the CE method provides a computational faster approach for searching for the optimal. For systems with 5 drugs a simple sorting algorithm that ranks combinations based on their performance suffices and is reasonably fast.We used a regression model that is linear in the log of the concentrations. The model is of the formExamining the eigenvalues of the correlation matrix To evaluate the convergence of the cross entropy method, we ran several simulations. First, one thousand different runs of cross entropy were executed, each using 45 samples per iteration. The same initial means and standard deviations were used for all one thousand runs. The results showed that the algorithm converged to combinations whose performance is within 16% of the maximum performance. Out of the one thousand runs, 556 converged within 5% of the maximum performance and 778 within 10% of maximum performance. A similar set of simulations was also conducted except that the initial means for the one thousand runs were randomly chosen, thereby starting with different parts of the combination space. All one thousand runs converged within 21% of the maximum. 557 runs converged to within 5% of the maximum performance, whereas 776 converged within 10% of the maximum performance.A similar set of simulations was also conducted in which the number of samples per iterations was increased to 100 samples, thereby sampling the combination space with a higher density. The results show that with all runs starting from the same initial set of means and standard deviations, all runs converged to combinations with a performance within 13% of the maximum performance. Out of the one thousand runs 730 converged within 5% and 922 within 10%. Starting with randomly chosen means at the beginning of every run resulted in similar numbers with all one thousand runs converging within 13% of the maximum performance, with 735 runs converging within 5% and 935 converging within 10%.In the above simulations, the algorithm used the performances of the top performing 16% of the samples within each iteration to update the means and standard deviations. Decreasing the number to 8% with 100 samples per iteration the algorithm converged within 12% of the maximum performance for all one thousand runs starting with the same initial set of means and standard deviations. 850 converged within 5% and 987 converged within 10%. Starting from randomly chosen means convergence was to within 16% of the maximum performance with 859 runs converging within 5% and 984 runs within 10%.In all, the simulations suggest that the optimization algorithm is capable of consistently identifying top performing combinations without requiring to test many samples. This also introduces an important question on whether the algorithm can be utilized to drive a set of experimental trials to optimize the reactivation of the virus reactivation. Such a result would provide validation of the computational approach and would also suggest a direct experimental approach that can be used to optimize drug combinations through a sequence of trials.


We introduce a new method for mesoscopic modeling of protein diffusion in an entire cell. This method is based on the construction of a three-dimensional digital model cell from confocal microscopy data. The model cell is segmented into the cytoplasm, nucleus, plasma membrane, and nuclear envelope, in which environment protein motion is modeled by fully numerical mesoscopic methods. Finer cellular structures that cannot be resolved with the imaging technique, which significantly affect protein motion, are accounted for in this method by assigning an effective, position-dependent porosity to the cell. This porosity can also be determined by confocal microscopy using the equilibrium distribution of a non-binding fluorescent protein. Distinction can now be made within this method between diffusion in the liquid phase of the cell (cytosol/nucleosol) and the cytoplasm/nucleoplasm. Here we applied the method to analyze fluorescence recovery after photobleach (FRAP) experiments in which the diffusion coefficient of a freely-diffusing model protein was determined for two different cell lines, and to explain the clear difference typically observed between conventional FRAP results and those of fluorescence correlation spectroscopy (FCS). A large difference was found in the FRAP experiments between diffusion in the cytoplasm/nucleoplasm and in the cytosol/nucleosol, for all of which the diffusion coefficients were determined. The cytosol results were found to be in very good agreement with those by FCS. Living cells are multifunctional organisms that exhibit remarkable dynamic phenomena including, e.g., cell motility, and vesicular, cytoplasmic and nuclear transport. The cytoplasm consists of a viscous liquid phase (the cytosol) and a non-liquid phase that will be called here the solid phase. The protein concentration in the cytoplasm has been estimated to be 100 mg/ml Diffusive motion of macromolecules and their binding-dissociation reactions with cellular organelles is a crucial component of cell function, which still need to be clarified. Laser scanning confocal microscopy (LSCM) has become very popular as it allows three-dimensional observation in living cells. LSCM can also be used to perform photo-manipulation experiments such as quantitative fluorescence recovery after photobleaching (FRAP). In FRAP, a region of the cell is exposed to high-intensity laser light, causing the fluorophores within that region to irreversibly lose their ability to fluoresce. Recovery of fluorescence in that region yields information about molecular diffusion and binding in the cell Since the invention of FRAP, several analytical models have been developed to quantify the recovery of fluorescence and thereby diffusion and binding dynamics Fluorescence correlation spectroscopy (FCS) is a method that probes the diffusion coefficient locally, while FRAP probes quite widely the cytoplasm (nucleus). Fluorescence fluctuation microscopy (FFM) combines FCS with LSCM, thereby being able to image the cell environment in which the FCS measurement is conducted. It is expected that the diffusion coefficients measured by FFM and conventional FRAP are quite different unless the internal structure of the cell is included in the latter. There are indeed large differences between the diffusion coefficients reported by FRAP and FFM measurements We introduce therefore a completely new approach to protein dynamics in the cell based on describing their diffusive motion in a realistic three-dimensional representation of the cell generated from LSCM data. As it is neither useful nor possible to simulate the dynamics of all proteins of a species in an entire cell at a molecular level of detail, we rely here on mesoscopic methods to model protein distributions instead. This approach is applied here to analysis of FRAP data on the same cell. The model cell takes into account the internal structure of the cell using the inhomogeneous fluorophore distribution at equilibrium. We introduce the new methods by determining the diffusion coefficient of a freely-diffusing model protein, enhanced yellow fluorescent protein (EYFP), in two continuous cell lines, fibroblast-like Norden Laboratory Feline Kidney (NLFK) Norden laboratory feline kidney (NLFK) The FRAP experiments were performed on a laser scanning confocal microscope FV1000 with an IX-81 microscope frame  using an Olympus UPLSAPO 60× (NA = 1.2) water immersion objective. The sample stage was heated to 37°C prior the experiments. To image the cell geometry, a confocal stack was acquired before and after the FRAP experiment. The voxel size was adjusted to (200 nm)ed cells . ImageJ The duration of the bleach process was measured by performing FRAP experiments in which 10 images were collected before the bleach pulse and 1 after the pulse. The bleach time was extracted by measuring the time when the frames immediately before and after the bleach pulse were taken. The average imaging time of one frame was subtracted, and the duration of the bleach process was plotted as a function of iterations (bleaching time), yielding a linear slope. In the LSCM used (Olympus FV 1000), the shortest possible bleach procedure (1 iteration) lasted 36 ms with an additional relay of 18 ms before the next image scan, amounting to 54 ms for the entire process. To achieve enough bleaching for the data analysis, 10 iterations were performed , and theThe raw images of the confocal microscope were converted to 8-bit grey scale images. Only linear adjustments of the image brightness and contrast were performed, avoiding saturation. The gray-scale images were colored with an appropriate look-up table and converted to RGB images.The fluorescence recovery was analyzed in the circular regions described above using the ImageJ The fluorescence intensity data were fitted by the free diffusion model of Soumpasis The Fluorescence Fluctuation Microscope (FFM) measurements were conducted with a self made setup in Heidelberg EYFP was excited with the 488 nm line of an argon-krypton laser from CVI Melles Griot . The emitted fluorescence from EYFP was recorded between 515 and 545 nm with an avalanche photodiode (APD) , after passing through appropriate dichroic mirrors and filters for spectral separation and selection. FCS measurements were carried out at laser intensities of 5 to 9 kW cmThe system was carefully calibrated as described in For each FRAP experiment we obtained two sets of data: a 3D stack of images depicting the intensity profile of EYFP and H2B-ECFP (histone H2B linked to enhanced cyan fluorescent protein)in the cell before the bleach, and a stack of 2D images depicting a certain cross-section of the cell during the FRAP measurement, 10 frames before the bleach and the rest of the frames from the fluorescence recovery phase. After de-noising the 3D stacks, we used the threshold function of the ImageJ program to segment in the cell the cytoplasm and nucleus using the EYFP and H2B-ECFP stacks, respectively. The nuclear envelope was then generated as a two pixel wide layer between the cytoplasm and nucleus using a self-made code.The spatial resolution of LSCM, about 200 nm, did not allow segmentation of the more detailed structure. As this ‘fine structure’ obstructs protein motion and thus affects protein diffusion, we considered the cytoplasm (nucleoplasm) as an ‘effective porous medium’ that is immobile during a FRAP measurement.From diffusion in porous media Due to the low imaging speed of the LSCM used, only a 2D cross section of the cell was imaged during the FRAP experiments. In order to be able to simulate the FRAP recovery in the entire cell, the initial bleach profile had to be extrapolated vertically into the rest of the digital cell. To this end we first determined the relative fluorescence reduction The cross section of the cell, which was imaged during the FRAP experiment, was determined by cross-correlating each frame of The spatial and temporal evolution of diffusion processes is described by the diffusion equation,In the case of complicated boundary conditions it is, for a numerical realization of Eq. 5, more convenient to start at a somewhat more microscopic level. We thus consider instead the Boltzmann equation When applied to modeling a FRAP experiment, the particle density A numerical code was constructed along the lines indicated above, which was capable of simulating the spatial and temporal evolution of the fluorescence intensity in the digital realization of the cell actually measured in the FRAP experiments. When the distribution of fluorescence intensity as measured right after the bleach was taken as the initial condition in the simulation, such simulations could very accurately reproduce the experimentally observed fluorescence recovery.At every time step during FRAP recovery, the fluorophore distribution was simulated in the whole model cell, and it was recorded in the same cross section as in the measurement. We compared the experimental and simulated frames by cross correlation such that the cross-correlation coefficient was given byThe experimental and simulated frames could be compared directly using this algorithm. In practice however, the cross-correlation results were improved greatly if the cell background was removed from all the images  method for the numerical realization of the diffusion equation. Other methods could also have been used, but the LB method allows an easy implementation of the boundary conditions and an easy generalization to binding-dissociation processes that we intend to include later.The new modeling instrument was applied to model FRAP experiments that are known to produce typically much lower diffusion coefficients for proteins, when conventional modeling is used to interpret the measured data, than FCS experiments. The fluorescence intensity distribution measured right after the bleach process was used as the starting point for the simulated (post-bleach) evolution of that distribution in the entire cell. Thus, in the new method, problems related within conventional modeling to, e.g., intensity normalization, finite volume of fluorophore distribution, and internal membrane structures, were all removed.As it was expected that the internal membrane structures in the cytoplasm (and nucleoplasm) play an important role in protein transport in the cell, special emphasis was put on properly describing their effect. As described above, such structures could be included as non-accessible regions for protein motion by describing both the cytoplasm and the nucleolasm as porous media. This is not, however, enough. The heterogeneous fluorescence intensity in the cytoplasm/nucleoplasm was interpreted such that it was homogeneous in their liquid phases in which the diffusive motion of proteins only takes place. Distinction was therefore made between diffusive motion in the liquid phases and in the whole cytoplasm/nucleoplasm. The former diffusion coefficients are intrinsic properties of the liquid phases independent of where bleaching is performed. In contrast with this, the cytoplasm/nucleoplasm diffusion coefficient depends on the local membrane structures in and near the region of interest, and varies appreciably.In order to better understand the distinction between the two types of diffusion coefficient, consider an artificial porous medium a cross section of which is shown in Diffusion of a small non-binding (non-specific binding was assumed to be negligible) fluorescent protein was then analyzed by FRAP, using the new as well as conventional methods, and by FFM, and two different cells were used in these analyzes for generality.average cytoplasm diffusion coefficient was about a third of that of cytosol, indicating a similar relative amount of membrane structures in the cytoplasm. FFM analysis of the cytoplasm resulted in diffusion coefficients that were very similar to those found by FRAP for the cytosol. This method probes rather closely the properties of the liquid phase, but if there are ‘solid phase’ structures near the region analyzed, they however affect cytoplasm diffusion coefficients in FRAP experiments, and they display strong variation. Evidently it is important to make a distinction in the interpretation of FRAP experiments between diffusion in the cytosol (nucleosol) and in the cytoplasm (nucleoplasm). Using a conventional modeling of the same FRAP experiments, much too low diffusion coefficients were found. The assumptions made in the conventional modeling were not realized in the experimental situation, and no difference was made either between cytosol and cytoplasm diffusion.Using FRAP combined with the new analysis method, the cytosol diffusion coefficients were found to be different in the NLFK and HeLa cells, indicating a different macromolecular concentration (‘viscosity’) in the cytoplasm. In both cases the Without fine tuning the nucleus and nuclear envelope results we found by the new FRAP method that the For clarity we considered here pure diffusion, but the methods introduced can be extended so as to include interactions of proteins with cellular organelles.


Trypanosoma brucei is a particularly well analysed example of a quantitative metabolic model, but so far it has been studied with a fixed set of parameters only. Here we evaluate the effect of parameter uncertainty. In order to define probability distributions for each parameter, information about the experimental sources and confidence intervals for all parameters were collected. We created a wiki-based website dedicated to the detailed documentation of this information: the SilicoTryp wiki (http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis). Using information collected in the wiki, we then assigned probability distributions to all parameters of the model. This allowed us to sample sets of alternative models, accurately representing our degree of uncertainty. Some properties of the model, such as the repartition of the glycolytic flux between the glycerol and pyruvate producing branches, are robust to these uncertainties. However, our analysis also allowed us to identify fragilities of the model leading to the accumulation of 3-phosphoglycerate and/or pyruvate. The analysis of the control coefficients revealed the importance of taking into account the uncertainties about the parameters, as the ranking of the reactions can be greatly affected. This work will now form the basis for a comprehensive Bayesian analysis and extension of the model considering alternative topologies.Kinetic models of metabolism require detailed knowledge of kinetic parameters. However, due to measurement errors or lack of data this knowledge is often uncertain. The model of glycolysis in the parasitic protozoan  Trypanosoma brucei, responsible for African sleeping sickness. We first collected all the information we could find about how the model parameters were defined on a website, the SilicoTryp wiki (http:///silicotryp.ibls.gla.ac.uk/wiki/). From this information, we were able to quantify our uncertainty about each parameter, thus allowing us to analyse the model while explicitly taking these uncertainties into account. We found that, even though the model was well-defined and most of its parameters were experimentally measured, taking into account the remaining uncertainty allows us to gain more insight into model behavior. We were able to identify previously unrecognised fragilities of the model, leading to new hypotheses amenable to experimental testing.An increasing number of mathematical models are being built and analysed in order to obtain a better understanding of specific biological systems. These quantitative models contain parameters that need to be measured or estimated. Because of experimental errors or lack of data, our knowledge about these parameters is uncertain. Our work explores the effect of including these uncertainties in model analysis. Therefore, we studied a particularly well curated model of the energy metabolism of the parasite  Moreover, a substantial number of important parameters have never been measured and the estimates included in models are based either on values measured in closely related species or on the general distribution of similar parameters Kinetic models of metabolism require quantitative knowledge of detailed kinetic parameters . However, our knowledge about these parameters is often uncertain. When the parameters are measured, various sources of error can affect the results: experimental noise at the technical and biological levels, systematic bias introduced by parameters being measured Trypanosoma bruceiT. bruceiHere we present an analysis of the effect of parameter uncertainties on a particularly well defined example of a quantitative metabolic model: the model of glycolysis in bloodstream form Explicitly considering the uncertainties of parameters in the analysis of the model allowed us to gain interesting new insights into its behaviour. Most importantly, our analysis allowed us to quantify the degree of confidence concerning diverse properties of the system, including the hierarchy of control which is relevant for prioritizing potential drug targets. The resulting quantitative profile of model uncertainties, including the identification of major fragilities and areas in need of further examination, provides a solid basis for future model extensions. These will in turn introduce new uncertainties and should be dealt with using the same general framework established here.http://www.wikimedia.org) website dedicated to the detailed documentation of the sources of parameters used in the latest version of the model of glycolysis in T. brucei (http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis) In order to specify the uncertainty associated with each parameter, we gathered all available information relating to the sources of the values used in the model. Information included data on how kinetics were measured, the number of replicates and the standard error of mean values when available, additional calculations used to estimate the parameter from the observed values, and any “corrections” for additional factors such as temperature or pH. For this purpose, we created the “SilicoTryp” wiki, a MediaWiki-based  is split into two 3-carbon products by aldolase. Anaerobically, the NADH formed in the pyruvate branch can only be reoxidized to The fixed-parameter version of the model  and/or pyruvate to unreasonable concentrations causes some models to reach steady-state at extremely high concentrations or to fail reaching steady-state within 300 minutes. This occurs when the maximum reaction rates  of the models we generated by sampling the parameters did not allow the model to reach steady-state within 300 minutes, due to the accumulation of either 3-phosphoglycerate or pyruvate in the cytosol. This phenomenon could be attributed to two individual parameters, the maximal reaction rates of phosphoglycerate mutase and pyruvate transport which, when operating below their mean value (but still very close to it), caused the accumulation of two metabolites (3-phosphoglycerate and pyruvate respectively). For the pyruvate transporter, the analysis suggested a mechanism that could avoid this problem: alanine aminotransferase has been shown, unexpectedly, to be essential in bloodstream form We then analysed the distribution of the steady-state fluxes between the pyruvate and glycerol producing branches of glycolysis both in aerobic and anaerobic conditions. In totally anaerobic conditions, the distribution was very well conserved. Indeed, this property is entirely constrained by the topology of the model and thus this result was expected. Our analysis shows that the distribution of the fluxes is more variable in aerobic conditions, consistent with previously unexplained variation in experimental observations .Further analysis of the steady-state concentrations allowed us to distinguish the metabolites that are only moderately affected by the parameter uncertainties and follow an approximate log-normal distribution, such as T. brucei, as they allow us to identify potential drug targets. Our analysis reveals that, although the reaction that has the most control over the glucose consumption flux is the glucose transporter in 40.3% of the models, two other reactions maximally control the flux in a significant proportion of the models: PGAM (31.1%) and GAPDH (28.5%). Moreover, the activity of GAPDH has been reported to be inhibited by an unknown metabolite in vivo, it might have an important role in the control of glycolytic flux. Interestingly, partial inhibition of GAPDH has been shown to affect parasite growth and glycolytic flux T. brucei enzyme have been shown to be trypanocidal Finally, we analysed the control coefficients of each enzyme using our collection of models. These properties are especially important in the case of glycolysis in The data derived from the work performed here point to several further studies, including analysis of the role of alanine amino transferase in the regulation of pyruvate concentration and more exact quantification of pyruvate transport and phosphoglycerate mutase kinetics. The detailed description of parameter uncertainty will now form the basis for a comprehensive Bayesian analysis and extension of the model using alternative topologies T. brucei first published by Bakker et al. in 1997 The model used in this paper is the last updated version To allow a straight-forward sampling of parameters, the rate equations were rewritten to contain the equilibrium constant instead of the ratio of http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis). The model in The list of sources used to compute the values of the equilibrium constants is available in supplementary In order to sample the model parameters, we needed to define a probability distribution for each parameter. These distributions can be defined empirically using arbitrary shapes, but for the sake of convenience it is usually appropriate to use standard shapes  and then to estimate the parameters of these distributions .These parameters represent concentrations, therefore they cannot be negative and our uncertainty about their values is best represented by a log-normal distribution.For each The parameter has been measured experimentally: a mean . This heterologous mean is used to compute the T. brucei, the T. brucei enzyme retrieved from BRENDA . However, if the 95% confidence interval calculated is bigger than The parameter has not been measured, but some indication of its mean is available, e.g. a value measured for a phylogenetically closely related species , the mean and standard-deviation of the distribution can be calculated from the various values reported in the literature (see supplementary text S3). When only one published value could be found, the standard deviation was calculated using the mean relative standard deviation of the other equilibrium constants in the model as described above.The maximum rate of the reactions  to maintain maximal compatibility with the published model No information is available about the uncertainty of these parameters. As these parameters are strictly positive, they are sampled using a log-normal distribution as are Bakker et al. ATP utilization is modelled using mass action kinetics with a single rate constant. As this reaction represents all of the cytosolic reactions that consume ATP and are not explicitly included in the model, the rate constant of this reaction is unknown. As for glycosomal transport reactions, this parameter was sampled according to a log-normal distribution. The mean used is the value fitted by Bakker et al. The glucose transport across the cytosolic membrane is assumed to be symmetric All parameters were sampled using the MT19937 random number generator of Makoto Matsumoto and Takuji Nishimura The steady states were calculated using the SOSlib library The control coefficients were computed using the methodology described by Bakker et al. Dataset S1Fixed-parameter model (sbml file).(XML)Click here for additional data file.Figure S1Examples of simulations of models unable to reach steady-state (within 1000 simulated minutes). (A) Simulation of pyruvate concentration in a model unable to reach steady-state because of pyruvate accumulation. Models of this type will never reach steady-state. (B) Simulation of glycosomal 3-PGA concentration in a model unable to reach steady-state because of 3-PGA accumulation. Models of this type will eventually reach steady-state, but at extremely high concentrations of 3-PGA.(TIFF)Click here for additional data file.Text S1Distributions of the sampled parameters.(PDF)Click here for additional data file.Text S2Distributions of the steady-state concentrations of the metabolites in mmol/l.(PDF)Click here for additional data file.Text S3Sources used for the calculation of the equilibrium constants mean and standard deviations.(PDF)Click here for additional data file.


Blurry organ boundaries and soft tissue structures present a major challenge in biomedical image restoration. In this paper, we propose a low-rank decomposition-based method for computed tomography (CT) image sequence restoration, where the CT image sequence is decomposed into a sparse component and a low-rank component. A new point spread function of Weiner filter is employed to efficiently remove blur in the sparse component; a wiener filtering with the Gaussian PSF is used to recover the average image of the low-rank component. And then we get the recovered CT image sequence by combining the recovery low-rank image with all recovery sparse image sequence. Our method achieves restoration results with higher contrast, sharper organ boundaries and richer soft tissue structure information, compared with existing CT image restoration methods. The robustness of our method was assessed with numerical experiments using three different low-rank models: Robust Principle Component Analysis (RPCA), Linearized Alternating Direction Method with Adaptive Penalty (LADMAP) and Go Decomposition (GoDec). Experimental results demonstrated that the RPCA model was the most suitable for the small noise CT images whereas the GoDec model was the best for the large noisy CT images. Accurate display of anatomical detail, in the form of small structures, features and objects, is a key requirement of computed tomography (CT). These details carry important information that may be associated with distinction between normal and pathological diagnosis. However, blurring of the CT images often compromises the visibility of such fine details.Generally, CT modality is an economical way to generate high-resolution images of human anatomy. CT images show more complex details of bones structures, compared to magnetic resonance imaging (MRI) images. However, one side CT images are degraded by blurring due to many reasons, such as the imperfect resolution of the imaging system, data loss in acquisition, and acquisition noise, to name a few. These artifacts and data loss result in weak contrast and blurry organ boundaries. Furthermore, streak artifact around thick cortical bone results in degraded visibility of some soft tissue tumors present in low contrast regions. Therefore, contrast enhancement for CT images is critical to facilitate evaluating the extent of disease in soft tissue area Recently, many CT image deblurring methods have been studied to visualize miniature-sized features. Jiang et al proposed a deblurring method for spiral CT image based on edge signal-to-noise ratio in 2003 All the deblurred methods mentioned above only deal with a single CT image without considering the context of image sequence. these methods can also deal with CT image sequences via one by one, which just likes to deblur repeat single image several times with the same operations and the information between adjacent frames are not considered. There may be time-consuming. In this study, we will explore a new image sequence deblurred algorithm by using sparse representation and low-rank decompose model. For the reason that we always obtained CT image sequences from CT medical imaging system and the doctors judge the state of illness according to the changes of the CT image sequence, so we think that dealing with CT image sequence is more significant than dealing with a single CT image. Our method is also suitable for a single CT image, the difference is that we deblur the low-rank component working out the average low-rank image for sequence image but on own rank of a slice CT for single image. The result may slightly worse than using the average rank of image sequence if sequence image have big difference from slices. It is the fact that a single image can use information between adjacent slices. Recently, low-rank technology is used to decompose image sequence into a low-rank component and a sparse component. In low-rank model, noise and blur information is considered to exist in the sparse component of decomposition image, whereas original image information exists in the low-rank component A CT medical imaging system can be modeled as a linear transformation of an incoming analog signal, which is corrupted by intrinsic measurement fluctuations or electronic noise. A blurred image The main cause of degradation in medical CT images is the imperfect resolution of the imaging system, and the degradation function of a two-dimensional medical CT image is generally approximated as an isotropic two-dimensional Gaussian Point Spread Function (PSF) Image restoration technique aims to recover an image from its observation, degraded with blur and noise. In order to restore the image, prior knowledge of the degradation and inverse filtering must be obtained. Direct inverse filtering is usually used. Unfortunately,it is invalid when noise is taken into consideration. Another, degradation process typically happens in CT medical imaging, which includes blurring caused by imperfect resolution of the imaging system and noise by random fluctuations in signal intensity. Therefore, Wiener filtering We can obtain the expression of the formulaThis study was approved by Key Lab of Intelligent Perception and Image Understanding of Ministry of Education and by the institutional review board (IRB) of The School of Oncology, Peking University . The doctors obtained signed informed consent forms from all selected patients prior to the routine clinical course of CT examinations.Generally, we obtained CT image sequences from CT medical imaging system, but the existing deblurred methods always focus on the single image. In fact, each CT image in the same sequence is similar with its adjacent frames or maybe with a little change. Another, it was shown that a low-rank matrix could be recovered from incomplete sampling of its entries by computing the matrix of minimum nuclear norm the data Sparse and low-rank decomposition is widely used in background modeling and shadow removal; it usually focuses on image sequences due to their intrinsic sparse characteristics. Medical CT image sequence has strong correlation between adjacent frames, and it is pointed out that medical CT images are sparse , whereBy using theThen its Lagrangian function Formula This algorithm solves the RPCA problem through the Lagrange multiplier method, which recovers a low-rank matrix with an unknown fraction of its entries arbitrarily corrupted.The decomposition problem based on model 2 can be converted into the following optimization problem:Its augmented Lagrangian function This is the LADMAP algorithm. It solves the low-rank representation problem through the alternating direction method, and linearizes the quadratic penalty term adaptively. Compared with the traditional alternating direction method, this method has a novel rule to update the penalty so that it converges fast, without the need to introduce auxiliary variables or to invert matrices during the operation process. It has found wide applications in computer vision and machine learning.The decomposition problem based on model 3 can be converted into the following optimization problem Formula which is equivalent toThis is the GoDec algorithm, which is a low-rank approximation method based on bilateral random projections. The algorithm can approximate the low-rank component, the sparse component and the noise component of the input data matrix. It has the advantage of small relative error and high decomposition speed.To sum up, RPCA and GoDec share similar motivations in that they both explore the low-rank and sparse structures in the given data matrixIn this paper, sparse and low-rank matrix decomposition was applied to the problem of medical CT image sequence restoration. For the blurred CT image, it is necessary to recover its low-rank component, because it conveys major information on the latent image. The sparse component, on the other hand, normally reflects the majority of blurring. In practice, CT images differ in their characteristics: some contain high level of noise that seriously degrades image quality and affects visualization; in others, the noise level is relatively low and has little impact on the visual quality of the image or diagnosis of the lesions. Therefore, it is necessary for us to select the appropriate low-rank model based on the image characteristics, and to perform low-rank decomposition and restoration in order to obtain the desirable recovery results.We propose a new CT image sequence restoration model based on low-rank decomposition as follows:Also, there exist several methods using the information of the adjacent frames, such as the methods introduced in ref. In natural imaging, the image blur can be regarded as atmospheric turbulence affecting the observed scene captured by the camera due to fluctuations of the refraction index of the medium This degradation function we provided was inspired by the blurring natural image and then we think the turbulence also exist in CT imaging based on the reference The detailed steps of our algorithm are as follows:Algorithm: CT image sequence restoration based on sparse and low-rank decompositionInput: the blurred CT image sequenceOutput: the latent CT image sequenceStep 1: Input the medical CT image sequenceStep 2: Use all the CT images in the sequenceStep 3: select a reasonable low-rank model to decompose the high dimensional matrix in step 2 into high dimensional sparse matrix, low-rank matrix and noise matrix according to the actual situation of the CT image sequenceStep 4: convert the high dimensional sparse matrix, low-rank matrix and noise matrix into sparse image sequenceStep 5: Using our restoration model In order to objectively evaluate the performance of the image restoration algorithm, we use standard deviation, image information entropy and image quality measurement function value The formula of standard deviation is as followsInformation entropy is one of the key indicators to measure how much image information is: the greater the value, the larger the amount of information contained in the image, its expression isImage quality measurement function value is defined asThe greater the image quality measurement function value, the more uniform the gray level distribution, and the better the image quality.Based on the methods we described in Section 3, we investigate the most appropriate low-rank models for various types of CT images, differing in their noise levels and properties. Each image in our CT image sequences is 512 by 512 in size, with RGB color, obtained on a Discovery CT750 HD at the Beijing Cancer Hospital. We used We first use the chest CT image sequence to evaluate the contrast of different low-rank models. The noise is small on each image of the CT sequence and does not affect the basic visualization. We decompose the input chest CT image sequence into a sparse component and a low-rank component in the RPCA model, and then recover the two components using wiener filtering, we useth original image of the chest CT image sequence and its recovery images in different models are shown in In order to analyze the scope of application of the three different low-rank models, we applied all decomposition models to the same chest CT image, and restored the chest CT image sequence. To illustrate the effectiveness of the proposed method in recovering the CT image sequence, the 10To further compare the recovery effect of the three models, we list in From The same comparative experiments were also performed on a stomach CT image sequence, which has a much larger noise component. The results of comparison are shown in From To illustrate the effectiveness of the proposed method, we make several groups of contrast experiments between different methods which are shown in 4,For the chest CT image comparative experiment, we used varianceThe four groups of comparison of evaluation index values reveal that our method have advantages in all the evaluation index values when deal with the low level noise CT image. But the information entropy values of our method is lower than some of the others in case of high level noise CT images. What we want to clear is that there is no more other effective evaluation index to address this problem so far, So we used information entropy to try it on. Overall, our method is more effective in CT image sequence restoration than the alternative methods.This paper proposed image sequence restoration for CT scan image using Wiener filtering, based on sparse and low-rank decomposition. One of the key points to this method is uniting the CT image restoration under the framework of low-rank models: we first decompose the CT image sequence into sparse component and low-rank component in the RPCA model if noise level is low, and then restore both the two components using wiener filtering; in the presence of high level noise, it is better to select the GoDec model to decompose the images into three components, namely a sparse component, a low-rank component and a noise component, and then restore the sparse component and low-rank component using wiener filtering. It takes about 1.5s for our algorithm to recover a CT image of size 512


Many pain assessment tools for preschool and school-aged children are based on facial expressions of pain. Despite broad use, their metrics are not rooted in the anatomic display of the facial pain expression. We aim to describe quantitatively the patterns of initiation and maintenance of the infant pain expression across an expressive cycle. We evaluated the trajectory of the pain expression of three newborns with the most intense facial display among 63 infants receiving a painful stimulus. A modified “point-pair” system was used to measure movement in key areas across the face by analyzing still pictures from video recording the procedure. Point-pairs were combined into “upper face” and “lower face” variables; duration and intensity of expression were standardized. Intensity and duration of expression varied among infants. Upper and lower face movement rose and overlapped in intensity about 30% into the expression. The expression reached plateau without major change for the duration of the expressive cycle. We conclude that there appears to be a shared pattern in the dynamic trajectory of the pain display among infants expressing extreme intensity. We speculate that these patterns are important in the communication of pain, and their incorporation in facial pain scales may improve current metrics. Tabl of pain . If this of pain , 7. Howe of pain –11. This of pain . Moreove of pain , 13, 14. of pain .This study focuses on 3 selected infants showing extreme facial expression intensity to a common pain stimulus. Our goal is to examine the dynamics of their expression , describe its progression and timing, and search for patterns, if any, along the pain display. If pain facial expression is universal with common features across time, then these patterns may hold important cues about the representation of pain intensity in FPSs and hold potential for their improvement by clarifying meaning and facilitating communication with younger children. A clearer understanding of the way humans express and subsequently recognize pain may advance assessment of pain at the bedside. baseline picture derived from the video (immediately before heel-stick) to a picture or video frame showing peak pain expression. Measurements were expressed as percent of facial width to preclude issues of individual differences in face anthropometrics and image size. In this analysis, we applied a similar methodology to that same data set and explored facial movement, but rather than measuring two video frames per infant, baseline and peak movement, we measured the change across each video frame, recorded at 11.6 frames per second, from baseline through to peak movement. We aimed to assess the progression of the PFP across time, thus the fullest or extreme display  provided the best chance to do so descriptively. In other words, assuming that the PFP is the currency of facial pain expression, it is necessary to analyze infants displaying a full, peak, or prototypical facial expression of pain, thus characterizing all of the presumed range of pain expressions said to be portrayed by a common FPS . In order to select the three infants for the present study, we rank ordered the 63 infants on overall display intensity and identified the three infants whose display intensity was the highest  during this first expressive cycle as measured by the point-pair system [We previously reported on an evaluation of 63 term neonates of both sexes and various racial/ethnic backgrounds using a computerized “point-pair” method to measure facial movement in response to a painful stimulus . Parentar system . See Tabfirst expressive cycle comprises facial action across time from baseline through to peak movement. We define peak movement as the point of maximal expression intensity during the first expressive cycle immediately following the pain stimulus as measured by our point-pair system. The specific physiologic movements of interest, long ago shown to be characteristic of neonatal pain expression [Observation reveals that the facial expression of pain in newborns following a heel-stick can be described as cyclic in nature and consisting of bursts of facial movement coinciding with the breathing cycle: exhalation accompanied by increased facial tension, followed by inhalation and a temporary relaxation of the movement, followed again by exhalation and facial tension, and so on. These cyclic patterns are more evident or characteristic of infants with higher display intensities. The pression , 18, areupper face. Similarly, point-pairs 4 and 5 were summed and designated as lower face. With upper face, point-pairs 1, 2, and 3 draw in towards each other ; therefore, point distance decreases or is negative across the expression. The opposite occurs in the lower face, with point-pairs 4 and 5 moving away from each other ; there, point distance increases or is positive across the expression. To facilitate graphic comparisons between upper and lower face action, we switched the sign in upper facial action to match that of lower facial action  and those controlling mouth movement . Thus, wl action . Since iOur previous analysis looked at intensity of pain expression in neonates across key areas of the face and found that although not identical, overall facial movement in reaction to a painful stimulus is quite similar in newborns regardless of their sex or race/ethnic background . We termIn more general terms, individual differences in emotional facial expression are greatly influenced by genetic mechanisms, especially in this population given the relative little social learning accessible to 2-day-old neonates , 20, 21.The cases chosen for this detailed temporal analysis were those infants whose facial displays of pain in response to heel lance, measured by the point-pair method, were the most intense. There are many individual and technical influences on intensity of pain expression in this context, including the handling and the behavioral state of the infant before the procedure, the duration of the procedure, the possible lingering effects of obstetric medications and procedures, and potentially the sex and ethnicity of the infant. None of these other influences were controlled, raising the question of generalizability of the findings. However, while the intensity of pain expression in the present sample was not representative of all infants, we consider it unlikely that the sequence of movements identified here would have been influenced by such external factors.It is reasonable to assume that the PFP is vital to the identification of pain or generalized distress in humans, specifically in the context of communication and its evolutionary necessity. If this is the case, then it seems imperative that current FPSs portray it accurately; we know of no current FPSs that portray the four natural intervals identified here. The current study identifies a unique and shared progression in extreme facial pain expression in infants that current metrics do not reflect. Future research should address the significance of these natural intervals on pain metrics. For example, do these shared patterns mark or coincide with self-reported pain intensity in older children? Are there possible thresholds in the pain experience associated with corresponding expression or communicative patterns? Does a more accurate portrayal of the expression in an FPS affect the validity of its scores? That is, would improving the faithfulness of the pain display aid in the communication of pain with younger children who are cognitively challenged by current tools? The small number of cases studied here limits application of the findings. Additionally, there may be other temporal subtleties at the point-pair level or movement in other areas not captured by this “upper versus lower face” approach. However, these findings call attention to a need to take a more objective approach to the future development and refinement of pain measurement tools such as FPSs.There appears to be both shared morphology and temporal dynamics of movement in the occurrence of the PFP across the first expressive cycle in newborns expressing more extreme facial intensity. These commonalities in the pain display further support the universality of the pain expression, and may help to identify patterns, and thus inform the objective development and improvement of faces pain scales in terms of more anatomically faithful intervals. A more accurate graphic portrayal in FPSs, true to natural patterns, may facilitate the communication and measurement of pain in younger children.


Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit models to situations where the response is continuous on the interval . Consequently, beta regression is a convenient tool for analyzing percentage responses. The classical approach to fit a beta regression model is to use maximum likelihood estimation with subsequent AIC-based variable selection. As an alternative to this established - yet unstable - approach, we propose a new estimation technique called boosted beta regression. With boosted beta regression estimation and variable selection can be carried out simultaneously in a highly efficient way. Additionally, both the mean and the variance of a percentage response can be modeled using flexible nonlinear covariate effects. As a consequence, the new method accounts for common problems such as overdispersion and non-binomial variance structures. Ecology in 2008/09 dealt with the analysis of percentage data.The analysis of percentage data is a common issue in quantitative research. Percentage data arise in many scientific fields, for example in ecology regression models for percentage outcomes, which may be biased and inefficient if the specific nature of percentage outcomes is not taken into account. Although it would be convenient to use percentage responses as outcome variables in ordinary least squares (OLS) regression, this approach is problematic because OLS regression does not account for the fact that percentages are bounded by the interval c From a statistical perspective, the analysis of percentage data is a challenging problem. This problem primarily concerns the development of In the literature, various alternative methods to model percentage data have been proposed. A well-known strategy is to transform the percentage outcome An alternative approach for the analysis of percentage outcomes is to use regression models that are based on the binomial distribution beta regressionTo overcome the aforementioned problems and limitations, we consider In the statistical literature, beta regression has been established as a powerful technique to model percentages and proportions variable selection in beta regression models are needed.1. Scientific databases often involve large numbers of potential predictor variables that could be included in a regression model. Consequently, if maximum likelihood estimation is used to fit a beta regression model, the model may become too complex and may thus overfit the data. This usually leads to a large variance and to a high uncertainty about the predictor-response relationships. As a consequence, techniques for multicollinearity problems, meaning that predictor variables are highly correlated. Also, observations of the response variable may be affected by spatial correlation, which is, for example, a common problem in ecology 2. Statistical models often suffer from nonlinear in nature 3. In many applications, predictor-response relationships are overdispersed, meaning that they show a larger variability than expected by the binomial distribution. Classical beta regression models conveniently account for overdispersion by including a precision parameter 4. Percentage outcomes that are based on the binomial model boosted beta regression. Following the approach by Ferrari & Cribari-Neto boosting method to fit generalized additive models for Location, Scale and Shape  Survey The rest of the paper is organized as follows: In the next section, boosted beta regression is presented in detail, along with a description of the classical beta regression and gamboostLSS approaches. Additionally, we briefly review the arcsine square root and logit transformation approaches and discuss their limitations when used for modeling percentage outcomes. The characteristics of boosted beta regression are demonstrated in the results section of the paper, where the new method is benchmarked against a number of alternative regression models. Using the NLA data, we further show how to apply the new method to derive an easy-to-interpret regression model for the EPHEptax response. A summary and discussion of the main findings of the paper is given in the final section of the paper. Technical details on boosted beta regression are presented in the Supporting Information of the paper.In this subsection, we briefly review transformation models for percentage outcomes. This model class comprises both classical OLS regression and OLS regression with arcsine-square-root-transformed response. Transformation models are based on the model equationAs noted in To overcome the problems with classical OLS regression, it is a common strategy to transform transformed meanRegardless of the choice of the transformation function, a major problem of transformation models remains: Unless the identity transformation To overcome the problems and limitations discussed in the previous subsection, Ferrari & Cribari-Neto In the following, we assume that  by  see . Hence t (2) see . Note thTo relate the conditional mean In contrast to logistic regression, however, the conditional variance betareggamlssIn cases where overdispersion depends on the values of the predictor variables, it is further possible to extend the beta regression model by regressing the precision parameter Following its introduction by Ferrari & Cribari-Neto boosted beta regression. Boosted beta regression is based on the gamboostLSS algorithm, which has been introduced in To address the issue of variable selection in beta regression models, we propose a new fitting method called The most important feature of gamboostLSS is its ability to carry out variable selection during the fitting process. This is accomplished by (a) assessing the individual fits of each predictor variable, and by (b) updating only the coefficient of the best-fitting predictor variable in each iteration. Also, when using gamboostLSS to fit a beta regression model, variable selection is carried out successively for both the mean model (3) and the precision model (4). After a finite number of iterations, the algorithm is stopped, so that the final model only contains the subset of best-fit predictor variables. A schematic overview of boosted beta regression is as follows:1. Set the initial values for 2. In each iteration….(a)…keep the current value of the estimate of (b)…keep the current value of the estimate of 3. Repeat steps (a) and (b) until the stopping iteration of the algorithm  and (b) is fundamentally different from the Newton-type method proposed in ep 2 cf. , boostedAn important question is how to choose the stopping iteration of gamboostLSS. Usually, the stopping iteration of a boosting algorithm is chosen such that prediction accuracy of the model becomes highest An attractive feature of gradient boosting  is that the linear predictors continuous predictors are modeled using one-dimensional P-spline estimators Categorical predictors (such as Köppen-Geiger climate regions) are modeled using dummy coded binary variables. Hence the resulting estimates for categorical predictors have the same interpretation as in classical linear models.Concerning the analysis of the NLA data, we proceed as follows: The functions spatial predictor effects. These functions depend on the coordinates of the site locations and are added to the other functions specified in (5) and (6)  cf. . To estiIn the following we will use boosted beta regression to model biological condition in lakes in the conterminous U.S. The outcome considered in our study is the percentage of benthic macroinvertebrate taxa in the order Ephemeroptera (EPHEptax). In addition to analyzing boosted beta regression, we compare the new method to conventional approaches such as OLS regression with transformed response. The first subsection starts with a description of the study design and the NLA database. Statistical analysis results are presented in the second subsection.Statistical analysis is based on data from the 2007 U.S. National Lakes Assessment program (NLA), during which 1,157 lakes were sampled in the summer from across the conterminous U.S. see .Littoral zone sampling consisted of ten randomly selected quadrates around each lake littoral zone that were combined into a single sample. In each sample, benthic macroinvertebrates were collected and physical habitat assessed. Habitat condition was measured by visual estimates of riparian vegetation condition, shoreline substrate (at the water’s edge), fish cover, aquatic macrophytes, and littoral bottom substrate in the samples. In addition, human disturbance or presence was estimated in each sample by identifying human activities  in the water or in adjacent riparian areas. Sampling at the deepest point of the lake (index site) included all other biological and chemical measures. Water column profiles of temperature, dissolved oxygen, conductivity, and pH were taken using a multi-probe sonde.The NLA database also contains estimates of lake drainage conditions . To provide estimates of lake connectivity and colonization sources, we calculated the number and total surface areal coverage of other lakes .  regions  to the m regions . Our resFinally consider the estimated spatial surface function a concentration on the logarithm of the precision parameter a concentration levels tend to increase the variance of EPHEptax. The variation decreases until levels of a concentration levels larger than By way of example, we also present the effect of the chlorophyll- rameter  . BecauseIn summary, the results presented in Linear regression with normally distributed errors is arguably the most prominent analysis tool in applied statistics. The popularity of linear regression is based on the fact that random variations in observed data can often be approximated by a normal distribution with constant variance. If the response variable in a regression model is a rate or percentage, however, the normal approximation is no longer appropriate. For this reason, and because the analysis of percentages is an important issue in many fields of research, developing statistically valid analysis tools for percentage data is of high practical interest.Several approaches to remedy the problems with linear regression have been proposed in the literature. The first approach is to transform the percentage response and to hope that linear regression with the transformed response will result in (approximately) normally distributed errors with constant variance. This is, for example, the rationale of arcsine square root transformation. As shown in the methods section of the paper, however, response transformation models may result in poor model fits because the normal approximation often fails. Based on the results obtained from the NLA data, we agree with Warton & Hui boosted beta regression, which is a flexible alternative to logistic regression and response transformation models. Because beta regression is a generalization of logit regression to situations where the dependent variable is a proportion In this paper, we have proposed A key aspect of boosted beta regression is its ability to carry out variable selection during the fitting process. This implies that only a small subset of the available predictor variables is included in the final model for the percentage response. Variable selection is of high practical interest in applications where large amounts of potentially important predictor variables are available. Consequently, one is often interested in determining the most informative predictor variables and in discarding those predictors that have a negligible effect on the response. In case of the NLA data, for example, boosted beta regression selected only 15 informative predictor variables out of the total set of 78 available predictors.gamlss, It is important to note that the variable selection mechanism in boosted beta regression is fundamentally different from earlier approaches to selecting predictor variables in statistical regression models. For example, because beta regression is a member of GAMLSS model class, one could alternatively fit the model using maximum likelihood techniques and apply AIC-based methods for selecting informative predictor variables Click here for additional data file.


The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops  in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample  consistent with empirical knowledge; in the latter, we have effectively corrected thermodynamically infeasible flux configurations.The operation of biological systems is constrained under all circumstances by the laws of physics. Thermodynamics, in particular, dictates preferential directions in which biochemical reactions should flow at stationarity. When applied to cellular reaction systems (like metabolic networks), it favors the emergence of some  ways to organize the flow of matter while prohibiting others. The development of detailed predictive models for the biochemical activity of a cell relies on the possibility to integrate the laws of thermodynamics in genome-scale reconstructions of cellular metabolic networks. In this work we have devised an efficient relaxation algorithm to implement thermodynamic constraints in genome-scale models. Besides allowing to check for thermodynamic feasibility of reaction flow configurations, it is also capable of providing information on other relevant physico-chemical quantities. We have applied it to two cellular metabolic networks of different complexity, namely that of human red blood cells and that of the bacterium  Constraint-based models of cellular metabolism are important tools to analyze and predict the chemical activity and response to perturbations of cells without relying on kinetic details that are often unavailable. In such frameworks, the metabolic capabilities of a cell are inferred from the overall configuration space compatible with minimal physico-chemical constraints describing the non-equilibrium steady state of the underlying reaction network. First, feasible reaction flux vectors need to satisfy mass-balance conditions. Then, according to the second law of thermodynamics, in an open chemical network at steady state and constant temperature and pressure the direction of each reaction should ensure a decrease in Gibbs energy. Thermodynamic consistency of flux configurations satisfying mass-balance alone is in general not guaranteed due to the presence of infeasible cycles Much work has been concerned with implementing thermodynamic constraints in genome-scale models of metabolism. The removal of thermodynamic inconsistencies was proved to be useful in estimating concentrations and affinities besides fluxes in Flux-Balance-Analysis The scalability of algorithms to solve mixed integer-linear (or non-linear) programming problems may become an issue when the underlying network size is large or when one is interested in sampling the solution space (for both free energies and fluxes) rather than focusing on a potentially small set of configurations (e.g. optima). Luckily, however, solutions to computationally hard problems can often be generated efficiently with the help of heuristic algorithms based on simple local rules. The use of message-passing algorithms to characterize the high-dimensional volume of the solution space of FBA models Our goal in this paper is to obtain information about the landscape of Gibbs free energies compatible with a given vector of reaction directions by following a route that allows to use all stoichiometric information via heuristics inspired by perceptron learning. In a nutshell, the method we propose consists in exploiting the network's structure to iteratively build up correlations between the chemical potentials of the reacting species starting from a seed of empirical biochemical knowledge, until a thermodynamically consistent profile is achieved. The resulting algorithm is completely scalable and can be employed for different purposes, like checking the feasibility of flux configurations, identifying and removing infeasible cycles, estimating reaction affinities, and obtaining bounds for (log−)concentrations and free energies of formation.Escherichia coli, iAF1260 In the following, we describe the method in detail, providing a mathematical proof of convergence as well as theoretical arguments highlighting the main idea behind the procedure. As applications, we focus on two metabolic networks of rather different complexity. First, we shall obtain a detailed reconstruction of the Gibbs energy landscape underlying metabolic activity in the human red blood cell (hRBC) starting from the flux maps obtained in Escherichia coli iAF1260, presented in Escherichia coli, we will consider the inner matrix of periplasmic and cytoplasmic reactions without repetitions, which consists of The cellular systems analyzed in this study are (i) the model of the hRBC metabolism developed in à la Von NeumannAccording to the second law of thermodynamics, in an open system at constant temperature see e.g. , Ch. 1 drives the gradual adjustment of chemical potentials by ensuring that, at every iteration, the least satisfied constraint  initializations of the above algorithm is a set of If there is no prior information on the direction of some reactions (e.g. because they are putatively reversible), the corresponding constraints (3) are formally absent, as if Finally, some observations are in order about the solution space of (3), which in general has the form of an unbounded cone passing trough the origin. If one is interested in uniform sampling the space of A number of interesting theoretical and computational questions arise at this stage, regarding e.g. the minimal amount of prior information on chemical potentials needed to bound the solution space of (3), or computationally efficient and scalable methods to obtain uniform sampling  has no solutions apart from the trivial one. In accordance with the Farkas-Minkowski lemma While running the algorithm to compute chemical potentials for a large number of iteration steps Search, within such subset of reactions, for a loop of length If a loop is found, change the direction of one of its reversible reactions chosen with uniform probability.In the http://chimera.roma1.infn.it/SYSBIO/.A computer code implementing the algorithms to compute chemical potentials and identify and remove infeasible loops is downloadable As a first application, we have employed the MinOver scheme outlined above to analyze the thermodynamic landscape of the hRBC metabolic network. As a starting point, we have considered the flux configurations obtained in see e.g. . VNC areaccording to according to As a first step, we tested the thermodynamic feasibility of these direction assignments, solving (3) by starting from the vector Results for the estimated concentrations and Gibbs energy changes (computed from (2) using the final chemical potential vectors) are showcased in We can now quantify the extent to which the solutions we generate are “close” to the prior. In Escherichia coli iAF1260 The application that we have just discussed shows that the algorithm we present can provide information on the Gibbs energy landscape, even correcting inconsistent input knowledge. We shall now employ the procedure outlined in the Since we are not focusing on the reconstruction of the Gibbs energy landscape but simply on the existence of solutions of (3), a detailed biochemical prior is not needed. Therefore, for the present purposes we have taken We have furthermore studied the set of loops that were thus identified and corrected. Quite remarkably this analysis revealed that thermodynamical infeasibility is related to the presence of a small set of cycles, 23 in total. These are reported in We remark that the corrected flux configurations thus obtained, like the starting ones (which were drawn from a uniform product measure over reactions), are not guaranteed to be consistent with any steady state assumption. On the other hand, see Supporting Ideally, constraint-based models of metabolic activity allow to appraise the energetic potential of cells based on minimal constraints related to local mass-balance and thermodynamic feasibility rules, possibly complemented with optimization principles that can encode for functional constraints. As a result, the flow of matter in non-equilibrium steady states could be characterized in terms of the Gibbs energy change of reactions, which specifies the directionality of interconversions, and of the average number of turnovers per time per volume, i.e. the flux, without the need of detailed information on enzyme kinetics or transport mechanisms. Thermodynamic constraints, strongly linked to overall intracellular conditions like ionic strength and pH Many important steps have been taken recently to tackle it. At one level, thermodynamic feasibility can be translated into topologic constraints (‘absence of loops’) for the flux configuration emerging from mass-balance constraints Escherichia coli, instead, we have focused on the problem of correcting thermodynamically infeasible flux states in the core formed by the periplasmic and cytoplasmic matrix. We have thoroughly analyzed a large ensemble of configurations of reaction directions, identifying the cycles responsible for thermodynamic inconsistency and correcting them in a very modest amount of CPU time. Quite intriguingly, we have related infeasibility to the existence of a relatively small number of short cycles in the flux configuration, whose removal suffices to ensure thermodynamic feasibility in worst-case flux configurations.The usefulness of the algorithm in the analysis of genome-scale networks has been tested in two different cases. For the metabolic network of the human red blood cell, our approach has proved capable of reconstructing the Gibbs energy landscape correcting inconsistent prior information. In turn, this has lead to predictions for intracellular metabolite levels. It is important to stress that the bounds on concentrations we have obtained (which vary rather heterogeneously across compounds) only reflect stoichiometric information. For the metabolic network of The main advantage of our method consists in our view in its efficient implementation. On the critical side, we point to two aspects that deserve further study. In first place, our tool requires flux configurations as inputs, i.e. it is still unable to produce thermodynamically feasible configurations of fluxes and chemical potentials starting from no previous reversibility hypothesis. However it may provide the basis of a more general procedure for the analysis of genome-scale metabolic networks that couples flux- and thermodynamic profiling, a challenging open problem in computational biology. Secondly, our method relies on prior biochemical information and it would be desirable for it to be effective even if much or most biochemical priors are unknown. As we pointed out, some information has to be injected into the problem for the sake of definiteness. The interesting question is therefore what is the minimum necessary prior needed to reconstruct the Gibbs energy landscape and how are predictions affected by restricted priors. Such problems are mathematical in nature and could bear a particularly high significance for modeling purposes.Dataset S1Stoichiometric matrix of the human Red Blood Cell metabolic network employed in this study.(TXT)Click here for additional data file.Dataset S2Thermodynamic potentials for the human Red Blood Cell metabolic network employed in this study.(XLS)Click here for additional data file.Table S1Escherichia coli metabolic network iAF1260.Detailed information about infeasible cycles (reactions and metabolites) identified in the (XLS)Click here for additional data file.Text S1A toy example of the computation of chemical potentials by MinOver with loop correction.(PDF)Click here for additional data file.