The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.Three parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality.The parameter estimation methodologies described in this work have provided an effective and practical approach in the estimation of kinetic parameters of stochastic systems from either sparse or dense cell population data. Nevertheless, similar to kinetic parameter estimation in other modelling frameworks, not all parameters can be estimated accurately, which is a common problem arising from the lack of complete parameter identifiability from the available data. Mathematical models form a cornerstone of systems biology and these models are usually constructed from available biological knowledge and data, which once validated, are subsequently analyzed to address specific biological questions. Many canonical modelling frameworks, from statistical Bayesian networks to differential equations, have been applied to capture a wide-variety of biological behaviours. Specifically, the dynamics related to cellular processes that involve low copy number of molecules, such as mRNA transcription, are best described as random and noisy events . For exaDespite the availability of high-throughput cell biology, the estimation of unknown (kinetic) model parameters from experimental data is still considered as the bottleneck in biological model identification, especially for dynamical models ,5. The dChemical master equation (CME) is the most commonly adopted modelling framework to describe stochastic cellular dynamics -3 and thEscherichia coli, gene expression network of galactose uptake model in Saccharomyces cerevisiae, and a bimodal system comprising of a genetic toggle switch in E. coli. Despite the use of CME models here, the methods are generally applicable to other stochastic models in which the system behaviour or output can be characterized by a PDF of the states.In this work, three kinetic parameter estimation methods for stochastic models were developed based on two criteria: maximum likelihood (ML) and density function distance (DFD). Two scenarios of practical application were considered involving both sparsely and densely populated datasets (i.e. low and high replicates). Since the distribution density functions are commonly constructed using histograms, an important aspect related to the binning strategy and the noise associated with finite sampling, has been incorporated in the parameter estimation framework. The efficacy of each method was evaluated and compared based on applications to three CME case studies: RNA dynamics in N species participating in M biochemical reactions. The CME of this system is given by . The density functions predicted by the CME were constructed using 10,000 SSA realizations with added i.i.d and N noise. In the case of low replicate datasets , only the DFD-CDF method was applied, in which the CDF of the experimental data was constructed according to: [The parameter search was constrained to a space bounded by ding to: l now denotes the index of the state in replicate vector after arranging the data in ascending order . This construction implicitly uses the differences between sorted data values as the bin sizes. As stated earlier, since the DFD-PDF method requires the histograms of experimental data, which in the case of low replicate datasets, are highly inaccurate, this method was only performed for cell population data . The DE optimization was implemented with a population size of 30 (10 × the number of parameters) for 4,000 generations and the optimization routine took about 1.5 hours for completion.where k1 is the most accurately determined parameter by all methods. At higher replicates, the DFD-CDF method converged to the true solution faster than the PDF and ML methods, in this order, which could be attributed to the difference in the shape of the objective function surface. As seen in Figure m = 10).Table G and a TetR repressor binding element 2xtetO2  to investigate the inherent cellular noise in the GFP gene expression, which is measured as the heterogeneity of fluorescence among the cells.The inherent stochastic nature of gene expression can lead to diversified responses in a  cell population, even when subjected to uniform external conditions. This diversity has been demonstrated in a cell population using fluorescence techniques such as flow cytometery (FACS). The second case study used in this work looks at the problem of estimating CME parameters from a cell population data. The model describes an artificial genetic construct with the green fluorescence protein (GFP) gene downstream of a galactose activated promoter UAS2 Figure . In the 1, PC2 and PC3 represent free/silent, intermediate complex, and pre-initiation complex promoter configurations, respectively, while the states RC1 and RC2 describe different forms of repressed promoter configurations. The transcriptional (RNA synthesis) and translational (protein synthesis) processes are modelled as single-step irreversible reactions . This cBoth ML and DFD methods were first applied to the reduced model, in which the DE optimization was done with 80 population members for 4000 generations, which took about 50 hours for convergence. The bounds on the parameter search space are given in Table The scalability of the methods discussed in this work was evaluated by performing the estimation of the complete model. In this case, the DE optimization was performed using 150 population members for 4000 generations and took approximately 60 hours for convergence. In this case also, the CDF method again generally outperformed the PDF and ML Table . But somTwo other estimation criteria based on the maximum density function distance, in the form ofandfor PDF and CDF, respectively, have also been evaluated, showing similar performances and observations. The outcome of the application of these criteria to the estimation of parameters in the reduced and complete yEGFP gene expression pathway is described in supplementary data [Additional File E. coli to show the ability to synthesize such motif. The synthetic switch consisted of two repressor-promoter pairs, with (i) PLs1con-lacI repressing Ptrc-2 promoter and (ii) vice versa Ptrc-2-cIts  repressing PLs1con promoter [cIts. The ON switch was accomplished by an inducer, isopropyl β-D-thiogalactosepyronoside (IPTG), that represses the activity of lacI  were estimated using the DFD-CDF and -PDF methods, with DE parameters: 150 population members and 4000 generations. Both CDF and PDF criteria took about 48 hours for completion. The parameter bounds and estimates are given in Table As the ML performed consistently poorer than the DFD methods in the previous case studies, the stochastic rate constants here  single cell datasets with low and high replicates. As the methods rely on a histogram construction of density functions from a finite sample of experimental data and Monte Carlo simulations, the objective function evaluation has a trade-off between low accuracy when using bins that are too wide, and high sensitivity to noise when bins are too small. In order to balance this trade-off, the binning was done such that the narrowest bin has at least ten occurrences. The noise associated with this binning strategy is also taken into account in the objective function in the DFD methods, which is modelled according to a binomial distribution.The proposed methods are developed while considering a few practical issues when dealing with real biological datasets, such as data sparsity (low replicates), data noise and relatively coarse sampling intervals. The methods developed here do not require fast time-sampling like in , which mSl,i when normalized with the respective probability, i.e. the coefficient of variation (CoV) Fe of indicates that the CDF construction becomes less affected by finite sampling noise with increasing Fe.The case studies above showed that methods based on matching density function shapes between model and data generally performed better than maximizing likelihood function. Furthermore, the DFD-CDF distance is more sensitive to parameters than both the DFD-PDF and ML, and thus is the most effective method developed in this work. The higher sensitivity of the CDF with respect to parameter variations is expected as a result of the cumulative sum of the PDF sensitivity. This is evident from comparing the normalized objective function surfaces as shown in Figure. 2, in which the CDF objective functions have the steepest curvature. The increased curvature leads to a faster convergence to the minima in the DE optimization of the CDF than the PDF, though both methods eventually converge to optimal parameter estimates with similar accuracy. In addition, the CDF is generally less sensitive to noise from finite sampling as can be seen from the noise weighting factor Similar to the parameter estimation in deterministic models, parameter identifiability is a key issue in the estimation of the CME parameters. Such problem is commonly encountered in the parameter estimation of deterministic ODE models . FollowiMost of the computational cost of the parameter estimation related to CME is due to the large number of SSA realizations needed to construct the solution of the CME. Furthermore, every generation of DE requires multiple computations of the objective function according to the population size setting and each of population members in turn requires the SSA solution as mentioned previously. One way to alleviate the computational burden would be to lower the SSA realizations in constructing the density function. This would however increase the binning noise, and could possibly reduce the speed of convergence to the optimal solution and the accuracy of parameter estimates . Table S6 lists the parameter estimation results of the Schlögl model.Click here for fileSupplementary figure of the manuscript file. Comparison of actual experimental data and CME model prediction using SSA simulations with the parameters estimated in case study 2.Click here for fileSupplementary text of the manuscript file. Details of the SSA formulation and the parameter estimation method used in the Schlögl case study.Click here for file


It is reasonable to consider the thalamus a primary candidate for the location of consciousness, given that the thalamus has been referred to as the gateway of nearly all sensory inputs to the corresponding cortical areas. Interestingly, in an early stage of brain development, communicative innervations between the dorsal thalamus and telencephalon must pass through the ventral thalamus, the major derivative of which is the thalamic reticular nucleus (TRN). The TRN occupies a striking control position in the brain, sending inhibitory axons back to the thalamus, roughly to the same region where they receive afferents.The present study hypothesizes that the TRN plays a pivotal role in dynamic attention by controlling thalamocortical synchronization. The TRN is thus viewed as a functional networking filter to regulate conscious perception, which is possibly embedded in thalamocortical networks. Based on the anatomical structures and connections, modality-specific sectors of the TRN and the thalamus appear to be responsible for modality-specific perceptual representation. Furthermore, the coarsely overlapped topographic maps of the TRN appear to be associated with cross-modal or unitary conscious awareness. Throughout the latticework structure of the TRN, conscious perception could be accomplished and elaborated through accumulating intercommunicative processing across the first-order input signal and the higher-order signals from its functionally associated cortices. As the higher-order relay signals run cumulatively through the relevant thalamocortical loops, conscious awareness becomes more refined and sophisticated.I propose that the thalamocortical integrative communication across first- and higher-order information circuits and repeated feedback looping may account for our conscious awareness. This TRN-modulation hypothesis for conscious awareness provides a comprehensive rationale regarding previously reported psychological phenomena and neurological symptoms such as blindsight, neglect, the priming effect, the threshold/duration problem, and TRN-impairment resembling coma. This hypothesis can be tested by neurosurgical investigations of thalamocortical loops via the TRN, while simultaneously evaluating the degree to which conscious perception depends on the severity of impairment in a TRN-modulated network. The subjective experience of consciousness is central to our everyday life. However, whether such subjective experiences have neural correlates remains unsolved and open to hypothesis and investigation. For instance, Lamme  supporteIn addition to regarding consciousness as a biological phenomenon, we cannot deny that there is a genuine phenomenon of consciousness in the ordinary sense and that it has distinctive features that should be investigated when seeking to fully characterize it. One of the general agreements is the quality of 'being aware.' Hence, an information-input mechanism can be considered essential to initiate conscious awareness (see Appendix 1), no matter what is evoked inside or outside of the body. It then becomes reasonable to consider the thalamus one of the primary candidates for the seat of consciousness, given that the thalamus has been referred to as the gateway of nearly all sensory inputs to the corresponding cortical areas . As showAs the cortex has gradually evolved to be competent in higher cognition, the thalamus has evolved in parallel . All theSynchronization within a certain neuronal ensemble is achieved by means of GABAergic inhibitory neurons. For instance, it has been reported that neuronal synchronization is completed via a GABAergic internetwork in some pace-making sources such as the suprachiasmatic nuclei  and hipp+ conductance is fully suppressed by the metabotropic effects of monoamines or excitatory amino acids  'Consciousness' is referred to as thalamocortical response modes controlled by the TRN and is embodied in the form of dynamically synchronized thalamocortical networks ready for upcoming attentional processes.[2] 'Attention' is neurophysiologically substantiated by a highlighted neural ensemble among a number of synchronized thalamocortical candidates, the topographical maps of which are projected onto the TRN.[3] Thalamocortical looping via the TRN is necessary for the 'conscious awareness' of an attended object.We can test these hypotheses experimentally. For example, the degree of conscious awareness could be evaluated along with the severity of the impairment of the TRN. We can also assess the degree of modality-specific conscious perception while investigating the extent of impairment in its functionally relevant thalamocortical loops. The influence of neuroanatomical abnormal connections (whether they are on the first-order track or on higher-order networks) could also tell us more about the significance of iterative thalamocortical loops in accomplishing improved conscious perception. Most likely, the phenomenon of masking  presentsThe TRN-mediated model could reconcile several major hypotheses for conscious awareness. According to the so-called 'global workspace' model of consciousness , incominCompared to the global workspace model, the TRN-mediated model seems more plausible in the following respects. The model-specific sectors on the TRN provide us with a deeper understanding of modality-specific conscious awareness. In addition, although the prefrontal cortex is an important center for conscious awareness in the global workspace model generally, the prefrontal cortex is sometimes not necessary to produce a kind of modality-specific awareness in the TRN-mediated model. Based on the TRN-mediated model, the TRN is responsible for controlling thalamocortical networks to be consciously processed, and the prefrontal cortex may work for the conscious evaluation of highlighted thalamocortical networks.As shown in Figure In particular, as Lamme  emphasizAs discussed so far, the TRN model does not underestimate the significance of cortical roles in conscious awareness. It simply highlights the physiological significance of the central roles of the TRN, such as controlling, screening, and accumulating neural signals through thalamocortical loops during conscious awareness. Most likely, the cortical layers communicate regularly through their corticocortical connections . In addiIn addition, the possibility that thalamic relay mixtures such as intralaminar or midline thalamic nuclei play a role in integrating information processes for consciousness cannot be excluded, as expected in the TRN. However, compared to the TRN, they appear to make different contributions, because they are connected principally with the striatum apart from the cerebral cortex . Further1. To clarify the descriptions used throughout this paper, I tentatively use the term 'consciousness' as a general mental state of being capable of awareness. In addition, the term 'awareness' is used to represent a specific mental state of being acquainted with something in a conscious manner (conscious perception).2. Some empirical evidence regarding the neurophysiology of the TRN used in this paper is based on animal studies; hence, there are limitations regarding the generalization of the TRN-modulation hypothesis of human consciousness. However, as the human TRN might have evolved from the TRN of animals, I believe that such implications concerning our consciousness have considerable value for future studies.3. It is another question as to which brain region is responsible for deciding what to attend to. This is perhaps controlled by top-down signals from higher cognitive stages . This issue remains controversial and open to investigation.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The genetic architecture of a quantitative trait influences the phenotypic response to natural or artificial selection. One of the main objectives of genetic mapping studies is to identify the genetic factors underlying complex traits and understand how they contribute to phenotypic expression. Presently, we are good at identifying and locating individual loci with large effects, but there is a void in describing more complex genetic architectures. Although large networks of connected genes have been reported, there is an almost complete lack of information on how polymorphisms in these networks contribute to phenotypic variation and change. To date, most of our understanding comes from theoretical, model-based studies, and it remains difficult to assess how realistic their conclusions are as   they lack empirical support.A previous study provided evidence that nearly half of the difference in eight-week body weight between two divergently selected lines of chickens was a result of four loci organized in a 'radial' network . Here, we study the relationship between phenotypic change and genetic polymorphism in this empirically detected network. We use a model-free approach to study, through individual-based simulations, the dynamic properties of this polymorphic and epistatic genetic architecture. The study provides new insights to how epistasis can modify the selection response, buffer and reveal effects of major loci leading to a progressive release of genetic variation. We also illustrate the difficulty of predicting genetic architecture from observed selection response, and discuss mechanisms that might lead to misleading conclusions on underlying genetic architectures from quantitative trait locus (QTL) experiments in selected populations.Considering both molecular (QTL) and phenotypic (selection response) data, as suggested in this work, provides additional insights into the genetic mechanisms involved in the response to selection. Such dissection of genetic architectures and in-depth studies of their ability to contribute to short- or long-term selection response represents an important step towards a better understanding of the genetic bases of complex traits and, consequently, of the evolutionary properties of populations. For decades, evolutionary and quantitative geneticists have suspected that genetic interactions are important for phenotypic evolution. In numerous empirical studies, genetic interactions (epistasis) have implied important contributions to differences among and within species for various quantitative traits, such as plant morphology and growth -3, animaThere is an almost complete lack of insight on mechanistic contributions of genetic interactions to phenotypic change. Thus, it is important to identify such mechanisms empirically and utilize them as realistic starting points for in-depth theoretical explorations of the importance of genetic architecture on phenotypic evolution. For instance, an expectation from theoretical models is that certain forms of epistatic interactions may promote sustained long-term responses to selection, reaching an ending point that is much higher than what could be predicted from the observable genetic variation in the initial population e.g. -24). Rec. Rec24])The availability of high-quality datasets with good estimates of the phenotypes corresponding to each genotypic combination of a genetic architecture of interest (genotype-phenotype map) facilitates explorations of the link between genetic interactions and phenotypic evolution, by providing functional estimates of epistasis independent from allelic frequencies in the population ,30. Data2 population. The data allowed direct estimation of phenotypic means for 77 of these 81 genotypes.In traditional statistical genetic models, epistasis describes the multiple locus genetic effects that cannot be explained by additivity and dominance . HoweverGrowth9, according to [Growth4, Growth6 and Growth12). Figure Growth9. In homozygous Growth9 HH individuals, H alleles lead to a heavier body weight, while these same H alleles decrease body weight in a Growth9 LL genetic background. Each of the radial loci thus reveals (or buffers) the genetic effect of Growth9. In the studied F2 population with intermediate allelic frequencies at all loci, only part of the maximum effects of the network can be described using marginal additive effects. This explains why Growth9 was the only genome-wide significant quantitative trait locus (QTL) in a standard analysis [Further analysis shows that the effect of the central locus of the network (labeled rding to ) is veryanalysis : on averin silico to arbitrary selection pressures, designed to mimic the artificial selection performed in the original selection experiment to generate the high and low body weight selected chicken lines.The evolutionary properties of the four-locus genotype-phenotype map were explored using computer simulations. Each individual in the simulated population is represented by its genotype and by its phenotype, calculated as the sum of the genotypic value from the genotype-phenotype map and a random environmental effect (see Methods). Artificial populations were submitted f0(H)  leads to symmetrical responses during bi-directional selection [The rate of phenotypic change, as well as the final outcome of the selection process, depends on the initial H-allele frequency ) Figure . As the election . Low H ff(H) were studied for each of the four loci in the network under upward and downward directional selection  displays the largest individual additive effect with the same sign in all genetic backgrounds. As a result, Growth9 is systematically fixed first, for H and L alleles in the high and low lines, respectively, in all evaluated scenarios. The effects on the phenotype (either high or low) from the radial loci  are gradually revealed by increases in Growth9 f(H) and as a result they are fixed after Growth9. Under directional selection, Growth4, Growth6 and Growth12 are fixed for H alleles in both the high and low lines. This result is rather surprising, given that, by definition, L alleles were called 'L' owing to their origin in the low line.The dynamics of n Figure  and 4B. According to standard quantitative genetics theory, genetic variance consists of additive, dominance and interaction components . The addA general observation in selection experiments for decreased body weight is that the response ceases after a number of generations owing to physiological constraints. In the Virginia lines, the response in the low line has been small since generation 30 Figure . The resMany empirically observed selection responses where genetic interactions are implied, e.g. the Virginia chicken lines, the Illinois corn lines and others , are neaArtificial selection experiments generally provide dynamic data, such as heritability, changes in response to selection and estimates of environmental perturbations. Combining these empirical data with the results from a QTL analysis based on an intercross between selected lines is likely to enhance the understanding of the genetic architecture underlying the dynamical properties of the population. Unfortunately, several details of the selection will always remain unknown and thus preclude attempts to directly fit the output of the simulations with the observed selection response.2 population. As illustrated in additional file Advances in analytical methods for QTL detection has made it possible to unravel gene interaction networks affecting complex traits ,26. QTL 2 population and will thus be affected by sampling effects, in particular for the completely homozygous genotypes. The sampling could have an impact, in particular, on the selection limit, but less of an effect on the overall dynamics , it appears that the empirically measured phenotype sometimes evolves in the direction opposite to the selection pressure . These factors can be accounted for in simulations, and we used an effective population size resembling that used in the production of the Virginia lines, as well as an environmental effect based on the amplitude of the non-genetic effects measured in the F results ,39-42 prIt is widely acknowledged that the link between the genetic architecture and responses to selection is not direct , and thaThe state of the initial population, which remains one of the main unknowns when parameterizing the simulations, can also be successfully addressed. We know that the base population of the original selection experiment was formed by the crossing of seven partly inbred chicken lines. There are, however, no empirical estimates of the initial frequencies of the H and L alleles in these lines. We have therefore explored the dynamics in the selection response for a large range of initial states of the base population. The results show that the expected dynamics of the network changes dramatically depending on the initial frequencies of alleles, from almost no phenotypic improvement  to very fast (a few generations) fixation of the best genotype. None of these extreme dynamics correspond to the regular response to selection observed empirically during the artificial selection process, and can therefore be ruled out: the allelic frequencies of H and L alleles were probably roughly even in this particular initial population. This also suggests that, in a polymorphic genetic background, no allelic marginal effect seems to be sufficiently high to allow spread (from very low frequency to fixation) in the time scale of the selection experiment. It is thus unlikely that new mutations, i.e. alleles that were not present initially, would have had a major impact on the selection response in this particular case, and the initial population was probably already polymorphic for all loci of the network.in silico explorations of the reconstructed gene network by submitting it to directional selection facilitates a better understanding of the respective roles of the different components of the genetic architecture. The simulations show that the effects of the major genes in the network were probably rather weak at the beginning of the selection experiment, and that responses during the very early generations were likely to be partly a result of minor genetic factors. In all simulations, the central locus was the first fixed, and its fixation enhanced the effects of the other loci, which then subsequently contributed to the selection response. Our results therefore suggest that the selection response is composed of different stages that lead to the observed linear phenotypic change when they overlap. Dissecting genetic architectures and identifying their ability to contribute in the short or long term to selection response may represent an important step towards a better understanding of the genetic bases of complex traits and, consequently, of the evolutionary properties of populations.Furthermore, theoretical Genetic networks can be defined at any interaction level, from molecular to high-level complex phenotypes, such as, in our example, body weight. The evidenced gene network has been defined through significant epistatic interactions that were detected by a QTL analysis. One cannot deduce whether these four loci correspond to genes that are part of the same metabolic pathway or, on the contrary, participate in independent high-level functions  involved in a complex way in the expression of body weight. In any case, the fact that each of the radial components of the network has a similar effect on the phenotype, both in nature and in amplitude, through similar interactions with a unique central component  when selected towards heavier body weights, where the effects of the H alleles reinforce each other. Such directional epistasis is known to induce a different response to selection than that expected from the traditional additive model , and, andper Studying crosses between divergently selected or evolutionary distant populations remains a powerful way to infer the genetic architecture underlying selection response to natural or artificial selection (e.g. ). One ofA surprising, but intriguing, result in our study is that the genotype-phenotype map contains several genotypes that display lower phenotypes than the genotype of the selected 'low line'. The lowest weights are obtained for the genotype with LL homozygosity for the central locus and H alleles at the radial loci. The low line illustrates a scenario where the artificial selection experiment was disturbed by natural selection that eliminated extreme phenotypes: the smallest chickens in the low line were often unable to reproduce or even to survive until reproductive age . This caGrowth4, Growth6 and Growth12 and the conclusion from the QTL experiment would have been that a single QTL, Growth9, was the major factor of the selection response in both lines. Consequently, the complexity of the genetic architecture that has contributed to the phenotypic evolution would remain unknown and, furthermore, as the effect of this locus is entirely dependent on its context, this could be a problem in future efforts to clone the underlying gene or use it, for example, in marker-assisted selection.It is often assumed that the part of the genetic variability that cannot be detected in the experiment is a result of numerous minor QTLs, QTLs in a repulsion phase or epistasis. Minor effect QTLs and, to a lesser extent, epistasis could potentially be detected by increasing the quality of the data . Here we indicate a genetic architecture that no line-cross-based QTL experiment, regardless of the accuracy of the statistical tools or the number of sampled individuals, would be able to evidence as the same allele is fixed in all lines; only the central locus will be found and implied to have a major additive effect. Indeed, if natural selection would have been bypassed in the experiment, then the final fixed genotype would likely have been the same in both high and low lines for 2 were genotyped for 145 genetic markers. A standard QTL analysis for eight-week body weight in the F2 population revealed only one genome-wide significant QTL located on chromosome 7 (Growth9). Three additional loci, Growth4, Growth6 and Growth12  were evidenced by a pairwise analysis [Growth9. Growth9 emerges as the central point of a radial epistatic genetic network  and the other towards low weights . After 46 generations of artificial selection ,47,48, tanalysis , all of 2 design. Among the 34 = 81 possible genotypes, we obtained information (i.e. an estimate of the average phenotype) for 77 genotypes, with between 1 and 38 phenotyped individuals per genotype. The total phenotypic variance in this dataset is 4 and the residual variance  is 4. The four missing phenotypes were estimated from the mean of the closest genotypes, and simulations with different values have been run to confirm the minor impact of these estimates on the general dynamics of the system  and by its phenotype Pi. The artificial selection used relied on a truncation process. In each generation, a given number of individuals NS were allowed to reproduce depending on their phenotype . For simplicity, the sex ratio was considered as even. For each of the NT individuals expected in the following generation , two parents  were randomly drawn. Each parent gives a 'gamete' , and both gametes were merged to constitute the genotype of the new individual i. The phenotype Pi was then computed by Pi = Gi + εi, where Gi is the phenotypic value of the genotype gi directly read from the genotype-phenotype map and εi is a random factor following a normal distribution N, corresponding to environmental effects.Individual-based computer simulations were performed to explore the dynamics of the four-locus system when submitted to artificial selection. Each individual One of the main unknowns of the system is the state of the initial population. The selection experiment, started in 1957, was initiated from a polymorphic population obtained by crossing seven partly inbred chicken lines (inbreeding coefficient around 50%). Unfortunately, no tissue or DNA samples exist from these lines and any initial allelic frequency is potentially realistic for each of the four loci, leading to many possible initial scenarios. However, for simplicity we considered that the polymorphism of the four loci in each of the seven initial inbred lines can be neglected and, thus, allelic frequencies at generation 0 were a multiple of 1/7.NT = 300, while the actual number of individuals fluctuated depending on the environmental and economical conditions . Simulations evidenced that random fluctuations of the population size have no effect on the overall dynamics , estimating from the mean of the neighbor genotypes and estimating from the regressions of Figure 4 g, estiClick here for fileImpact of the simplification of the model. Simulations were simplified compared with the actual selection experiment. One of these simplifications was to consider an even and constant number of males and females selected each generation; the other was to consider that the population size was constant in both lines. Simulations show that the results remain consistent when these hypotheses are relaxed.Click here for file


Tissue specific somatic mutations occurring in the mtDNA control region have been proposed to provide a survival advantage. Data on twins and on relatives of long-lived subjects suggested that the occurrence/accumulation of these mutations may be genetically influenced. To further investigate control region somatic heteroplasmy in the elderly, we analyzed the segment surrounding the nt 150 position (previously reported as specific of Leukocytes) in various types of leukocytes obtained from 195 ultra-nonagenarians sib-pairs of Italian or Finnish origin collected in the frame of the GEHA Project. We found a significant correlation of the mtDNA control region heteroplasmy between sibs, confirming a genetic influence on this phenomenon. Furthermore, many subjects showed heteroplasmy due to mutations different from the C150T transition. In these cases heteroplasmy was correlated within sibpairs in Finnish and northern Italian samples, but not in southern Italians. This suggested that the genetic contribution to control region mutations may be population specific. Finally, we observed a possible correlation between heteroplasmy and Hand Grip strength, one of the best markers of physical performance and of mortality risk in the elderly. Our study provides new evidence on the relevance of mtDNA somatic mutations in aging and longevity and confirms that the occurrence of specific point mutations in the mtDNA control region may represent a strategy for the age-related remodelling of organismal functions. It has been recognized for a long time that age-related random damages to mtDNA and the consequent decrease in the respiratory chain capacity are among the major contributors to the aging process Interestingly, it has been found that the CR heteroplasmic point mutations are over-represented in centenarians with respect to younger subjects in the Italian population. Data on MZ and DZ twin pairs have proposed that the heteroplasmic levels of 150C and 150T alleles were genetically controlled To get more insights about such complex phenomenon, in this study we took advantage of the population samples collected in the frame of the Genetics of Healthy Aging (GEHA) project. The GEHA consortium aimed to collect an unprecedented number of 90+ years old sib-pairs, from several European areas Linear regression analyses showed a significant correlation in heteroplasmy between siblings in both cell types (We then studied the heteroplasmy in a group of sib-pairs from Finland (Tampere). For this sample, DNAs from buffy coats (BC) were available. PARFAH method was used to specifically detect and quantify the heteroplasmic C150T mutation. In order to check the sensitivity of the PARFAH method, we first screened a series of samples with known levels of the heteroplasmic C150T mutation. We found that the method can reliably detect a mutant load as low as 2.5% .In For this analysis, we considered only the elder sib from each pair. In addition, we pooled the Italian samples, for which we had data for both Lymphomonocytes and Granulocytes. We found a correlation between heteroplasmy in Lymphomonocytes and adjusted Hand Grip scores . Further, a marginal correlation was found  when we performed the same analysis on the heteroplasmy of the C150T transition. Finally, we observed a correlation  between the heteroplasmy in Lymphomonocytes not due to the C150T mutation and adjusted Hand Grip score. It may be worth noticing that if one uses the Bonferroni correction for multiple testing the significance threshold is 0.017, and then the observed correlations could not be considered significant.No correlation whatsoever was observed between Hand Grip strength and the heteroplasmy level observed in the Granulocytes.There is increasing evidence that tissue specific heteroplasmic mutations in the mtDNA CR may favor longevity. Moreover, the occurrence and the accumulation of these mutations may be genetically influenced The strong correlation of the total CR heteroplasmy and the C150T heteroplasmy between sibs seems to confirm that CR heteroplasmy is genetically influenced. However, we found that CR heteroplasmy not related to C150T mutation is correlated between sib-pairs only in the Finnish and northern Italian samples but not in the southern Italian sample. These results suggest that the genetic contribution to CR mutations may be population specific. Thus, it is likely that nuclear genes, environmental factors or their interaction may have different effects on the occurrence or accumulation mtDNA somatic mutations. The analysis of heteroplasmy in GR and LY showed a high level of correlation, but also revealed some subjects with quite different heteroplasmy in the two cell types. This confirms that CR heteroplasmy is a somatic event, which occurs quite late in the differentiation of these two cell types with a common origin. Thus, the intra-individual correlation may be due to the genetic control of heteroplasmy, although we can not exclude the possibility that the somatic acquisition of heteroplasmy occurs in stem cells during haematopoiesis in most cases and after their differentiation only in a few cases.The analysis of mtDNA haplogroups in our sample showed no correlation between CR mtDNA hetroplasmy and inherited mtDNA variability. This finding, in keeping with previous reports, confirms that the genetic factors affecting CR mtDNA hetroplasmy are likely to be nuclear genetic factors The correlation between Hand Grip strength and CR heteroplasmy in Lymphomonocytes suggested by our data is quite interesting although it will need to be verified in a larger sample. If confirmed, this data will further support the positive effect of CR point somatic mutations on longevity. In fact, Hand Grip strength is one of the best markers of health status in the elderly and it has been shown to be the best single survival predictor On the whole, our study has provided new important clues on the relevance of mtDNA somatic mutations, and of the consequent heteroplasmy, for aging and longevity. We confirmed the high incidence of somatic point mutations and the consequent heteroplasmy in the mtDNA CR of long-lived subjects. In addition, we showed that CR heteroplasmy is significantly correlated with physical performance in oldest olds. On the other hand, we showed that mtDNA heteroplasmy in Leukocytes may be due to the previously described C150T mutation, but also to other mutations, the occurrence of which may be influenced in a population-specific way. In any case, the genetic control of the mtDNA CR heteroplasmy suggests that the occurrence of mtDNA somatic mutations may represent an important strategy for the age-related remodeling of organismal functions.The sampling was carried out in the frame of the GEHA project A total of 195 sib-pairs (390 subjects) were analyzed: 63 sib-pairs (126 subjects) were recruited in the south of Italy , 67 sib-pairs (134 subjects) in the north of Italy (Bologna) and 65 sib-pairs (130 subjects) in Finland (Tampere). For the Italian sib-pairs we analyzed DNAs coming from two different cell-types, Granulocytes (GR) and Lymphomonocytes (LY), for a total of 520 DNA samples ; for the Finnish sib-pairs we analyzed 130 DNAs coming from Buffy Coats (BC).According to the standard operating procedure the biological samples  were stored locally and shipped to the National Public Health Institute , where DNA extraction, quality control and storage of the extracted DNA were performed. An aliquot of these DNAs was sent to us for the genetic analysis.The mtDNA region under study  was amplified and submitted to DHPLC Quantification of the C150T mutation was carried out by PARFAH  In order to check the sensitivity of the PARFAH method, we analyzed, in three independent experiments, a series of standard mixes in which the percentage of mutant mtDNA varied from 0 to 100%.MtDNA variability was analyzed by defining subhaplogroup of one subject of each sib pair. The analysis was carried out by sequencing the entire mtDNA control region from nucleotide position (np) 16024 to np 576. This was followed by a hierarchical survey of haplogroup and sub-haplogroup diagnostic markers in the coding region Physical performance was evaluated by means of Hand grip strength. Hand grip strength was measured by using a handheld dynamometer while the subject was sitting with the arm close to his/her body. The test was repeated three times with the stronger hand; the maximum of these values was used in the analyses. The scores obtained were subsequently adjusted for sex, age and height as these parameters turned out to be significantly correlated with Hand Grip strength.r) measures the strength and the direction of a linear relationship between two variables; while the p-value measures the probability of getting a correlation as large as the observed value by random chance, when the true correlation is zero. The p-value is computed by transforming the correlation to create a t statistic having n-2 degrees of freedom, where n is the number of data pairs.The two-tailed Pearson test was used to perform correlation analyses. The linear correlation coefficient . A significance level of α = 0.05 was chosen in all the tests.Table S1Phylogenetic classification of the samples analyzed according to the haplogroup classification in comparison with the levels of heteroplasmy.(0.65 MB DOC)Click here for additional data file.


A reliable and valid clinical tool to capture symptoms and signs of diabetic sensorimotor polyneuropathy (DSP) for use in clinical research trials is urgently needed. The validated Toronto Clinical Neuropathy Score (TCNS) was modified to improve sensitivity to early DSP changes. We aimed to assess the reproducibility of this modified tool, the mTCNS and to determine its validity relative to the precursor TCNS.Sixty-five patients  with diabetes duration 13 ± 8 years were accrued from four study sites and examined on 2 days for internal consistency and inter- and intra-rater reliability of the mTCNS. In the absence of a single quantitative gold-standard measure for DSP, results of the mTCNS were compared with the precursor TCNS for the purpose of estimating validity.Internal consistency of the two domains within the mTCNS was good . Very good inter-rater reliability for the mTCNS was demonstrated by an intra-class correlation coefficient for the mTCNS of 0.87 , which was similar in magnitude to that of the TCNS . Intra-rater reliability testing of the mTCNS showed moderate to good correlation for individual symptoms and sensory tests . The mTCNS shared moderate correlation with the precursor TCNS .The mTCNS, a clinical score with higher face validity for tracking mild to moderate DSP, has sufficient reliability and validity relative to its precursor TCNS for use in clinical research. Although therapeutic agents such as aldose reductase inhibitors have the potential to restrict the progress of diabetic sensorimotor polyneuropathy (DSP), none have proven efficacious . A possiThe Toronto Clinical Neuropathy Score TCNS;  can be uIn a nerve biopsy study of the aldose reductase inhibitor ranirestat, with a 15-month extension study, the TCNS showed a statistically significant improvement in the drug-treated patients compared with baseline assessment ,12. In tIn view of these potential advantages of the mTCNS over the TCNS for clinical research involving drugs that could modify the early pathophysiology of DSP, we aimed to assess the reproducibility of the mTCNS (measured by inter- and intra-rater reliability). Secondly, in the absence of a single quantitative gold-standard measure for DSP, we aimed to simply validate the mTCNS relative to its precursor, the validated TCNS.We performed a multi-centre study at four centres, three in the USA and one in Canada (see below for list of study centres). The local Institutional Review Board at each of the four sites approved the study protocol prior to enrolment of patients.Sixty-five patients were enrolled (10–22 patients per site). Inclusion criteria included age 18–70 years, presence of diabetes mellitus, a sural nerve amplitude response of 1.0 µV or more and the presence of symmetrical distal DSP as defined by the modified San Antonio Criteria, in which two of symptoms, signs, abnormal nerve conduction parameters or abnormal vibration perception thresholds (VPT) were required . PatientEach patient was examined on the same day by 1–3 raters for inter-rater reliability testing and then tested again within 48 h by one rater for the intra-observer reliability testing. The raters were all trained at a single training session before starting the study in order to standardize the clinical assessments. Ten raters participated in the study in four study sites.At the first visit, demographic information was collected and the TCNS and mTCNS were performed. Details of the TCNS have been presented previously . The mTCOther procedures done at the first visit included: MNSI, MDNS, the NDS, nerve conduction studies (NCS) and quantitative sensory testing (QST). NCS included motor nerve conduction studies of the dominant peroneal and tibial and non-dominant median nerves with corresponding F wave latencies and sensory nerve conduction studies of bilateral sural, non-dominant median, radial and ulnar nerves. QST included VPT and cooling detection thresholds measured using the method of limits and the Medoc device .On day 2, each patient had the TCNS and mTCNS performed by 2–4 raters, including the rater from day 1. The assessments were performed at least 15 min apart to reduce memory effects. The time interval of less than 48 h between assessments was selected to minimize the potential for change in symptoms. All examinations were masked to the results of all other testing, including the results of previous TCNS and mTCNS tests. The TCNS was selected as the criterion standard for DSP in this study in the absence of a single, universally accepted gold standard for DSP and the prior demonstration of validity of the TCNS against the morphological criterion of sural nerve fibre density .The NCS, QST, TCNS and mTCNS were reviewed by a central Neurological Core Laboratory for quality control according to established control procedures .To determine the acceptability of the mTCNS to patients, a cognitive debriefing substudy was conducted in 12 randomly selected patients (three from each study site) after the completion of their two study visits. The cognitive debriefing constituted a qualitative semi-structured one-to-one interview that included questions pertaining to the importance of each component of the mTCNS in the opinion of the patients.n = 2–4) were considered random effects. Intra-rater reliability reflects the agreement between responses when the instrument is administered by the same rater on more than one occasion. It was determined by the Cohen's kappa statistic [Internal consistency was assessed for the mTCNS and TCNS using Cronbach's alpha . Inter-rtatistic ,18 for ttatistic . ValiditConstruct validity was assessed by correlations of the mTCNS with the TCNS, NCS, QST, MDNS and NDS.All 65 patients completed the two visits and all study procedures. Details of their clinical characteristics are shown in Ten raters, eight of whom were physicians, participated from the four centres, with a minimum of two raters per site. Three of the raters were neurologists or neurophysiologists, one was an endocrinologist and six had other specialties. The 10 raters had a mean of approximately 3.5–4 years’ experience with the TCNS and other similar clinical scoring systems. They had less experience with the mTCNS (mean 2.6 years). Four (40.0%) raters indicated that the TCNS was the scale with which they were most familiar; other scales were most familiar to 1–3 raters each. The raters had a mean of 11.5 years of experience with neurological examinations and approximately 8 years of experience with monofilament sensory tests and vibration perception threshold testing.The components of both the mTCNS and the TCNS showed good to very good internal consistency. The total scores showed good internal consistency . Within the symptom score and sensory test domains, internal consistency was very good for the mTCNS . Rather than very good, the internal consistencies for the equivalent TCNS domains were good .Inter-rater reliability was very good for the total scores of the mTCNS and TCNS and comparable in magnitude . The corIntra-rater reliability was assessed only for individual symptoms and signs and not the total or domain scores because of the nature of Cohen's kappa that is used to analyse discrete parameters. It uses the counts of cases where there is agreement between two assessment times. Ninety-nine per cent of paired values were concordant within a maximum absolute difference of three points for the mTCNS. For precise concordance of the exact integer scores, generally Cohen's kappa values indicated moderate to very good agreement for the symptoms  and sensory tests . Measures of intra-rater reliability were non-significantly higher for the TCNS as compared with the mTCNS and are summarized in the second section of The mTCNS demonstrated moderate correlation with the TCNS (Pearson correlation coefficient of 0.58). Comparison of the symptom score and sensory test domains showed very good and good correlation . Other than the moderate correlation seen between the mTCNS and the MNSI , in most cases correlation was poor to fair with other clinical scales. For example, the Pearson correlation coefficient was 0.40 with the MDNS and 0.04 with the NDS. Correlation with individual quantitative objective tests was also poor. For example, correlation was 0.13 with VPT and –0.13 with the summed sensory amplitudes from NCS. However, the Pearson correlation coefficients with the sensory score domain of the mTCNS were higher for these parameters—for example, correlation of this domain with summed sensory amplitude was –0.45. As such, lower (impaired) sensory amplitudes correlated with higher sensory test scores.The results of the cognitive debriefing indicated that most patients understood the meaning of the questions relating to DSP symptoms that are part of the mTCNS. In the opinion of the 12 respondents, they generally reported that the symptoms in the mTCNS are ‘important’ to ‘very important’ in terms of their relevance to DSP. Details for each symptom in the mTCNS scoring system are shown in This study demonstrates that the modification of a well-validated score, designed to capture the manifestations of the early processes of DSP better than the precursor score, produces a measure with similar internal consistency, inter-rater reliability and intra-rater reliability. The resultant measure, the mTCNS, maintains acceptable correlation with the precursor score, the TCNS.Although this speaks generally to the validity of the mTCNS simply because the TCNS represents well the morphological and functional change in peripheral nerves seen in those with diabetes ,10, fullAlthough the mTCNS correlates with the TCNS and other clinical scales measuring DSP, in many cases the degree of correlation is lower than would be expected from scales that make use of similar symptoms and signs. For example, MNSI shares a Pearson correlation coefficient of 0.63 with the mTCNS, even although they have in common similar elements on the semi-structured questionnaire and examination. However, perfect correlation between the mTCNS and the other clinical scales  would indicate that the new modified scale would offer no potential advantage over the existing metrics for neuropathy. As such, the degree of correlations observed might indicate advantages of the mTCNS over the other scales that generally include variables associated with advanced neuropathy and may therefore be less sensitive to milder degrees of change in nerve function. Specifically, the MNSI includes examination of the feet for deformities and reflexes (not components of the mTCNS), while the NDS excludes assessment of symptoms in place of reflexes.Similarly, correlation with specific quantitative sensory tests (cold detection thresholds) may also relate to the inability of this test to represent the full DSP phenotype as well as a scale that includes more sensitive components such as a quantitative representation of symptoms. Furthermore, cold detection thresholds are characterized by significant error variability that may also explain poor correlation with the mTCNS.The reproducibility of a quantitative measure for DSP is of fundamental importance as a tool for identifying changes in DSP severity that are of small magnitude. The very good inter-rater reliability of the mTCNS in this study (Kraemer's kappa 0.87) is comparable with that reported previously from a study of the TCNS . That thAlthough serving to quantify the reliability of the mTCNS and to establish its validity in a patient group with mild to moderate DSP severity, this analysis has some limitations. First, the assessment of any proxy score for DSP is hindered by the lack of a single quantitative gold standard measurement for neuropathy. As such, the validity of the mTCNS can only be inferred by its association with the TCNS and components of objective tests. Second, although performance of the mTCNS was generalizable among study centres by different study staff, these centres represent a certain expertise that may limit our knowledge of the applicability of this test in broader clinical settings, such as in primary care clinics.Taken together, the results of this multi-centre study have implications for future treatment trials in DSP. Patients in this study were selected for mild to moderate levels of DSP as evidenced by the presence of bilateral sural nerve responses. This feature of the study group makes it similar to the patient populations in prior therapeutic studies of agents such as aldose reductase inhibitors ,21. As cVB and RAB have been reimbursed by Dainippon Sumitomo Pharma for consultation fees. ST is an employee of Dainippon Sumitomo Pharma USA. BAP has nothing to declare.


Inflammation is a highly complex biological response evoked by many stimuli. A persistent challenge in modeling this dynamic process has been the (nonlinear) nature of the response that precludes the single-variable assumption. Systems-based approaches offer a promising possibility for understanding inflammation in its homeostatic context. In order to study the underlying complexity of the acute inflammatory response, an agent-based framework is developed that models the emerging host response as the outcome of orchestrated interactions associated with intricate signaling cascades and intercellular immune system interactions.An agent-based modeling (ABM) framework is proposed to study the nonlinear dynamics of acute human inflammation. The model is implemented using NetLogo software. Interacting agents involve either inflammation-specific molecules or cells essential for the propagation of the inflammatory reaction across the system. Spatial orientation of molecule interactions involved in signaling cascades coupled with the cellular heterogeneity are further taken into account. The proposed in silico model is evaluated through its ability to successfully reproduce a self-limited inflammatory response as well as a series of scenarios indicative of the nonlinear dynamics of the response. Such scenarios involve either a persistent (non)infectious response or innate immune tolerance and potentiation effects followed by perturbations in intracellular signaling molecules and cascades.The ABM framework developed in this study provides insight on the stochastic interactions of the mediators involved in the propagation of endotoxin signaling at the cellular response level. The simulation results are in accordance with our prior research effort associated with the development of deterministic human inflammation models that include transcriptional dynamics, signaling, and physiological components. The hypothetical scenarios explored in this study would potentially improve our understanding of how manipulating the behavior of the molecular species could manifest into emergent behavior of the overall system. The acute inflammatory response (AIR) is the initial response of the host to a diverse array of biological stressors including infection, burns, trauma and invasive surgery. Under normal circumstances the dynamics of acute inflammation are tightly regulated and self-limited Despite the growing understanding of the cellular and molecular mechanisms of systemic inflammation Although both modeling approaches (EBM and ABM) have both advantages and disadvantages The key elements in ABMs are the agents, which are entities that represent a certain aspect of the system, for instance a family of cells and/or molecules that are able to adapt and interact with the environment and with each other based on a specific set of rules The work discussed in this report seeks to address the possibility of an agent based modeling approach that defines the propagation of a perturbation across the system taking into account spatial orientation at the molecular level as well as cellular interactions and heterogeneity. Driven by the premise that peripheral blood leukocytes (PBLs) are major effectors in response to endotoxin and that PBLs represent a composite mixture of several cellular subpopulations we opted to simulate the stochastic interactions particularly in the macrophages and T helper cells. During the onset of the inflammatory response, the secretion of pro-inflammatory cytokines from macrophages stimulates the activation of precursor T helper cells (Th0) and induce them to exhibit the type 1 T helper cell (Th1) phenotype thatin turn facilitates the secretion of various pro-inflammatory cytokines Our agents of choice reflected the characteristics of biological molecules. This allowed us to focus on the intracellular dynamics of the NF-kB signaling module and further illustrate the subsequent intercellular interactions through the up-regulation of inflammatory mediators. The stochastic behavior of the agents was partially attributed to the random motion of the molecules. The probability that determined whether an interaction should occur relied on the spatial configuration of the participants. Cells were not considered as reactor spaces with an even distribution of molecules. To accommodate for this, some of the agent-based rules regarding the mobilization of molecules were implemented Table 1,Inevitably there is a level of abstraction that needs to be considered when representing molecular reactions as discrete events that follow somewhat arbitrary rules. The validity of our approach will be demonstrated through its potential to reproduce biologically relevant scenarios indicative of the non–linear dynamics of systemic inflammation described as the following scenarios: (1) a self-limited response where the inflammatory stimulus was cleared successfully, (2) a persistent infectious response where the inflammatory stimulus was not eliminated, leading to an aberrant inflammatory response, (3) a persistent non-infectious inflammatory response that can be elicited under high concentrations of the inflammatory stimulus, causing an inflammatory insult that can disturb the dynamics of the host response leading to an unconstrained inflammatory response; and finally, (4) two scenarios associated with endotoxin tolerance and potentiation effects followed by perturbations in the regulatory (NF-kB) signaling module.in vivo human response to endotoxin, we recently proposed a receptor mediated indirect response model that couples extracellular signals with the transcriptional response In an effort to study the non-linear dynamics of an Prior to any external perturbation, NF-kB is inactive in the cytoplasm forming a complex with its primary inhibitor, IkBa. Upon stimulation, NF-kB translocates to the nucleus activating the transcriptional machinery for the up-regulation of the critical transcriptional events A self-limited inflammatory response to the endotoxin stimulus corresponds to resolved dynamic profiles for all the elements constituting the model. The objective was to produce the dynamic profiles of a successful inflammatory resolution as shown in High concentrations of LPS, corresponding to an increase in the strength of the inflammatory insult, can be responsible for the amplification of the host immune response An acute pro-inflammatory cytokine “burst” results from intravenous administration of high concentration of LPS into the system of healthy subjects. The subsequent effect is associated with the host's inability to resolve the inflammatory reaction followed by the persistent infectious challenge (unsuccessful clearance of endotoxin) The pre-exposure of the host to controlled levels of inflammatory agents affects the eventual fate of the response. It has been observed that repeated doses of endotoxin insult might lead to a less vigorous innate immune response Endotoxin hypo-responsiveness is associated with an emergent acquired dynamic state of the system that modulates the response of the system not to respond rigorously to the primary endotoxin challenge. On the other hand, the successive administration of sublethal doses of endotoxin can potentiate the system in that, because of the lack of an acquired state in the dynamics of the system, such an insult may dysregulate the host response dynamics leading to an exacerbated inflammation that cannot resolve. Thus, based on our agent-based model we further explore the behavior of the system when it is either pre-exposed to lower levels of endotoxin for “adequate” time as well as when the system has not manifested its “dynamic memory” to tolerate the second endotoxin challenge Another mode of perturbation of the underlying dynamics of the probed system was related to the presence of a “prior” insult that coupled with the LPS stimulus. It accounted for an increased production of pro-inflammatory mediators as shown in We have demonstrated the ability of our model to simulate the trajectory of an unconstrained inflammatory response. Further, the potential of the proposed model was also demonstrated through its capability to respond to an intervention strategy that intended to modulate the dynamics in favor of a balanced immune response. In Our model exhibited a bistable behavior which implied the co-existence of two steady states. Physiologically, such dynamics would reflect either a successful inflammatory resolution or the progression of a systemic inflammatory response syndrome. Such bistability is an essential characteristic of the non-linear dynamics of inflammation as suggested from various animal studies In conclusion, an agent based modeling framework is proposed as an alternative modeling approach to study the complex, non-linear dynamics of acute human inflammation. We specifically proposed an agent based model that couples critical aspects of the host response to endotoxin. Predicated upon our prior research effort where a deterministic approach has been taken to couple extracellular signals and intricate signaling cascades with the transcriptional response level, the work discussed in this study explored the potential of an agent based modeling approach to improve our understanding of how a system gives rise to a response through its interacting molecules (or cells). Agent based models offer a promising approach in that they can express the dynamics through intuitive multiple interactions between the agents over time. A well known feature of ABMs is their ability to generate surprisingly complex and emergent behavior from very simple rules. However, this modeling framework is not without its own limitations. A key limitation of agent-based modeling has to do with the difficulty in applying a formal analysis to the relationship between the agent rules and the behavior of the system http://www.ncbi.nlm.nih.gov/geo/) under the accession number GSE3284. The data have been appropriately de-identified, and appropriate IRB approval and informed, written consent were obtained by the glue grant investigators The data used in this study were generated as part of the Inflammation and Host Response to Injury Large Scale Collaborative Project funded by the USPHS, U54 GM621119 In order to integrate high-throughput transcriptional data we recently introduced a systems level approach The inflammatory response is activated when endotoxin is recognized by pathogen recognition receptors The pro- and anti-inflammatory mediator profiles (P and A) and the energetic response of the macrophages (E) were used as a primary indication of a constrained or unresolved inflammatory response. During the progression of systemic inflammation, pro-inflammatory (P) molecules specifically reflect the presence of IL-12 mediators that are circulating in the system. The primary reason for such a selection stems from the fact that the role of IL-12 has been implicated in the differentiation of Th-0 cells. However, each essential transcriptional signature  as it previously mentioned, serves as the aggregate signal that describes complex inflammatory reactions. Thus, (P) would qualitatively reflect the secretion of cytokines and chemokines such as TNFSF2 (TNF), IL1A, IL1B, CXCL1, CXCL2, CCL2, CXCL8 (IL-8) and CXCL10. Similarly, the anti-inflammatory arm of the system (A) reflects either the number of IL-4 molecules upon endotoxin simulation or mediators such as IL1RAP, IL1R2, IL10 and TNFRSF1A. We would like to comment that while these two quantities specifically measures the amount of a particular species, they are however a qualitative description to indicate the state of the system. By the same token, although the energetic response (E) is given as a quantity in “molecules” in the model, it is only a descriptive quality as a marker to track the state of the system and does not have a physical manifestation in physiology. The energetic response (E) refers to those transcriptional signatures that participate in the cellular bio-energetic processes, mainly in the ATP producing pathways Agents are the main components that follow specific instructions on how they should behave and interact with other agents. The types of agents are listed in As the model is executed, it performs a list of procedures in an order. The execution is an iterative process where each iteration represents a “tick” or a discrete time point. Each procedure governs the behavior of a specific class of agent; it contains instructions on how an agent should move, whether to bind to a receptor or “bounce” off of the cell membrane, etc. The instructions are conditional (rule) based (if-then) and may involve multiple agents, such as when two molecules bind together, both molecules' parameters change due to the binding, for instance, they now move in the same pattern. Moreover, the instructions are derived from literature regarding relevant mechanisms for LPS activation The movement of LPS molecules is characterized by a random walk routine, namely, each molecule heads to a random direction and moves several steps forward. When one LPS molecule comes in contact with its signaling receptor on the surface of the macrophage, it will have a chance to bind to it. Once bound a molecule will no longer be moving freely; it will move in accordance with its counterpart. Such process triggers the production of the proximal inflammation-specific mediator, TNF-a causing a decrease in receptor's sensitivity. Receptor sensitivity determines the probability by which one LPS molecule will bind to its endotoxin receptor. Bound LPS molecules are degraded shortly, freeing up the receptor. Molecules of TNF-a also move randomly where they can diffuse into the cell (move past the cell membrane agents) and bind to their appropriate receptors either from the cytoplasm or from outside of the membrane. The activated receptor will trigger downstream a signal transduction cascade that stimulates IKK activity. Activated IKKs move randomly inside the cytosol while they are not capable in moving past the cell membrane agents or enter the nucleus region. They activate the NF-kB complex by dissociating the bound between NF-kB and its inhibitor, IkBa. This is achieved through the phosphorylation of the inhibitory protein IkBa where dissociated IkBa is therefore ubiquitinated and degraded by the proteasome. Activated NF-kB then moves into the nucleus region initiating the transcriptional machinery program which up-regulates the transcription of IkBa, of pro-inflammatory cytokines (P) followed by a decrease in the energetic state of the macrophage. Activated IkBas are capable of moving into the nucleus, binding to activated NF-kB molecules, and deactivate them, as they retrieve nuclear concentrations of NF-kB by forming an inactive complex in the cytoplasmic region.The pro-inflammatory (P) agents are limited by cell membranes and their presence excites the production of anti-inflammatory cytokines (A) and the migration of undifferentiated T-helper cells (Th0) which are not present under conditions of no infec7tious challenge. However, the secretion of pro-inflammatory (P) molecules by macrophages during the progression of the inflammatory reaction induces Th0 cells to enter the “virtual world”. This event signifies the migration of cytokines into the spleen, within which the differentiation of Th0 cells takes place. In this model the role of T-helper cells is to regulate the feedback loops associated with pro-(P) and anti-inflammatory (A) mediators. Further, the binding of (A) molecules with their signaling receptor will stimulate an energy expenditure causing nearby bound TNF-a to degrade faster. In addition to Th0 cell type under conditions of an abundance of bound anti-inflammatory (A) cytokines with their receptors it will morph into a Th2 cell. If it happens that the presence of (P) molecules on the surface receptors to outweigh the (A) response, then Th0 will become of Th1 type which potentiates the pro-inflammatory response. Conversely, Th2 cell type response potentiates the secretion of anti-inflammatory cytokines (A).In order to facilitate the translation from literature evidence into a programming language, it is necessary to provide a feasible framework that integrates disparate research into a conceptually valid scheme, taken into account the abstractness and limitations of the model. Some of the goals are outlined in literature Due to the inherent stochasticity of the ABM development, calibration is oftentimes performed on a trial and error basis. This process involves generating multiple sets of results by systematically varying the model parameters at each set. Also known as “parameter sweeping”, this process allows us to explore the possible behaviors of the model and determine which parameters will engender the patterns that best represent the behavior of interest. For instance, we first examine the signaling agents that will have the most leverage on repressing the inflammatory response. After each simulation, we adjust the parameters such as the production rate of P and TNF-a, the movement speed of LPS, or the probability that an interaction will occur between two colliding signaling molecules. These parameter values were manipulated so that the simulations lie in qualitative agreement with the self-limited inflammatory response. This implies that from among the multiple runs we select those that can effectively reproduce dynamic profiles associated with the successful elimination of the inflammatory stimulus within the first 2 hr post-endotoxin administration while followed by a subsequent transcriptional resolution within 24 hr. We define the parameters that can produce the self-limited profile as a basis set and based on this set we simulate the LPS dosage dependent responses. A set of parameters is considered satisfactory if the model is capable of simulating the dynamics of a self-limited inflammatory response (resolution within 24 hr post-LPS administration) as well as successfully generating the series of unconstrained (non-linear) responses as previously discussed in this paper. The results of the simulations are compared on a qualitative manner with our prior equation-based host response models as shown in This ABM is developed using NetLogo , a freeware that constructs agent based models.


Missing values frequently pose problems in gene expression microarray experiments as they can hinder downstream analysis of the datasets. While several missing value imputation approaches are available to the microarray users and new ones are constantly being developed, there is no general consensus on how to choose between the different methods since their performance seems to vary drastically depending on the dataset being used.We show that this discrepancy can mostly be attributed to the way in which imputation methods have traditionally been developed and evaluated. By comparing a number of advanced imputation methods on recent microarray datasets, we show that even when there are marked differences in the measurement-level imputation accuracies across the datasets, these differences become negligible when the methods are evaluated in terms of how well they can reproduce the original gene clusters or their biological interpretations. Regardless of the evaluation approach, however, imputation always gave better results than ignoring missing data points or replacing them with zeros or average values, emphasizing the continued importance of using more advanced imputation methods.The results demonstrate that, while missing values are still severely complicating microarray data analysis, their impact on the discovery of biologically meaningful gene groups can – up to a certain degree – be reduced by using readily available and relatively fast imputation methods, such as the Bayesian Principal Components Algorithm (BPCA). During the past decade, microarray technology has become a major tool in functional genomics and biomedical research. It has been successfully used, for example, in genome-wide gene expression profiling , tumor ck-nearest neighbour approach [Although gene expression microarrays have developed much during the past years, the technology is still rather error prone, resulting in datasets with compromised accuracy and coverage. In particular, the existence of missing values due to various experimental factors still remains a frequent problem especially in cDNA microarray experiments. If a complete dataset is required, as is the case for most clustering tools, data analysts typically have three options before carrying out analysis on the data: they can either discard the genes (or arrays) that contain missing data, replace missing data values with some constant (e.g. zero), or estimate (i.e. impute) values of missing data entries. Many imputation methods are available that utilize the information present in the non-missing part of the dataset. Such methods include, for example, the weighted approach  and the approach . Alternaapproach , GO annoapproach  or additapproach , can be While most of the imputation algorithms currently being used have been evaluated only in terms of the similarity between the original and imputed data points, we argue that the success of preprocessing methods should ideally be evaluated also in other terms, for example, based on clustering results and their biological interpretation, that are of more practical importance for the biologist. The motivation is that, even though there are substantial differences in the imputation accuracy between the methods at the measurement level, some of these differences may be biologically insignificant or simply originate from measurement inaccuracies, unless they can also be observed at the next step of the data analysis. Moreover, the imputation methods have conventionally been developed and validated under the assumption that missing values occur completely at random. This assumption does not always hold in practise since the multiple experimental measurements (arrays) may involve variable technical and/or experimental conditions, such as differences in hybridization, media or time. Accordingly, the distribution of missing entries in many microarray experiments is highly non-random, which may have resulted conclusions regarding the relative merits of the different imputation methods being drawn too hastily.In this paper, we systematically evaluate a number of imputation strategies based on their ability to produce complete datasets for the needs of partitional clustering. We compare seven imputation algorithms for which ready-to-use implementation is freely available and easily accessible to the microarray community. Beyond the imputation accuracy on the measurement level, we evaluate the methods in terms of their ability to reproduce the gene partitions and the significant GO terms discovered from the original datasets. The imputation methods are compared on eight real microarray datasets, consisting of microarray designs often encountered in practice, such as time series and steady state experiments. The diversity of these datasets allows us to investigate the effects on the imputation results of various data properties, such as the number of measurements per gene, missing value rate and distribution, as well as their correlation structure. Some recommendations for the microarray data analysts on the use of imputation methods in different situations are given in the discussion.We tested imputation algorithms on eight different cDNA datasets  error (Eq. 3). The results were summarized over all k values using the average normalized ADBP error . To study the effect of different missing value mechanisms, we also generated missing values in the Spahira04B dataset completely at random and compared the resulting NRMSE and ADPB error rates to those obtained when the true column-wise missing value proportions were preserved. Spahira04B was used as an example dataset in this comparison because of its most non-random missing value distribution  are presented in Table kNN. This method seemed to benefit somewhat from a strong global correlation structure, as is present in the Spahira04A and Yoshimoto02 datasets. kNN performed at its worst when there was weak correlation between the genes, i.e. in the Spellman98E and Hirao03 datasets.Imputation accuracies in terms of the NRMSEs of the different imputation methods are shown in Figure The imputation accuracy of the more advanced imputation methods  depended heavily on the properties of the dataset being imputed, and therefore it was difficult to find a clear winner among these methods. However, if we count the number of times that a method was best or second best across all of the datasets, then iLLS and BPCA were the two best methods when assessed in terms of the NRMSE imputation accuracy. A limitation of the iLLS method is that its implementation produces, in some cases, inconsistent results which led to a large variation among the replicate datasets  of missing values had a noticeable impact on the clustering results. If the proportion of missing values was 5% or more, then the disagreement between the original and the reproduced clustering became relatively high in many of the datasets. In each case, however, any type of imputation was a significantly better than leaving the data without imputation (the Nimp trace). This result indicates that valuable information is lost when using the average Euclidean distance alone.The imputation algorithms were next compared by measuring how well the clustering of the original complete dataset was preserved when clustering the imputed datasets with different levels of missing values . The surprisingly consistent ability to identify the original partitions across all of the datasets was also supported by the results of Figure The most striking observation was that the clear differences observed in the NRMSE between the different imputation methods were barely visible in the clustering results. While, as expected, the ZERO and RAVG imputation methods were still consistently the two poorest methods also when assessed in terms of the ADBP error, the differences between the more advanced methods became almost negligible. This was true also for the simpler The effect of generating missing values completely at random is highlighted in Figure k-means clustering. To test the impact of cluster initialization, we repeated clustering on the same example dataset (Spahira04B) using 10 random cluster initializations (k = 5). The average ADBP values from the 10 different initializations shown in Figures Further, we studied whether the negligible differences in the ADBP error rates between the advanced imputation methods could be due to instability of the  Spahira0B using 1We have carried out a practical comparison of recent missing value imputation methods by following the typical microarray data analysis work flow: the given dataset is first clustered and then the resulting gene groups are interpreted in terms of their enriched GO annotations. Our key finding was that clear and consistent differences can be found between the imputation methods when the imputation accuracy is evaluated at the measurement level using the NRMSE; however, similar differences were not found when the success of imputation was assessed in terms of ability to reproduce original clustering solutions or biological interpretations using the ADBP error on the gene groups or GO terms, respectively. The observed dependence of the NRMSE on the properties of a dataset can seriously bias the evaluation of imputation algorithms. In fact, it enables one to select a dataset that favours one's own imputation method. Another potential pitfall lies with the missing value distribution. If the imputation algorithm uses the assumption of completely random missing values, for example in parameter estimation, when in fact this is not case, it may lead to sub-optimal imputation results.et al. examined the effect of imputation on the significance analysis of differental expression; they observed that missing values affect the detection of differentially expressed genes and that the more sophisticated methods, such BPCA and LinCmb, are notably better than the simple RAVG or kNN imputation methods [et al. also studied the influence of missing value imputation on the detection of differentially expressed genes from microarray data; they showed that the kNN imputation can lead to a greater loss of differentially expressed genes than if their LinImp method is used, and that intensity-dependent missing values have a more severe effect on the downstream analysis than missing values occurring completely at random [et al. studied the impact of imputation on the related downstream analysis, disease classification; they discovered that while the ZERO imputation resulted in poor classification accuracy, the kNN, LLS and BPCA imputation methods only varied slightly in terms of classification performance [et al. also studied the effect of missing value imputation on classification accuracy; they discovered that the BPCA and iLLS imputation methods could estimate the missing values to the classification accuracy achieved on the original complete data [Regardless of the evaluation approach used, our results strongly support earlier observations that imputation is always preferable to ignoring the missing values or replacing them with zeros or average values. In addition to the NRMSE validation, Jörnsten  methods . Scheel t random . Wang etformance . Shi et ete data .et al. concentrated on hierarchical clustering and the kNN imputation method only and did not consider biological interpretations of the clustering results; their main findings were that even a small amount of missing values may dramatically decrease the stability of hierarchical clustering algorithms and that the kNN imputation learly improves this stability [k-means, and to find out whether more advanced imputation methods, such as LLS, SVR and BPCA, can provide better clustering solutions than the traditional kNN approach. Our results suggest that BPCA provides fast, robust and accurate results, especially when the missing value rate is lower than 5%. None of the imputation methods could reasonably correct for the influence of missing values above this 5% threshold. In these cases, one should consider removing the genes with many missing values or repeating the experiments if possible.To our knowledge, only one other study has investigated the effect of missing values and their imputation on the preservation of clustering solutions. Brevern tability . Our resk-means algorithm since it is very fast, unlike e.g. hierarchical clustering, is widely used among biologists, and produces results which are relatively straightforward to interpret. The fast running time of k-means was especially important because of the large number of clusterings performed. Recent comparative studies have also demonstrated that partitional clustering methods often produce more meaningful clustering solutions than hierarchical clustering methods [k-means clustering, we used the KKZ initialization since it has been found to perform better than many other methods [c-means, together with alternative approaches for selecting good initializations and appropriate numbers of clusters for each dataset.A number of different clustering algorithms have been proposed for the exploratory investigation of gene expression microarray data . We chos methods . To avoi methods . Due to Missing values have remained a frequent problem in microarray experiments and their adverse effect on the clustering is beyond the capacity of simple imputation methods, like ignoring the missing data points or replacing them with zeros or average values. Biological interpretation of the gene clusters can, to a certain missing value rate, be preserved by using readily available and relatively fast imputation methods, such as the Bayesian Principal Components Algorithm (BPCA).M × N matrix G are the log2 expression ratios for M genes N measurements (i.e. the rows represent the genes and the columns stand for the different time points or conditions). In order to estimate a missing value in G, one typically first selects k genes that are somehow similar to the gene gi with the missing entry. A number of statistical techniques are available to estimate the missing value on the basis of such neighbouring genes. In one of the earliest methods, known as the weighted k-Nearest Neighbour (kNN) imputation, the estimate is calculated as a weighted average over the corresponding values of the neighbouring genes [Relative expression data produced by cDNA microarrays can be represented as an ng genes . The aveThe Local Least Squares (LLS) imputation is a regression-based estimation method that takes into account the local correlation structure of the data . The algkNN are implemented with C++. The kNN imputation method was run with default parameter (k = 10), and SVR with default parameters , since their optimization is not trivial and could have biased the results. The automatic parameter estimator was used with LLS and iLLS. The other methods do not contain any free parameters.All of the imputation methods included in the comparisons are freely available on the internet  initialization algorithm [C1 as the gene with maximal Euclidean norm, i.e. C1 ≡ argmax||gi ||. Each of the subsequent centroids j C, for j = 2,..., k, is iteratively selected as the gene whose distance to the closest centroid is maximal among the remaining genes. The KKZ method has turned out to be among the best initialization rules developed for the partitional clustering algorithms [k-means clustering  equals one if values gil and gjl are present both in genes i and j, and zero otherwise. A is the number of cases where there is a missing value in either of the genes, i.e., where kNN imputation. The problem with this modified measure is its significant loss of information when the number of missing values increases. In the worst case when, for a given gene pair , N equals A , it is not be possible to calculate the distance, even though half of the values of each gene may still be present. In this case, we define The average Euclidean distance is also used in the selection of the neighbouring genes in the U and V using the Hungarian method [k cluster pairs Cluster validation methods that compare clustering results with respect to a known set of class labels (the 'gold standard') are called external measures . To compn method , which fn(j u) and n(j v) are the cardinalities of the clusters uj and j v, respectively, and I{g ∉ uj } equals one, if the gene g does not belong to the cluster j u, and zero otherwise [Here, therwise . The finD is zero when the two partitions are identical and one when the partitions are totally different, thus making it easy to interpret the results and make comparisons between datasets. Once clustering has been performed, a biologist typically looks for the GO terms that are significantly enriched among the genes of each cluster. These terms can be used to characterize the functional roles of genes and thus to interpret the results of the microarray experiment. Enriched GO terms for a given cluster were found by calculating the so-called p-value for each GO term and then selecting the terms whose p-values were lower than a given threshold [p-value for each GO term t and for each cluster was calculated using the hypergeometric distributionThe ADBP error hreshold . This enb is the number of genes in the cluster, K is the number of genes in the cluster annotated with GO term t, B is the number of genes in the background distribution (i.e. the whole dataset), and T is the total number of genes in the background distribution annotated with GO term t [p-value can be interpreted as the probability of randomly finding the same or higher number of genes annotated with the particular GO term from the background gene list. We used the enrichment p-values to find between 1 and 20 most enriched GO terms for each cluster of partitions U and V. These clusters of GO terms were compared using the ADBP measure as for the clusters of genes, that is, we quantified the proportion of GO terms present in the original data that were also discovered in the imputed dataset.Here, O term t . The p-vy and imputed values y' of the missing entries, divided by the root mean squared original values in these entries:In addition to using the above cluster validation methods, we also evaluated the imputation accuracy of the methods using the conventional NRMSE measure . The NRMwhere mean stands for the arithmetic mean of the elements in its argument array. The normalization by the root mean squared original values results in the ZERO imputation always having an NRMSE value of one, thus providing a convenient reference error level when comparing different imputation methods and making the NRMSE results comparable among different datasets.+-dependent deactylaces [We used eight yeast cDNA microarray datasets for this study (see Table ctylaces . The Yosctylaces . The Wyrctylaces . The Spectylaces , which hi for which maxj gij - minj gij < 1.5. Datasets were then normalized on a gene-by-gene basis so that the average expression ratio of each gene became 0 and the standard deviation 1. As the Euclidean distance and Pearson correlation are directly proportional to each other after such standardization, and thus yield similar clustering results, we used only the Euclidean distance measure in the results.In gene expression clustering, a typical preprocessing step is to remove those genes which remain constant over all of the conditions under analysis, as the microarray experiment cannot reliably provide any insight into possible functional roles of such genes. Accordingly, each dataset was first filtered so that genes with low variation in expression values were left out. More specifically, we filtered out those genes JT implemented the algorithms, carried out the experiments, and participated in drafting the manuscript. LLE participated in the design of the study and in editing the manuscript. OSN assisted in the design of the study and in editing the manuscript. TA participated in the design of the study and in drafting and editing the manuscript. All authors read and approved the final manuscript.k-means on the ADBP error for genes.Effect of random initialization of Click here for filek-means on the ADBP error for GO terms.Effect of random initialization of Click here for filek-means on the ADBP error for genes.Effect of the number of clusters in Click here for filek-means on the ADBP error for GO terms.Effect of the number of clusters in Click here for file