Here, inter-trial variability in reaction times is modelled as reflecting the dynamics of the subjects' internal recognition process, i.e. the updating of representations (posterior densities) of hidden states over trials while subjects learn probabilistic audio-visual associations. We use this paradigm to demonstrate that our meta-Bayesian framework allows for (i) probabilistic inference on the dynamics of the subject's representation of environmental states, and for (ii) model selection to disambiguate between alternative preferences (loss functions) human subjects could employ when dealing with trade-offs, such as between speed and accuracy. Finally, we illustrate how our approach can be used to quantify subjective beliefs and preferences that underlie inter-individual differences in behaviour.In a companion paper  How can we infer subjects' beliefs and preferences from their observed decisions? Or in other terms, can we identify the internal mechanisms that led subjects to act, as a response to experimentally controlled stimuli? Numerous experimental and theoretical studies imply that subjective prior beliefs, acquired over previous experience, strongly impact on perception, learning and decision-making . We alsoperceptual model with subject-specific priors. The Bayesian inversion of this perceptual model derives from a variational formulation, through the minimization of sensory surprise . More precisely, the variational Bayesian approach minimizes the so-called “free energy”, which is a lower bound on  surprise about the sensory inputs. The ensuing probabilistic subjective representation of hidden states (the posterior belief) then enters a response model of measured behavioural responses. Critically, decisions are thought to minimize expected loss or risk, given the posterior belief and the subject-specific loss (or utility) function that encodes the subject's preferences. The response model thus provides a complete mechanistic mapping from experimental stimuli to observed behaviour. Over time or trials, the response model has the form of a state-space model  provides an approximate solution to the IBDT problem in that it enables comparisons of competing  models and inferences on the parameters of those models. This is important, since evaluating the evidence of, for example, different response models in the light of behavioural responses means we can distinguish between different loss functions (and thus preferences) subjects might have.Solving the IBDT problem, or not trivial. We argue that such an explanation must take into account the dynamics of subjective representations, such as posterior beliefs about the causes that generate stimuli, and their uncertainty, as learning unfolds over trials. Throughout the text, “representation” refers to posterior densities of states or parameters. We investigate these issues in the context of an audio-visual associative learning task This paper complements the theoretical account in the companion paper by demonstrating the practical applicability of our framework. Here, we use it to investigate what computational mechanisms operate during learning-induced motor facilitation. While it has often been found that (correct) expectations about sensory stimuli speed up responses to those stimuli e.g. , explainWe construct two Bayesian decision theoretic (BDT) response models based upon the same speed-accuracy trade-off c.f. , but difOf course, the validity of a model cannot be fully established by application to empirical data whose underlying mechanisms or “ground truth” are never known with certainty. However, by ensuring that only one of the competing models was fully consistent with the information given to the subjects, we established a reference point against which our model selection results could be compared, allowing us to assess the construct validity of our approach. Furthermore, we also performed a simulation study, assessing the veracity of parameter estimation and model comparison using synthetic data for which the ground truth was known.How does learning modulate reaction times? In this section, we first describe the associative learning task, and then the perceptual and response models we have derived to model the reaction time data. We then recall briefly the elements of the variational Bayesian framework which is described in the companion paper in detail and which we use to invert the response model given reaction time data. Next, we describe the Monte-Carlo simulation series we have performed to demonstrate the validity of the approach. Finally, we summarize the analysis of real reaction time data, illustrating the sort of inference that can be derived from the scheme, and establishing the construct validity of the approach.1 and C2), each predicting the subsequent visual cue with a different probability. The subjects were told that the relationship between auditory and visual stimuli was probabilistic and would change over time but that these changes were random and not related to any underlying rule. The reaction-time  was measured on each trial.The experimental data and procedures have been reported previously as part of a functional magnetic resonance imaging study of audio-visual associative learning face, given C1 was always the same as the probability of the alternative (house) given C2: a priori expectations about the outcome. In the original regression analyses in The probability of a given visual outcome or response cue, say A critical manipulation of the experiment was that the probabilistic cue-outcome association pseudorandomly varied over blocks of trials, from strong The conventional analysis of variance (ANOVA) of the behavioural measures presented in The first step is to define the candidate response models that we wish to consider. In what follows, we will restrict ourselves to two qualitatively different perceptual models, which rest on different prior beliefs and lead to different learning rules (i.e. posterior belief update rules or recognition processes). To establish the validity of our meta-Bayesian framework, the two models used for the analysis of the empirical data were deliberately chosen such that one of them was considerably less plausible than the other: whereas a “dynamic” model exploited the information given to the subjects about the task, the other (“static”) model ignored this information. This established a reference point for our model comparisons . These perceptual models were combined with a loss-function embodying the task instructions to form a complete BDT response model. This loss-function had two opposing terms, representing categorization errors and the decision time, respectively, and thus inducing the speed-accuracy trade-off of the task. We now describe the form of these probabilistic models and their inversion.face or house). This can be expressed as a likelihood that is a mixture of Gaussians:The sensory signals  vely see . We therhouse, face), and Here The sigmoid function We considered two perceptual models that differed only in terms of prior beliefs about the associative strength. Although both models have a prior expectation of zero for the associative strength, they differ profoundly in their predictions about how that associative strength changes over time. This is reflected by the different roles of the perceptual parameter static perceptual model, i.e.: The dynamic perceptual modela priori that the associative strength i.e., its volatility).The Note that the task information given to subjects did highlight the possibility of changes in cue strength. Therefore, from the point of view of the experimenter, it is more likely that the subjects relied upon the dynamic model to form their prior predictions. The choice of these two models was deliberate as it allowed for a clear prediction: we hoped to see that model comparison would show a pronounced superiority of the dynamic model (see section ‘Inverting the response model below’).th trial. Under a mean-field/Laplace approximation to the joint posterior, these sufficient statistics are (i) Given the perceptual models described above, we can now specify the recognition process in terms of their variational Bayesian inversion. The generic derivation of the recognition process is detailed in the companion paper face or house)Note also that the perceptual free energy Note that functional form of the sufficient statistics above depends upon the perceptual model, through the variance parameter We  estimate the parameter what decision is taken and when it is made. This cost is encoded by a loss-functionface or house) and Following the description of the perceptual models, we now define the BDT mapping from representations to behaviour. We assume that subjects decide on the basis of an implicit cost that ranks possible decisions in terms of expected loss, which is also referred to as posterior riskThis loss function is critical for defining optimal decisions: Note that because the expectation is taken with regard to the posterior density on the hidden states , optimal decisions :post-hoc prediction error.At each trial, the subject's representation is initialized at her prior prediction  out see  that, thpost-hoc prediction error and the delay cost is high enough. In other words, categorization errors are optimal decisions if the risk of committing an error quickly is smaller than responding correctly after a longer period.Note that in the present experimental context, the sensory evidence in favour of the outcome category is very strong. Hence, at convergence of the recognition process, there is almost no perceptual uncertainty about the outcome  and the prior density over the unknown model parameters iors see  on the pThe algorithmic implementation of the variational Bayesian inversion of the response model is formally identical to that of a Dynamic Causal Model , under the static (series A) and dynamic perceptual models (series B). In each series, the (log) perceptual parameters were sampled from the intervals ages see . We did It is interesting that the free-energy differences are two orders of magnitude larger for series B, relative to series A. In other words, when the data-generating model is the dynamic one, it is easier to identify the true model from reaction times than when the static model generated the data. This might be due to the fact that the static model is a limiting case of the dynamic model; i.e. when the volatility As expected there is also a clear effect of noise: the higher the SNR, the larger the relative log-evidences. This means that model comparison will disambiguate models more easily the more precise the experimental data.We next characterised the accuracy of parameter estimation under the best (correct) model, using the sum of squared error (SSE), in relation to the true values. We computed the Monte-Carlo empirical distribution of the SSE for each set of  parameters, for each simulation series (A and B) and SNR. Quantitatively, the parameters are estimated reasonably accurately, except for the perceptual parameter (prior precision on associative strength) of the static model. This reflects the fact that the prior on association strength has little impact on the long-term behaviour of beliefs, and hence on reaction times. This is because within the static perceptual model, The Monte-Carlo simulations above demonstrate the face validity of the method, in the sense that one obtains veridical model comparisons and parameter estimates, given reaction time data with realistic SNR. We now apply the same analysis to empirical reaction times from nineteen subjects We conducted a hierarchical (two-level) analysis of the data from the nineteen subjects. Note that the original study by ages see . Also, cages see –13 and aa priori that the cue-outcome association is varying in time) was consistent with the information delivered to the subjects (whereas the static model was not).In a second step, we performed a Bayesian group-level random effect analysis of model evidences ,Having established the dynamic model as the more likely model of reaction time data at the group level, we now focus on the actual estimates of both response and perceptual parameters. First, we tested for the reliability of the parameter estimates, that is, we asked whether the subject-dependent posterior densities Such inferences concern both subject-specific a priori beliefs  and preferences . To demonstrate the potential of our approach for characterizing inter-individual differences in beliefs and preferences, we present a subject-specific summary of the inverted response model  for two individuals (subjects 5 and 12). These results are summarized by First, we would like to stress that, as for the group as a whole, the SNR of empirical data from these two subjects is similar to the SNR of the Monte Carlo simulation series described above  that guided the actions of these two subjects, subject 12 displays a greater variability in her optimal decision times for very small post-hoc prediction errors  predictions about the next outcome. However, she is willing to make more categorization errors per second delay than subject 5. This is important, since she effectively needs more time to update her uncertain  prior prediction to arrive at a correct representation. In contrast, subject 5 is more confident about her prior predictions and is more willing to risk categorization errors in order to gain time.In a companion paper In this work, we have chosen to focus on modelling reaction time data and have deliberately ignored categorization errors. This is because considering both reaction time and choice data at the same time would have required an extension of the response likelihood. The difficulty here is purely technical: the ensuing bivariate distribution is Bernoulli-Gaussian, whose sufficient statistics follow from the posterior risk (equation 11). Although feasible, deriving this extended response model would have significantly increased its complexity. Since the focus of this article was to provide a straightforward demonstration of our theoretical framework (described in the companion paper), we decided not to include choice data in the response model. Clearly, this is a limitation as we are not fully exploiting the potential information about underlying beliefs and preferences that is provided by observed categorization errors. This extension will be considered in future work.In our model, categorization errors arise when incorrect prior predictions coincide with high delay costs (see equations 11 and 12). One might think that there is an irreconcilable difference between this deterministic scheme and stochastic diffusion models of binary decisions  will be We initially evaluated the method using Monte-Carlo simulations under different noise levels, focusing on model inversion given synthetic data and on how well alternative models could be disambiguated. This enabled us to assess both the efficiency of parameter estimation and veracity of model comparison as a function of SNR. Importantly, we found that even under very high noise levels , and therefore poor model fit, the model nevertheless (i) yielded efficient estimates of parameters, enabling us to infer and track the trial-to-trial dynamics of subjective beliefs from reaction time data, and (ii) robustly disambiguated correct and wrong models. We then applied the approach to empirical reaction times from 19 subjects performing an associative learning task, demonstrating that both model selection results and parameter estimates could be replicated across different cue types. Reassuringly, the model selection results were consistent with the information available to the subjects. In addition, we have shown that subject-to-subject variability in reaction times can be captured by significant differences in parameter estimates (consistently again across cue types) where these parameters encode the prior beliefs and preferences (loss functions) of subjects,Together, the simulations and empirical analyses establish the construct validity of our approach and illustrate the type of inference that can be made about subjects' priors and loss-functions. Our results suggest that the approach may be fairly efficient when it comes to comparing and identifying models of learning and decision-making on the basis of (noisy) behavioural data such as reaction times.Some readers may wonder why we have used a relatively complicated criterion to evaluate the relative goodness of competing models; i.e., an approximation to the log-evidence, instead of simply comparing their relative fit. Generally, pure model fit indices are not appropriate for comparing models and should be avoided cf. . There aAs with all inverse problems, the identifiability of the BDT model parameters depends upon both the form of the model and the experimental design. In our example, we estimated only one parameter of the perceptual models we considered. One might argue that rather than fixing the sensory precision . In turn, the perceptual representation discounts past sensory signals with an exponential weighting function, whose half-life is an affine transformation of the prior volatility In contrast to In summary, for the model in the present paper, the subject's learning rate depends on the prior volatility post-hoc prediction error, i.e. posterior minus prior expectation. Put simply, Another analogy concerns the optimal decision time derived from the speed-accuracy trade-off given in Equation 12 which is similar in form to Hick's law. This law relates the reaction times to the amount of extracted information c.f. . In its This paper has demonstrated the practical application of the meta-Bayesian framework described in the companion paper, using empirical reaction time data from an audio-visual associative learning task reported in Finally, we wish to emphasize that the “observing the observer” (OTO) approach for inference on hidden states and parameters can be obtained in a subject-specific fashion, as demonstrated by our empirical analyses in this paper see -13. ThisAppendix S1deciding when to decide’) is included as ‘supplementary material’. It summarizes the mathematical derivation of the optimal reaction times (as given in equation 12) from first principles, within the framework of Bayesian Decision Theory.Appendix S1 (‘(DOC)Click here for additional data file.


By varying the motor density on the surface, one can control the number  Motor proteins such as kinesin, dynein or myosin are unidirectional stepping motors, which are involved in force generation and active intracellular transport. Kinesin-1 and myosin-V are processive motors moving on microtubule (MT) or actin filaments, respectively, for example for intracellular cargo transport. Such cargo transport often involves groups of cooperating motor proteins. Whereas the stepping mechanism of single motor proteins is well-studied experimentally and theoretically, much less is known about the resulting cargo step sizes in collective transport. In a recent experiment by Leduc et al., labeled MTs were observed to perform stepwise motion as a result of the transport by stepping kinesin-1 motors with step size In gliding assays, the tails of molecular motors are immobilized on a planar substrate while their motor heads attach to filaments and pull them over the substrate In order to address these latter issues, we describe the gliding assays by microscopic Brownian (or Langevin) dynamics Motors pulling on the same filament take steps in an unsynchronized manner but these steps generate mutual load forces and, thus, correlations between the motors. Indeed, each motor step gives rise to an instantaneous load force within the polymeric motor stalk, which is described by the force-extension relation of the stalk. This load force is transmitted onto the filament and then affects, via the resulting filament motion, all attached motor heads and their stepping frequency.In addition to the microscopic Brownian dynamics, we also study the fractional steps of the filaments using a simplified description in terms of a force equilibrium model, in which the elastic forces of the motor stalks are mechanically balanced after each motor step. The force equilibrium model shows that motor step size, motor stalk length, and motor stalk elasticity are the essential motor parameters determining fractional filament stepping.Using the microscopic simulation model we investigate the resulting stepwise motion of the transported filaments. In particular, we study how the number quantitative agreement with the experimentally observed MT stepping behavior in Ref. For kinesin gliding assays our microscopic simulation model achieves squared step size of a single motor. For kinesin motors with a step size of We then consider gliding assays in general, i.e., built up from an arbitrary pair of cytoskeletal filaments and motors. We show that each such pair can be characterized by a critical motor number, average number So far, we have implicitly assumed that the overall filament trajectories can be decomposed into distinct segments, each of which is characterized by a fixed motor number Our microscopic simulation model is based on a gliding assay model which has been introduced in Refs. The simulation model contains three types of degrees of freedom: (i) the filament configuration as described by its center of mass and orientation in the two-dimensional substrate plane; (ii) motor heads, which can attach and move on the filament and are described by their position; (iii) motor stalks, which are stretched by the motion of motor heads and transmit their stretching forces both onto the filament and the motor head. To understand the origin of fractional filament steps it is crucial that the simulation model explicitly includes motor stalks, which act as force transducers and are modeled as polymeric springs. These springs are characterized by a force-extension relation, which specifies the stretching force for a given equilibrium distance between the substrate-anchored motor tail and the motor head.In order to simulate the filament motion we use Brownian (or Langevin) dynamics, which is based on the equations of motion for translations and rotations of the rigid filament under the influence of the external motor and thermal forces in the overdamped limit, i.e., neglecting inertia effects in comparison to frictional forces In each simulation time step, we first update the filament position and orientation according to the corresponding equation of motion. We then perform steps of the motor heads along the filament for the same time interval according to the motor force-velocity relation. Stepping of motor heads with surface anchored motor tails leads to forces that build up in the motor stalks that act as elastic springs. These forces are transmitted both onto the motor head affecting its stepping behavior and onto the filament to which the motor head is attached affecting the filament motion. Motor stalks equilibrate fast for given positions of the motor head and the anchoring point on the substrate. Therefore, motor stalk forces can be recalculated instantaneously after updating motor head or filament positions by applying the equilibrium force-extension relation of the motor stalk spring. We perform simulations by advancing motor head positions and filament position and orientation in discrete time steps Molecular motors are randomly distributed on the substrate surface with motor density et al. in Ref. There are a few experimental results on the elasticity of kinesin motor stalks For myosin-V, we use parameter values that have been reported for mouse myosin-V see . For proWe will compare different force-extension relations linear relation. A (I) of a zero rest length (II) a non-zero rest length The elastic coupling (I) also applies to linear force-extension relations nonlinear spring relation appropriate for a freely jointed chain (FJC) in three dimensions,(III) A nonlinear spring relation appropriate for an inextensible worm-like chain (WLC) with bending rigidity. We use the approximate relation as given by (IV) A Note that the zero rest length for the springs (I),(III), and (IV) only refers to the projected displacements in the gliding plane. The total displacement including the height coordinate can still exhibit a non-zero rest length: for a filament in the gliding plane, the interaction forces between the filament and the substrate surface have to be balanced by the perpendicular force components arising from the motor stalks.et al.The filament is taken to move within the quasi-two-dimensional gliding plane at approximately constant gliding height. Thus, we ignore the surface roughness of the underlying substrate surface. The rigid filament has then two degrees of freedom, its center of mass position If et al.The stretching force In Refs. We simulate the motion of molecular motors with a stochastic stepping mechanism which means that molecular motors move by a discrete step Because of the force dependence of the stepping rate, the order, in which the different motors perform a step, depends on the loading state of their motor stalks. Motors which are pulled backwards have a smaller stepping probability, motors which are pulled forward are more likely to move. We assume a fixed motor step size We will also use a more refined stochastic modelling for the detachment and attachment of motor heads from and to filaments as compared to the model employed in Refs. fixed number of attached motors between motor attachment or detachment events, see average number The attachment of a motor to the filament also represents a stochastic process depending on the force-extension relation of the polymeric motor stalk, which gives rise to the potential energy In the simulations we analyze the stepping motion of filaments by detecting the number walked distanceset al.First, we record trajectories of the filament center of mass and determine the histograms of pairwise distances along the filament trajectories. From the walked distances et al.Secondly, we calculate average number Finally, we use the model-independent step finding algorithm described in Ref. zero rest length First, we study fractional steps of MTs in a kinesin gliding assay. The simplest model for kinesin motor stalk elasticity is a linear spring model of the form (1) with a In the simulation motor stepping leads to a similar stochastic “stepping” motion for MTs, and the step size depends on the number of molecular motors attached on the filament as shown in the walked distances in tep size . Each tiMT steps of We also find fractional   motors , as can   motors  and clea  motors , which aSmaller steps for Thermal noise limits the observability of fractional steps. In our simulations, the thermal noise level at room temperature is too high to observe even smaller fractional The derivation of the critical motor number (9) did also not include possible effects from non-linear stalk elasticity. It should be applicable as long as these effects are small, which is the case for step sizes It is important to note that Motor stepping is much slower than the equilibration dynamics of the motor stalks and the filament position: For MTs the maximal motor speed In the force equilibrium model we consider a filament with We assume that filament rotation is slower, which is justified for sufficiently long filaments because linear force-extension relation with zero rest length, and should be observable for all The force equilibrium model explains that, in the absence of thermal noise, fractional unique apparent filament step size all fractional filament step sizes If one of the attached motors moves one step In simulations and experiments, we do not observe a sharp step size distribution for the linear spring (I) because of the additional thermal noise and, in the experiments, also because of noise from the filament position measurement. Such noise can be included in the force equilibrium (11) as additional, approximately Gaussian random forces. If the time interval between consecutive filament steps is short, steps can be missed by the step finding algorithm resulting in the detection of a double step instead of two consecutive single steps. This effect leads to a distortion of the step size distribution since a certain fraction The mechanical force equilibrium that is reached after one attached motor performed a step depends on the the number of motors attached to the filament and the elastic properties of the motor stalks. Therefore, using microscopic Brownian dynamics, we compare the influence of the different force-extension relations, a linear relation with (I) zero and (II) non-zero rest length, (III) a freely jointed chain relation, and (IV) a worm-like chain relation on the stepping motion of the MTs.non-zero rest length The linear spring (II) with   motors , the stecoupled and non-linear equations for the displacement vector These simulation results for the linear spring (II) can be rationalized in the framework of the force equilibrium model. For The force equilibrium is at displacements Finally, we investigated whether an intrinsically non-linear force-extension relation of motor stalks as described by the freely jointed chain (III) or the worm-like chain (IV) gives rise to similar effects in the step size distributions. The comparison of normalized step size distributions in linear regime at energies around the thermal energy To explain this result we note that, for parameter values corresponding to the same motor stalk contour length and linear spring constant at small extensions, both freely jointed chains and worm-like chains are well in their The comparison of simulated normalized step size distributions in We also simulated gliding assays consisting of actin filaments and myosin-V motors, for which fractional filament steps have not been studied experimentally so far. This system is interesting because of the much larger step size The critical number So far, we have implicitly assumed that the overall filament trajectories can be decomposed into distinct segments, each of which is characterized by a fixed motor number average number In contrast, the Thus, we performed simulations for actin/myosin-V gliding assays, for which the motor density has been adjusted to produce a certain average number We have investigated fractional filament steps For the kinesin gliding assays we found filament step size distributions and histograms of pairwise distances for transport by   motors , which sThermal fluctuations and additional experimental noise limit the observability of small fractional steps. We derived the criterion (9) that fractional steps are only observable for d up to  . In expeIn our simulations, we compared these results for stalks that act as linear springs with zero rest length to those that act as linear springs with non-zero rest length or as intrinsically non-linear freely jointed chains and worm-like, see Furthermore, effects from non-linearity are important if forces ibutions .On the other hand, our simulations show that a non-zero motor stalk rest length, which means a non-zero rest length for extensions within the gliding plane, has a much stronger effect and leads to a considerable broadening of the step size distributions for er than  . TherefoFor myosin-V gliding assays with the much larger step length  number  . This agUsing simulations for myosin-V gliding assays we also showed that fractional filament steps are still detectable in the filament step size distributions if the motor number


As an important epigenetic modification, DNA methylation plays a crucial role in the development of mammals and in the occurrence of complex diseases. Genes that interact directly or indirectly may have the same or similar functions in the biological processes in which they are involved and together contribute to the related disease phenotypes. The complicated relations between genes can be clearly represented using network theory. A protein-protein interaction (PPI) network offers a platform from which to systematically identify disease-related genes from the relations between genes with similar functions.We constructed a weighted human PPI network (WHPN) using DNA methylation correlations based on human protein-protein interactions. WHPN represents the relationships of DNA methylation levels in gene pairs for four cancer types. A cancer-associated subnetwork (CASN) was obtained from WHPN by selecting genes associated with seed genes which were known to be methylated in the four cancers. We found that CASN had a more densely connected network community than WHPN, indicating that the genes in CASN were much closer to seed genes. We prioritized 154 potential cancer-related genes with aberrant methylation in CASN by neighborhood-weighting decision rule. A function enrichment analysis for GO and KEGG indicated that the optimized genes were mainly involved in the biological processes of regulating cell apoptosis and programmed cell death. An analysis of expression profiling data revealed that many of the optimized genes were expressed differentially in the four cancers. By examining the PubMed co-citations, we found 43 optimized genes were related with cancers and aberrant methylation, and 10 genes were validated to be methylated aberrantly in cancers. Of 154 optimized genes, 27 were as diagnostic markers and 20 as prognostic markers previously identified in literature for cancers and other complex diseases by searching PubMed manually. We found that 31 of the optimized genes were targeted as drug response markers in DrugBank.Here we have shown that network theory combined with epigenetic characteristics provides a favorable platform from which to identify cancer-related genes. We prioritized 154 potential cancer-related genes with aberrant methylation that might contribute to the further understanding of cancers. Cancer is a complex multi-gene disease. For a long time, gene mutation has been considered to be related to cancer. A number of oncogenes and tumor suppressor genes linked to mutations have been shown to drive the neoplastic process by increasing tumor cell numbers -3. HowevFEN1 (flap endonuclease) in breast and other cancers is associated with CpG island hypomethylation of the promoter region in the tumor cells [TKTL1 (transketolase-like 1) had a high frequency of hypomethylation which induced the overexpression of the gene in head and neck squamous cell carcinoma (HNSCC) [BRCA1 is a well-characterized tumor suppressor gene which codes for proteins that have important roles in the regulation of the cell cycle and in the apoptosis of tumor cells. In breast and ovarian cancers, BRCA1 is inactivated by hypermethylation within the promoter region of the gene [Abnormal DNA methylation has been found in many different tumors, including brain tumor, breast cancer, and prostate cancer. DNA hypomethylation is often considered to activate oncogenes. DNA hypermethylation of the promoter region, on the other hand, may initiate the silencing of tumor suppressor genes. It has been reported that the overexpression of or cells . Similar (HNSCC) . BRCA1 ithe gene .Thus, as the number of epigenetic studies gradually increase, the importance of DNA methylation in cancer research is being recognized. Simultaneously, a series of methods for DNA methylation detection have been developed. The earliest DNA methylation detection methods were mainly single-gene sequence-specific methods such as methylation sensitive restriction endonucleases , methylaSome cancers have been identified as different subtypes based on the methylation level of CpG islands  and cancA human protein-protein interaction network, constructed using a machine learning method, has been shown to be of benefit when applied to the study the disease-related genes using network theory . Here, wIn this study, the workflow is shown in Figure Protein-protein interaction (PPI) networks can be more perspicuous for the representation of the complex relationships between large numbers of elements and better at depicting the structure and function of the elements. In this study, we used a PPI network to understand the DNA methylation patterns present in the development and progression of cancers. We constructed the network by integrating DNA methylation and protein-protein interaction features to prioritize cancer-associated genes. The genes were used as nodes and the correlations of DNA methylation among genes were used as the linkage weight. The linkages whose methylation correlations were below the threshold are removed. The weighted human PPI network (WHPN) that we built contained 17617 interaction pairs covering 7840 human genes (see Methods for details) Figure .We identified 127 seed genes for the four types of cancers  from PubMeth using text mining (see Method for details). The set of seed genes were classified into four types according to how many types of the four cancers the seed genes are associated with . When the degree distributions of WHPN and CASN were compared  than WHPN  Figure . As for degree < 1.9049E-095, Pclustering coefficient < 1.7775E-042, Paverage path length < 2.0008E-091, FDR = 0.01). We also generated 1000 random networks by keeping the same number of nodes and connections as in CASN. We found that, compared with the three different random subnetworks, the degree and clustering coefficient for CASN were much significant those of the three random subnetworks, suggesting that the nodes in CASN were not randomly distributed . Of the top 10 genes with the largest degrees in CASN, 5 were seed genes, 4 were optimized genes and only one was a rest potential gene which was ranked 10  were all in the top 10 genes with the highest degrees in WHPN.CASN genes were divided into three types: seed gene set, optimized gene set and rest potential gene set. The percentile 50 of degrees in the seed gene set, the optimized gene set and the rest potential gene set were 3.5, 4 and 2, respectively Figure . The resMAX), with the second highest number of degrees in CASN and the highest number of degrees (470) in WHPN, was prioritized as an optimized gene. The MAX protein coded by this gene is a member of the basic helix-loop-helix leucine zipper (bHLHZ) family of transcription factors. MAX usually forms heterodimers with other family members such as Mad, Mxi1 and Myc. Myc is an oncoprotein involved in cell proliferation, differentiation and apoptosis [The gene, MYC associated factor X . The differentially expressed genes were screened in the expression profiles for the four types of cancers by SAM . The canThese findings suggest that some of the optimized genes in our data set might be differentially expressed in the corresponding cancers, indicating that these genes may be regulated by aberrant methylation resulting in their involvement in the cancer-related pathways.MED1 (mediator complex subunit 1), one of the optimized aberrant methylated gene associated with cancers, was reported to be frequently methylated in ovarian and colorectal cancer cell lines and this had been to result in the low expression of MED1 [MED1 was also identified as a drug target. PRKCDBP, the gene that encodes the delta binding protein, protein kinase C, was reported to be significantly hypomethylated in breast cancers and the expression of the encoded protein was found to be down-regulated in various cancer cell lines [To evaluate the relationship between the optimized genes and cancers, we queried the PubMed database for publications that contained the combination of optimized gene, type of cancers and hypermethylation/hypomethylation . The res of MED1 . MED1 wall lines . This geWe also manually searched PubMed for an association between all the optimized genes and their use as diagnostic or prognostic markers. We found that 27 of the 154 optimized genes were in the literature as diagnostic markers, and 20 optimized genes were in the literature as prognostic markers for breast cancer, nasopharyngeal carcinoma, prostate cancer, and for other non-cancer diseases that included Rubinstein-Taybi syndrome, type II diabetes and familial dysautonomia  is more than the clustering coefficient for WHPN (0.0503). Therefore, in CASN, the genes connected with the seed genes may participate in the same or similar biological processes as the seed genes and may have the same or similar functions as the seed genes. Thus, it can be concluded that the deregulated DNA methylation may affect the development and progression of cancers.In this study, we ensured the reliability of the linkages in the WHPN by deriving the interaction data from five different PPI databases and by selecting only the PPIs which were validated by experiments or which have been reported in the literature. We then built the cancer-associated subnetwork (CASN) from WHPN. The network topological features evaluated using r values related to power law distribution indicate that WHPN is a typical scale-free network. Most biological networks constructed so far are scale-free networks with a degree distribution that follows the power law with degree exponents in the range 2 < r < 3 . AlthougWe prioritized 154 potential cancer-related genes with aberrant methylation using the neighborhood-weighting decision rule based on CASN. In the PubMed co-citations analysis for these 154 genes, we found 43 genes that were associated with cancers and aberrant methylation in PubMed. The PubMed co-citations analysis is only a rough assessment which may have a high rate of false positives . Of the In this study, we constructed a weighted human protein-protein interaction network (WHPN). Based on WHPN, a cancer-association subnetwork (CASN) was obtained using a set of seed genes derived from PubMeth. Comparing the topological features of the two networks, we found that CASN had a much denser network community than WHPN, indicating that the genes in CASN might be aberrantly methylated in cancers and likely participated in the same or similar biological processes as the seed genes. 154 genes were prioritized as potential cancer-related genes with aberrant methylation based on neighborhood-weighting decision rule. The enrichment analysis of GO and KEGG showed that the prioritized genes were generally enriched for biological processes related to apoptosis and programmed cell death and for pathways associated with cancers. Many of the optimized genes showed some degree of differential expression in the SAM analysis, revealing that these genes might be abnormally methylated in the cancer-related biological processes. Abnormal methylation would affect the expression level of these identified genes leading to the development and progression of cancers. In this study, we prioritized the cancer-related genes with aberrant methylation by integrating DNA methylation and protein-protein interaction characteristics based on the network theory. This method will be helpful for the further understanding of the mechanisms of the development and progression in cancers and may help develop new avenues for the prioritization of cancer-related genes with aberrant methylation for diagnosis and therapeutics.The protein-protein interaction data were obtained from five PPI databases, the Human Protein Reference Database (HPRD) , IntAct The genome-wide DNA methylation data sources were derived from patients with four types of cancer, glioblastoma (GBM), ovarian cancer, hepatocellular carcinoma and leukemia. The methylation data for glioblastoma and ovarian cancer were from TCGA (The Cancer Genome Atlas) which contained 26 samples for GBM and 394 samples for ovarian cancer. The methylation data for hepatocellular carcinoma and leukemia were obtained from ENCODE in the UCSC Genome Browser which contained two replicates of the HepG2 cell line and two replicates of the K562 cell line. These data were all generated using Infinium assays on the Illumina Infinium HumanMethylation27 BeadChip. In these assays, quantitative measurements of DNA methylation are made for 27578 interrogated CpG dinucleotides covering a genome-wide scale of 14475 genes at single-nucleotide resolution. The probes for the CpG sites were mapped to the corresponding genes using Entrez Gene IDs as the unique identifiers. For genes containing two or more CpG sites, the average methylation value of these CpG sites was used to represent the methylation level of the corresponding gene. Finally, the methylation values of the 27578 CpG sites were mapped to the 14475 genes using the Entrez Gene IDs.Seed genes were defined as the genes validated by experiments to be aberrantly methylated (hypermethylation or hypomethylation) in cancers. PubMeth, a database of methylation in cancer, contains genes reported to be abnormally methylated in various cancer types. PubMeth is based on automated literature mining which is then manually checked and annotated . We usedWe build the weighted network used in this study by combining the human PPI data with the DNA methylation data. Pearson correlations were calculated to assess the association of the methylation for each gene pair. The genes were used as the nodes, the interactions of the gene pairs were the edges and the correlation coefficient was used as the linkage weight. Linkages for which the methylation correlations were beneath the threshold were removed.Next, the weight thresholds of the network were determined. The DNA methylation data was perturbed for 1000 times; thereafter, the Pearson correlation coefficient of the random DNA methylation was computed for the gene pairs in each perturbed methylation dataset. The methylation correlation of the original gene pairs was compared with the methylation correlations of the perturbed gene pairs. All the values were ranked and compared with the true methylation correlation. If the true value was either in the top five percent or in the bottom five percent of the ranked correlations for the perturbed gene pairs , then the methylation correlation for that pair was considered to be significant and this correlation was used as the linkage weight of the connected gene pair. All gene pairs for which the methylation correlations were not within the top or bottom five percent were removed from the PPI network.The seed gene set obtained using the data from PubMeth was mapped into the weighted human PPI network. Thus, the cancer-associated subnetwork (CASN) is composed of the seed genes and the genes that are connected with the seed genes in the weighted PPI network.Random subnetworks were generated by randomly sampling the same number of nodes as in CASN from WHPN; the connections in the sampling nodes were kept in the random subnetworks. This process was repeated 1000 times. Topology-matched random subnetworks were generated by the method described by Li et al. in an earlier study . Similarhttp://www.cytoscape.org/, an open source software platform for visualizing complex biological networks [The networks were drawn using Cytoscape networks .Network theory provides a quantifiable description of networks for the biological systems. And degree, clustering coefficient and average path length are the three characteristic topological features used to measure complex networks. In this study, we examined these topological features that can be used to measure and compare the different complex networks .ik, is defined as the number of notes which the node i connects. And the average degree of the network is the average value of the degrees of all the notes, 2L/N, where L represents links and N represents notes.The degree (connectivity) of a node i, This measurement indicates that the variety trend of probability for the note whose degree is k with the change of the note's degree k, and it also means that the ratio of the number of notes with the degree of k accounting for all the notes in the network.Most biological networks are scale-free whose degree distribution follows a power law, at least asymptotically. That is,r is the index for the distribution. According toThe r values for the networks are calculated, looking for whether they asymptotically follow power law distribution.i kand the edge number of the linked neighbor notes is iE, the clustering coefficient of the note i isIf the degree of a note i is The clustering coefficient of the network is defined as the average value for clustering coefficient of all the notes, which reflects the overall cluster trend of interacted notes.In the network research, the general definition of the distance between two nodes is the shortest path connecting the two notes, and the network diameter is the maximum distance between any two notes, that isThe average path of the network < L > is the average value of the distances for all notes,iS:Candidate genes are defined as the genes that connect to seed genes . Given tij ωrepresents the linkage weight that between the candidate gene i and the seed gene j, viz. the Pearson correlation of the DNA methylation between the two genes. If the candidate gene i is not associated with the seed gene j, ij ω= 0. The scores of the candidate genes are calculated by the neighborhood-weighting decision rule.iS. Through the perturbation of DNA methyaltion data, the permuted weights for linkages are obtained. And then the permuted scores are also calculated by the Neighborhood-weighting decision rule. This procedure is repeated 1000 times and then the scores and the permuted scores are compared. The genes whose score is grater than all the corresponding permuted score are selected. It is believe that these genes have potential to be methylated aberrantly in cancers.And next, the candidate genes are prioritized according to the score The gene annotation enrichment analysis for the optimized genes was taken by DAVID , where tin, the number of times this gene appeared in the 1000 random differentially expressed gene sets was calculated. If i nwas > 900, then gene i was identified as a differentially expressed gene and the diff_i scorefor this gene was defined as,Using the gene expression profiles from NCBI GEO , the profiles of cancer samples and control samples were compared to find differentially expressed genes by SAM method . The genij dis the SAM score for gene i in the random dataset j. The differentially expressed genes were ranked according to their diff_iscore. SAM was performed using the R package samr.where, In the absence of a gold standard to assess the relationship between the cancers and the methylation level of the optimized genes, we used the public database PubMed to produce the reference lists. PubMed contains hundreds of thousands of citations to the biomedical literature. We systematically searched PubMed using query terms that included the optimized gene name, the cancer type and hypermethylation/hypomethylation, for the co-occurrence of these terms either in an abstract or in the title of previous publications .WHPN: Weighted Human Protein-protein interaction Network; CASN: Cancer-associated Subnetwork; GO: Gene Ontology; KEGG: Kyoto Encyclopedia of Genes and Genomes; PPI: Protein-protein Interaction; HPRD: Human Protein Reference Database; DIP: Database of Interacting Proteins; MINT: INTeraction Database; BIND: Biomolecular Interaction Network Database; HGNC: the HUGO Gene Nomenclature Committee; TCGA: the Cancer Genome Atlas; ENCODE: ENCyclopedia of DNA Elements; GEO: Gene Expression Omnibus; DAVID: the Database for Annotation, Visualization and Integrated Discovery; SAM: Significance Analysis of Microarrays.YZ and HQ conceived and designed the experiments. HL, JL and BL acquired the experiment data. HL, JS and HL performed the study. HL, JS, HL and JL carried out the data analysis. HL wrote this manuscript. All authors have read and approved the final manuscript.Category of seed genes. The first column is the Entrez Gene ID for the seed genes. In columns 2 to 5, 1 represents a seed gene that is related with this type of cancers and 0 represents a seed gene that is not related with this type of cancers. The last column shows the types of the seed genes. The seed genes were classified into 4 types; genes related with one type of cancers are marked with 1, genes related with two types of cancers are marked with 2, genes related with three types of cancers are marked with 3, and the genes related with all the four types of cancers are marked with 4.Click here for fileComparison of CASN and random subnetworks. Comparison between degree and clustering coefficient of CASN and the three kinds of random subnetworks.Click here for fileScores of the optimized genes. The first column is the Entrez Gene ID for the optimized gene. The second and the third columns are the true and random scores respectively, for the optimized genes by the neighborhood-weighting decision rule.Click here for fileCategory of optimized genes. The first column is the Entrez Gene ID for the optimized gene. From columns 2 to 5, 1 represents an optimized gene that interacts with the seed genes related with the type of cancers and 0 represents an optimized gene that does not interact with the seed genes related with the type of cancers. The last column shows the types of the optimized genes. The optimized genes were classified into 4 types, the genes related with one type of cancer are marked with 1, the genes related with two types of cancers are marked with 2, the genes related with three types of cancers are marked with 3, and the genes related with all the four types of cancers are marked with 4.Click here for fileDegree of the genes in WHPN and CASN. The genes are on the x axes and the degree of the genes is on the y axes. (A) The degrees of the CASN genes (red dots) and non-CASN genes (blue dots) in WHPN; (B) The degrees of the seed genes (red dots), optimized genes (blue dots) and rest potential genes (yellow dots) in CASN.Click here for fileComparison of CASN and non-CASN genes. Comparisons are based on mean, median, minimum, maximum and the percentiles 25, 50 and 75.Click here for fileComparison of seed genes, optimized genes and rest potential genes. Comparisons are based on mean, median, minimum, maximum and the percentiles 25, 50 and 75.Click here for fileGO enrichment analysis for WHPN genes. The GO enrichment analysis of CASN genes and non-CASN genes in WHPN are shown in Additional file Click here for fileGO enrichment analysis for CASN genes. The GO enrichment analysis of seed genes, optimized genes and rest potential genes are shown in Additional file Click here for fileKEGG enrichment analysis for WHPN genes. The KEGG enrichment analysis of CASN genes and non-CASN genes in WHPN are shown in Additional file Click here for fileKEGG enrichment analysis for CASN genes. The KEGG enrichment analysis of seed genes, optimized genes and rest potential genes are shown in Additional file Click here for fileSAM score for the differentially expressed genes. Of the 154 optimized genes, 52 differentially expressed genes and they are ranked by their diff_iscore.Click here for filePubMed co-citations of the optimized genes. The first column is the Entrez Gene ID for the optimized genes. Of the 154 optimized genes, 43 genes that were found from a preliminary analysis to be associated with cancers and aberrant methylation in PubMed. The star (*) in the first column marks a gene that was subsequently validated to be methylated aberrantly in cancers by text mining the literature in PubMed.Click here for fileDiagnostic, prognostic and drug marker validation of optimized genes. After searching PubMed manually, 27 genes were identified as diagnostic markers and 20 genes were identified as prognostic markers for cancers and other complex diseases. Mapped into DrugBank target list, 31 genes can be target as drug response markers.Click here for file


ERMS, the LV synchronous contraction and the hemodynamics improved more with mechanical optimization strategy. Therefore, measures of mechanical dyssynchrony improve the sensitivity and specificity of predicting responders more. The model was subject to validation in future clinical studies.An optimal electrode position and interventricular (VV) delay in cardiac resynchronization therapy (CRT) improves its success. However, the precise quantification of cardiac dyssynchrony and magnitude of resynchronization achieved by biventricular (BiV) pacing therapy with mechanical optimization strategies based on computational models remain scant. The maximum circumferential uniformity ratio estimate (CURE) was used here as mechanical optimization index, which was automatically computed for 6 different electrode positions based on a three-dimensional electromechanical canine model of heart failure (HF) caused by complete left bundle branch block (CLBBB). VV delay timing was adjusted accordingly. The heart excitation propagation was simulated with a monodomain model. The quantification of mechanical intra- and interventricular asynchrony was then investigated with eight-node isoparametric element method. The results showed that (i) the optimal pacing location from maximal CURE of 0.8516 was found at the left ventricle (LV) lateral wall near the equator site with a VV delay of 60 ms, in accordance with current clinical studies, (ii) compared with electrical optimization strategy of  Congestive heart failure (CHF) is a common heart disease caused by dilated cardiomyopathy or damage to the excitation conduction system. Biventricular pacing (BiVP), or cardiac resynchronization therapy (CRT), was a major breakthrough in the treatment for patients with advanced CHF complicated by discoordinate contractions caused by inter- or intraventricular conduction delays . CRT hasOver the past decade, many studies have examined the pathophysiology of cardiac dyssynchrony and tested the effect of cardiac resynchronization on heart functions and the efficacy of symptoms enhancements. Most of these researches have focused on the ECG characteristic of distinct responders versus nonresponders to CRT. For example, left and right ventricular leads were placed in different locations to attain the shortest QRS duration during biventricular stimulation. Presently, the optimal electrode setups and timing delays are also determined by measuring the cardiac index using magnetic resonance tagging (MR tagging), nuclear imaging (NI) or Doppler flow imaging and so on –15, mostHowever, it may be not sufficient for clinicians to formulate a scientific and reasonable treatment scheme for CRT optimization with only physical examination of ECG or medical imaging. Quantitative information and precise programming of the optimal stimulation delays and lead positioning accordant with the physiological function are needed. For example, although it is generally accepted that the posterior-lateral wall is the preferred location for LV lead location in CRT, other LV pacing sites have also been shown to offer superior benefits for selected patient population. In other words, there is no universally accepted best LV pacing site, nor the best V-V interval. Therefore, patient-specific CRT optimization is needed. There are both intersubject variability and intrasubject variability . Modeling of heart can provide a useful supplementary tool to investigate the dynamical behaviour of heart quantitatively and thus enhance our understanding of the cardiac electrophysiological and mechanical properties under physical and pathological conditions. Consequently, the computer modeling of a patient-specific heart appears to be a reasonable solution for solving this problem, which can determine the optimal AV and VV timing pre- or postoperatively with respect to the lead positions in patients undergoing CRT. ERMS, was used as an optimization assessment index and automatically computed for 12 different electrode positions with different AV and VV intervals. Their results showed the importance of individually adjusting the electrode position, beside the timing delays, to the patient's anatomy and pathology in accordance with current clinical studies. Mohindra et al. recorded 120-electrode body-surface potential mapping (BSPM) data and calculated the epicardial potentials and isochrones of activation for different V-V intervals by means of an electrocardiographic inverse solution based on a ventricular computer model [Many scientists have concentrated on the study of individual optimization of lead position and pacing delays of CRT by means of heart modeling and simulation with the progress of mathematical modeling techniques. The electrical-based optimization approach, for example, minimizing the QRS duration, has been widely accepted due to its simplicity. Therefore, most of researches have concentrated on the electrical strategies of optimizing parameters in CRT. Reumann et al. simulated an atrio-ventricular (AV) and a left bundle branch block (LBBB) with different reductions in the interventricular conduction velocity based on computer models of the Visible Man and a patient's heart . They aser model . They user model , the simer model . Thus, wERMS) optimization strategy for CRT. The present study resolves this question through the simulation of the cardiac electrical activation spread and the mechanical strain maps based on our previous electromechanical canine model of HF combined with a complete LBBB (CLBBB) [Compared with previous electrophysiological models for CRT optimization, the present heart model in this paper is extended to include a mechanical contraction model for the optimization of the pacing lead locations and the interventricular delays (VVds) of CRT. Since the spatial distribution of local wall mechanics was very sensitive to the choice of myofiber orientations, specific data of real fiber orientations were used for true description of cardiac deformation in this study. The ventricular mechanical dyssynchrony is evaluated by the assessment of a circumferential uniformity ratio estimate (CURE) , 19. The (CLBBB) . The anatomical canine heart model used in this study was reconstructed from the MR scans of an intact dog heart derived at the Duke University Medical Center for In Vivo Microscopy, Durham, NC, USA Figures . The spaμA/cm2 and duration of 0.5 ms was added to the right bundle branch while blocking the conduction of the left bundle branch, leaving the rest of the conduction tree intact. Latest depolarization time in LBBB simulations occurred at 108 ms , , 7), we s before .Mechanical dyssynchrony is a potential indicator for predicting responses to CRT. For example, novel echocardiographic image speckle tracking applied to routine midventricular short-axis images can quantify dyssynchrony by calculating the radial strain from the multiple circumferential points averaged to several standard segments and thus predict the response to CRT . DyssyncAccording to the report , short-aεcc over the entire LV-midwall (y-axis) at 30 circumferentially-distributed locations around each short-axis section (x-axis), and plot εcc versus spatial position for each time-frame. The more oscillatory the plot, the greater was the dyssynchrony among the segments around the short axis. To explain this, we can plot circumferential strain versus spatial location of the segment as Compute circumferential strain A02 and A12 are the spatial and temporal sums of the zero- and first-order power terms, respectively. The ratio of mean to “mean plus first-order power” provides the CURE index, and the maximal value for CURE is 1 with all segments contracting synchronously; whereas symmetrically dyssynchronous contractions produce a CURE = 0 [Plots for the four mid-wall short-axis slices are then subjected to Fourier analysis with a function of fft in Matlab7.0.1, and the results are averaged over space and time to yieldCURE = 0 , 26, 27.A further description of calculating zero and first-order power terms of layer 6 to 9 around equator sites at a given time was given in Compute the CURE for each electrode pair and each VVD and choose maximum CURE as optimal result of CRT. Because the left ventricular dyssynchrony is an important determinant of CRT response, the CURE calculated from LV and septum is chosen alternatively as the criterion for predicting the response to CRT in the simulation.The optimization method was then applied to the electromechanical canine heart model of LBBB. The optimization parameter of the CURE was sequentially calculated for each combination of the pacing location and VVD. The optimal result of CRT can be determined by the combination that provided the maximum CURE. ERMS can be found in many published reports. Briefly, it is assumed that the optimal cardiac output is to be achieved through the sinus rhythm and the normal electrophysiological parameters [ERMS between the physiological excitation during the sinus rhythm and pathological excitation as below:N is the whole number of voxel elements, xi dedicates the activation time of voxel i under the sinus rhythm, and ei is the activation time of voxel i under the pathological condition. Thus, by minimizing the ERMS, the activation of the heart will be as close as possible to the healthy activation and will provide an optimal combination of the pacing site and timing delay in CRT. The description of the electrical optimization strategy with rameters . TherefoERMS) optimization strategy for CRT, two objective function are defined as below.In order to make a contrast analysis of cardiac function improvement between mechanical (CURE) and electrical , can help determine the cardiac hemodynamics effect. LVEF is defined asIn this study, BiVP was chosen for CRT simulations. In clinic, doctors often choose the branches of coronary sinus as the LV pacing lead site as shown in ERMS through adjustment of the pacing location and VVD.Generally, the activation of the sinus node serves as the reference time for the AV delay. Several studies have pointed out that the VVD should be optimized according to the changes in the AV delay to obtain the maximum hemodynamic benefit . HoweverSimulation of the cardiac excitation anisotropic propagation throughout the ventricular myocardium is computationally very expensive. Thus, high-performance computing techniques should be used. By using an operator-splitting scheme, adaptive time step, and backward differentiation formulation techniques in a parallel implement, we solved the monodomain equations of the cardiac excitation anisotropic propagation successfully . For a cThe maximal value of CURE was 0.8516, with pacing site at point LAT-E and a VVD of 60 ms see , which cERMS of 37.26 ms. The optimal stimulation site was also at point LAT-E, but with a VVD of 0 ms. With the electrical optimization strategy, an optimal pacing location and VVD were also found with a minimal error To find the potential relationship between CURE and VVD, a diagram of the CURE-VV delay time column map was plotted in Furthermore, CURE values of LV pacing sites near ventricular equator sites were all larger than those at base for VVD ≥ 12 ms. However, the CURE of LV pacing location near the lateral wall at equator site, that is, pacing location LAT-E, was always the largest. It can also be found that the CURE values were smaller when the pacing lead was at the anterior wall near base, that is, pacing location ANT-B and ANT-E. ERMS  was plotted as the optimal result of CRT from the electrical index , we have adopted the mechanical optimization strategy CURE as the synchrony assessment index in the research. As we know, the main function of heart is to pump blood and exchange the metabolites. Therefore, the mechanical function of heart and the cardiac hemodynamics were the most basic characteristics and essential criteria for evaluating the cardiac function.The clinical findings of CRT have demonstrated that the adjustment of pacing lead position and VVD were very important for an individual to get the best improvement in hemodynamics . HoweverThe implantation location of LV pacing lead was proven to be very important for the improvement of the ventricular systolic synchrony . From FiHowever, with the increasing of VVD, especially for VVD ≥ 48 ms, CURE varied little and the same thing happened when VVD ≤ −48 ms. For VVD ≥ 48 ms, LV was the first ventricle to be paced. However, when RV was paced, the intrinsic excitation or excitation from LV pacing lead had spread to the RV beforehand. Due to the influence of refractory period, the pacing lead of RV (point RVA) would not play a role. Therefore, CURE values make no variations when VVD was larger than a certain value.From ERMS) strategy, Maximum Strain-Time curves were plotted in ERMS) had a worse synchrony  for the optimal parameters of CRT. It also confirmed the fact that the CURE could better reflect the LV synchrony and hemodynamic result, although biventricles may not obtain the best electrical synchrony [ERMS as optimization strategy for CRT. The thickening of the cardiac walls also improved after CRT with the peak maximum principle strain (PMPS) increased from 0.70 in the LBBB model to 0.77 in CRT optimization model based on the CURE strategy as shown in ERMS strategy was larger, with a value of 0.98 as shown in To further observe the enhancement of LV synchronization after CRT optimization and to contrast the optimal result between mechanical (CURE) and electrical  to optimize the parameters of CRT, the problem could be solved. Alternatively, an improved mechanical coordination and function may be inducible in the LBBB-CHF hearts without generating electrical synchrony. The difference of optimal delays and pacing sites was due to the difference of heart geometry, electrical and mechanical properties, and also the time regional differences in the time between electrical excitation and mechanical contraction at one part of the model versus another part. Therefore, clinicians would not always choose the lateral wall for the pacing locations. With the help of a patient-specific computation heart model, quantitative information will be obtained to enhance our understanding of cardiac dyssynchrony and decrease the blindness of CRT. dPmax/dt ) that were usually used as the optimal parameters of CRT in clinic [In this study, however, there are still some defects in our optimization model of CRT. Because of the lack of the atria data, the construction of a whole heart model was not feasible and consequently, the adjustment of the AV delay has not been considered. Furthermore, the hemodynamics parameters should be taken into account in future modeling, such as the cardiac output and the n clinic , 36. In ERMS. We also demonstrated that the mechanical dyssynchrony measure was able to predicts well the effect of CRT, better than the electrical dyssynchrony measure.By using a coupled biventricular electromechanical models of the canine heart, the optimization of the electrode positions and VV delay timings for CRT with the BiVP have been investigated,  with both the mechanical criterion of CURE and electrical criterion of  In comparison with other computational optimization models of CRT, the mechanical contraction and deformation was included in our model, and the mechanical index CURE was calculated. The results indicated that the LV pacing lead positioning was a very important factor that affecting the consequence of CRT and the hemodynamic changes. Also, the changes of VVD will lead to a variation in the mechanical synchrony and should be considered in the optimization of CRT. Therefore, it was very important for an individual to adjust the electrode position as well as the timing delays to the patient's anatomy and pathology, in accordance with current clinical studies , 37, 38.


Tandem repeats are multiple duplications of substrings in the DNA that occur contiguously, or at a short distance, and may involve some mutations . Tandem repeats have been extensively studied also for their association with the class of repeat expansion diseases (mostly affecting the nervous system). Comparative studies on the output of different tools for finding tandem repeats highlighted significant differences among the sets of detected tandem repeats, while many authors pointed up how critical it is the right choice of parameters.TReaDS - Tandem Repeats Discovery Service, a tandem repeat meta search engine. TReaDS forwards user requests to several state of the art tools for finding tandem repeats and merges their outcome into a single report, providing a global, synthetic, and comparative view of the results. In particular, TReaDS allows the user to (i) simultaneously run different algorithms on the same data set, (ii) choose for each algorithm a different setting of parameters, and (iii) obtain a report that can be downloaded for further, off-line, investigations. We used TReaDS to investigate sequences associated with repeat expansion diseases.In this paper we present TReaDS we discover that, for 27 repeat expansion diseases out of a currently known set of 29, long fuzzy tandem repeats are covering the expansion loci. Tests with control sets confirm the specificity of this association. This finding suggests that long fuzzy tandem repeats can be a new class of cis-acting elements involved in the mechanisms leading to the expansion instability.By using the tool We strongly believe that biologists can be interested in a tool that, not only gives them the possibility of using multiple search algorithm at the same time, with the same effort exerted in using just one of the systems, but also simplifies the burden of comparing and merging the results, thus expanding our capabilities in detecting important phenomena related to tandem repeats. However, cases of repeating units with 4, 5 and 12 nucleotides have been discovered thus we talk more generally of repeat expansion diseases. Recent surveys devoted to DNA repeats [At present 29 diseases are classified as ses (RE) -3, and t repeats .The locus of expansion can be located in various regions of the resident gene: in the coding sequences, in the 5'- untranslated region (5'-UTR), in the 3'- untranslated region (3'-UTR), in introns and in promoter regions. Two main questions are related to the study of these diseases from a genetic point of view: (a) which mechanisms or conditions lead to the repeat expansion? and (b) how do repeat expansions result in diseases?long fuzzy tandem repeats as a novel cis-regulating element for repeat expansion, thus contributing to investigating question (a).Only a small fraction of all the tandem repeats found in the human genome expand and result in a disease. Thus researchers have tried to identify which unusual structural features favor such expansion, and found a propensity to forming hairpins  as a key mechanism leading to expansion. Several studies also tried to identify cis-regulating elements that do favor the onset of the above structural features and of the expansion. Our study falls in this category and proposes Several papers tackle the problem of determining cis-acting factors associated with loci of TNR instability. In particular one quite studied factor is the proximity and orientation of DNA replication initiation regions (IR) w.r.t. the TNR instability locus ,9. In 88 the posFuzzy tandem repeats (FTRs) have been recently proposed as a new genomic feature worth of study ,14. InfoSaccaromyces cerevisiae [Escherichia Coli [Analysis of TNR instability has been conducted also in other model species, e.g. revisiae  and Eschhia Coli .in vitro, usually involving a relatively short repeating sequence (a trinucleotide unit repeated 16 or 17 times) and a promoter sequence. In these experiments the role of the native flanking regions is factored out or in some cases different (non-native) flanking sequences are used. Evidence of hairpin formation with the natural flanking sequence for SCA3, SCA6 and Dentatorubropallidoluysian atrophy (DRPLA) is reported in [In several cases it has been noticed that the TNR RNA coding sequences tend to form hairpin structures -19 or RNorted in . Notice For the subfamily of nine polyQ repeat diseases the corresponding polyglutammine peptide has been studied in some detail ,23. SuchA second class of repeat expansion diseases involve repetitions of the imperfect GCN triplets that encode the Alanine amino acid. Such REs are characterized by relative low copy numbers . In addition the expanded polyA repeats are stable both in the somatic and intergenerational transmission, unlike polyQ repeat expansions. A list of such diseases is reported in table Non-polyQ and non-polyA expanding repeats may have motifs of length 3,4,5, and 12. They may be located in several sections of the gene sequence. A list of such diseases is reported in table In  we noticThe present research originated from the hypothesis that this fact (a long fuzzy TR covering the unstable locus) could be observed in a large number of trinucleotide repeat disorders. Consequently, FTR could be exposed as a novel cis-regulatory element not yet studied in literature.TReaDS in order to quickly collect and organize the output of several TR finding algorithms into a single easy to read report in support to this hypothesis.We employ the tool Tandem repeats (TRs) of different forms  have been studied extensively because of their role in several biological processes. In fact, TRs are privileged targets in activities such as fingerprinting or tracing the evolution of populations ,25; seveThe scope and depth of the research on TRs have been boosted by the availability of efficient non-trivial algorithms for finding TRs, even when mutations occur with non-negligible probability. Tandem Repeat Finder (TRF) , CRISPRFComparative studies ,35, for TReaDS - Tandem Repeats Discovery Service, a TRs meta search engine that forwards the user requests to different tandem repeat finding services and aggregates the results. More in detail, TReaDS allows the user to (i) simultaneously run different algorithms on the same data set, (ii) choose manually, for each algorithm, a different parameter settings, or express her/his request in a simple and concise way , delegating to TReaDS the burden of choosing the right choice of parameters for all the systems, and (iii) get back a report that can be downloaded for further, off-line, investigations.In this paper we present TReaDS is currently interfaced with five services based on different algorithmic principles and techniques, thus a joint use of them is likely to lead to increased precision. In order to improve the quality of service TReaDS offers to its users, we plan to add to TReaDS other existing systems and new ones at the time they become available.TReaDS is a web application, and it has been completely developed by using Java-based technologies. In particular, a pool of Servlets takes care of handling the users' request , and collects the results generated by the systems involved in the query. TReaDS merges the results received from the external services and produces the final report with the support of the JasperReports publicly available libraries [ibraries  On the cTReaDS has the proper structure of a meta search engine, with options for changing the set of parameters of each algorithm, and for choosing the output format. The publicly available web tools for finding tandem repeats currently supported by TReaDS are: ATRHunter [TReaDS is interfaced with the version of these tools available on-line. Note that a binary version of these systems can be also downloaded and, in some cases, there are some small differences between the web-based and the downloadable versions, especially in terms of the number of parameters that can be customized. Furthermore TReaDS supports TRStalker [TRHunter  mreps [3TRHunter  TandemSWTRHunter  and TRF TRHunter . TReaDS RStalker , an algoTReaDS is essentially composed of four sections: (1) Algorithms, (2) Parameter Settings, (3) Report, and (4) Sequence  the simple mode, where it is possible to specify the kind of TRs to look for, by setting the minimum and maximum motif length, the minimum exponent (i.e. the number of repetitions), and the maximum percentages of allowed substitutions and in/dels (insertions and deletions); (ii) the advanced mode, where the user can run each system with manually selected parameters, if she wants a fine-grained control over the settings.In the Report section the user:In the 1. decides if she wants in the final report a graphical visualization of the found TRs;2. chooses if the input sequence (or a part of it) must be included into the final report;flanking sequence; and3. sets the length of the 4. chooses the final report format among the available ones: HTML, Excel, PDF, and RTF.Sequence section it is possible to submit a sequence as a file, or to paste it in a given text area; furthermore the user can chose if the whole sequence or just a part of it must be analyzed. TReaDS takes as input either a FASTA or plain text genomic sequence. The size limit for an input sequence corresponds to the present limit of ATRHunter: 2Mbp.In the The user can decide to wait on-line for the result or to receive them via email by providing a valid email address.TReaDS merges the results and produces a report containing the following sub-reports:Once the responses coming from the TR finding services have been received, Sequence sub-report. The sequence sub-report contains the sequence, if requested, and some information such as length and distribution of the different bases , and the response time. It is also provided a chart that shows a comparison of the systems (the comparison is simply based on the number of TRs found) , starting and ending positions of the covered segment, list of TRs that form the cluster, and some details for each TR . If the user has chosen to include the images in the final report, it is also possible to view each cluster in a graphical form , while minimizing the measure of the union of fuzzy TRs of the same type in that sequence.First, we run In most cases a single covering FTR has been found. In one case (SCA10) two partially overlapping FTRs cover the expansion locus. The FTRs found have copy number roughly between 2 and 3 in most cases. In principle, a FTR containing an EL may arise from a large self-overlapping of the EL segment in the FTR. Thus we need to show that such self-overlapping does not influence our data. Simple consideration based on the ratio of the lengths of the FTR and EL segments imply that no self-overlapping can occur when the ratio is greater or equal to 2. For a ratio 1.8 at most the overlap can be of the order of 10% of the length of the EL.We also measure the total length of the regions of the sequence covered by FTR of the same type  as the one identified as covering the expansion locus. The ratio of this length and the length of the sequence gives a conservative estimate to the probability that a randomly chosen position in the sequence is covered by a FTR of the type considered. The value of such probability is quite small for almost all of the sequences, resulting in an average probability over all the sequences associated to repeat expansion diseases of 0.12.The list of the major diseases due to repeat expansion are taken from ,3.An important subfamily is composed of polyglutammine diseases (polyQ) since the repeated triplet motif is the codon CAG, in a coding region, that encodes the glutamine (Q) amino acid . We have chosen this subclass since it has been extensively studied in literature. The statistics for this type of repeats have been collected in  listing Four sequences have been investigated in literature for their potential role in diseases table .Polymorphism of the the CAG repeat in protein RAI1 has been found to influence the onset age in patient affected by the spinocerebellar ataxia type 2 (SCA2) . Data shFor the remaining 13 sequences table  we have TReaDS. Results reported in table In this section we explore the issue of the specificity of FTR covering mutation loci linked to pathological conditions. We explore two different types of mutations, the first one is due to single nucleotide substitutions (SNP). The data base dbSNP (Human Build 135) ,48 listsTReaDS. Data in table The data base dbSNP (Human Build 135) lists, as of today, 391 records of pathogenic short in/dels for sequences of Homo Sapiens. We have selected a sample of such sequences  there is a long fuzzy TR covering the expansion locus. The ratio of the length of the fuzzy TR to the expansion locus ranges from a minimum of 1.608 and a maximum of 15.194. Also the specificity of the association has been investigated for the set of genes with CAG-encoded polyglutammine tracts, for pathogenic SNPs, for pathogenic in/dels, and for the non-pathogenic sections of the sequences. This specificity analysis shows that in just about 15% of the control cases there is an association to fuzzy TRs. These preliminary results indicate that fuzzy TRs may be an important novel cis-element that influences the instability of the expansion locus. However, a more in depth analysis and consideration of causal mechanisms involved is needed to confirm the correlation between fuzzy TRs and RE diseases.TReaDS, a web application which provides a single user interface and enables a simultaneous application of different techniques on the same data set. With TReaDS the user can express the characteristics of her request through a simple and unified interface, or she can customize the set of parameters of each system. The user gets back a report that contains a global and comparative view of the results. The report can be downloaded for a deeper off-line investigation. This way, TReaDS allows to harness the power of different web-based TR search engines with a minimal effort.As large scale studies are being pursued, it is important to facilitate the use of the TR search engines publicly available. In the literature, the comparison of several TR finding tools highlighted significant differences among the sets of results. Other work made evident the importance of tuning the parameters of operation. In this paper we presented Furthermore, merging and comparing the outcome of different search tools on the same data can be useful for gaining higher confidence that all the relevant TRs in the data set have been found.TReaDS is the first meta search engine for tandem repeats and there is no similar and comparable system freely available.To the best of our knowledge TRbase [TReaDS, in order to suggest hypothesis on possible roles for fuzzy TRs in that context.The database TRbase  maintainTRbase ). For thIn this paper we studied those trinucleotide expansion (and repeat expansion) leading to the manifestation of diseases. However, polymorphic microsatellites and ministatellites are very common in the human genome , thus one could advance the hypothesis that FTR may have a facilitating role in such polymorphisms (independently from the manifestation of a pathology). Testing this far-reaching hypothesis which is our next objective, is far from trivial since comprehensive maps of polymorphic/monomorphics TRs for the human genome, (even restricted the coding regions) are just being produced ,51.DRPLA: Dentatorubropallidoluysian atrophy; EL: Expansion locus; FTR: Fuzzy tandem repeats; HD: Huntington disease; IR: Initiation region; polyA: polyalanine; polyQ: polyglutammine; RE: Repeat expansion; SCA: Spinocerebral ataxia; TFBS: Transcription factor binding site; TNR: Trinucleotide repeat; TR: Tandem repeat; TReaDS: Tandem repeats discovery service.The authors declare that they have no competing interests.Project name: TReaDS• Project home page: http://bioalgo.iit.cnr.it/treads• Operating system(s): Platform independent• Programming language: Java• Other requirements: JavaScripts Enabled (on the client side)• License: Lesser General Public License (LGPL)• Any restrictions to use by non-academics: None, TReaDS is a web application free and open to all users• TReaDS to repeat expansion sequences, performed experiments, drafted the final manuscript and exercised general supervision. All authors read and approved the final manuscript.AV conceived of the application tool, participated in its design and development, and helped to draft the manuscript. MER participated in the design and development of the application, performed the testing and debugging phases, performed experiments, and helped to draft the manuscript. MP conceived the application of TReaDS) applied to finding novel cis-acting factors in repeat expansion diseases - supplementary information --" contains NCBI codes of analyzed sequences and dbSNP codes for the analyzed SNPs and in/dels"Tandem repeats discovery service (.Click here for file


Up to five statistical monolayers were deposited on the surfaces by spreading DPPC solution. It was found that even on five statistical DPPC monolayers, the hysteresis of a given liquid depends on the kind of solid support. Also on the same solid support the contact angle hysteresis is different for each probe liquid used. The AFM images show that the heights of roughness of the DPPC films cannot be the primary cause of the observed hysteresis because the heights are too small to cause the observed hystereses. It is believed that the hysteresis is due to the liquid film present right behind the three-phase solid surface/liquid drop/gas (vapour) contact line and the presence of Derjaguin pressure. The value of contact angle hysteresis depends on both the solid surface and liquid properties as well as on intermolecular interactions between them.Advancing and receding contact angles of water, formamide and diiodomethane were measured on 1,2-dipalmitoyl- Although contact angle hysteresis phenomenon has been well known for several decades , its natAs is well known, practically on all real solid surfaces contact angle hysteresis is observed, and one may claim that all real surfaces possess some roughness and/or chemical imperfections of the surface structure on the molecular scale. The microscopic contact angle can vary across such surfaces, and the experimental macroscopic advancing and receding contact angles measured using a few microlitre droplet settled on the surface are averaged values of the microscopic angles. Various aspects concerning relations between microscopic and macroscopic contact angles, also in relation to contact angle hysteresis, were published by Decker et al. . Among oDifferent origins of hysteresis, which appears even on molecularly smooth solid surfaces, have been recently presented by Starov and Velarde . They cosn-glycero-3-phosphocholine (DPPC) layers deposited on three different solid supports, i.e. glass, mica and poly(methyl methacrylate) (PMMA). Up to five statistical monolayers were deposited on each solid surface. It seemed to us interesting to learn whether and how much the kind of solid support, covered with the same amount of DPPC monolayers, affected the contact angle and its hysteresis. Another question was whether on the same surface the amount of hysteresis was different depending on the liquid used. For the bare solid surfaces and surfaces with two statistical DPPC monolayers deposited the AFM images were recorded.Therefore, the purpose of this study was to investigate contact angle hysteresis of water, formamide and diiodomethane on phospholipid 1,2-dipalmitoyl-DPPC  was purchased from Sigma and used without further purification. The probe liquids employed for contact angle measurements were: water from Milli-Q Plus system , formamide  and diiodomethane .2 area for a DPPC molecule and the geometric surface of the solid plate. The consecutive layer was deposited on the previous one by depositing the same volume of the solution on the surface covered with dried DPPC layer(s). This procedure was repeated up to deposition of five monolayers. The details of the layers preparation by spreading from solution were described elsewhere , 1312, 12 on the two to five monolayer-thick layers  than apolar diiodomethane. The surface tension and its components of the probe liquids are different, as well as size of their molecules and the vapour pressure at room temperature. The hysteresis is larger on the DPPC layers deposited on the surfaces having strong polar interactions, i.e. glass and mica, than on weakly polar PMMA . For water and formamide, the hysteresis increases with the layer thickness increase, but for diiodomethane, it increases only on the layers deposited on PMMA and decreases on the layers deposited on glass and mica. Such behaviour clearly indicates that interrelation between solid support and liquid properties is decisive for the contact angle and its hysteresis on the same kind of layer, here DPPC. It is believed that in the studied systems, the contact angle hysteresis does not result from the surface (film) roughness, which is only a few nanometers high, but that it is due to the liquid film presence behind the drop (Derjaguin pressure) in the receded state of the droplet. Additional information can be obtained by calculation of the apparent surface free energy from the contact angle hysteresis, where both the advancing and receding contact angles are taken into account. Thus, the obtained results give better insight into liquid/solid surface interactions which depend both on the liquid and the surface properties.


The profile hidden Markov model (PHMM) is widely used to assign the protein sequences to their respective families. A major limitation of a PHMM is the assumption that given states the observations (amino acids) are independent. To overcome this limitation, the dependency between amino acids in a multiple sequence alignment (MSA) which is the representative of a PHMM can be appended to the PHMM. Due to the fact that with a MSA, the sequences of amino acids are biologically related, the one-by-one dependency between two amino acids can be considered. In other words, based on the MSA, the dependency between an amino acid and its corresponding amino acid located above can be combined with the PHMM. For this purpose, the new emission probability matrix which considers the one-by-one dependencies between amino acids is constructed. The parameters of a PHMM are of two types; transition and emission probabilities which are usually estimated using an EM algorithm called the Baum-Welch algorithm. We have generalized the Baum-Welch algorithm using similarity emission matrix constructed by integrating the new emission probability matrix with the common emission probability matrix. Then, the performance of similarity emission is discussed by applying it to the top twenty protein families in the Pfam database. We show that using the similarity emission in the Baum-Welch algorithm significantly outperforms the common Baum-Welch algorithm in the task of assigning protein sequences to protein families. Structure and function determination of newly discovered proteins, using the information contained in their amino acid sequences, is one of the most important problems in genomics The The The PHMM is specified as a triplet The Baum-Welch algorithm works by guessing initial parameter values, then estimating the likelihood of the observation under the current parameters. This likelihood then will be used to re-estimate the parameters iteratively until a local maximum is reached. The Baum-Welch algorithm finds Based on the MSA, one-by-one dependencies between corresponding amino acids of two current sequences that model the similarity between them can be appended to the PHMM. This approach in spirit is similar to the works proposed by Holmes But in our approach, the dependency between two current sequences based on the similarity between them can be appended to the PHMM. Based on the fact that with a MSA, the sequences are biologically related, we can use the MSA to find the areas of similarity between two current sequences. So, the MSA is used for consideration of the one-by-one dependency between observations. In other words, the dependency between corresponding amino acid located above the residue and the residue can be combined with the PHMM. Therefore the new parameters of PHMM called similarity emission (SE) probabilities are created and should be estimated.It should be noted that the similarity emission probabilities are estimated from the MSA and then combined with the common emission probabilities estimated from Baum-Welch algorithm to generalize the Baum-Welch algorithm. In other words, both aligned and unaligned sequences are used to generalize the Baum-Welch algorithm: aligned sequences for estimation of the similarity emission probabilities and unaligned sequences for estimation of the common emission and transition probabilities.In this paper, we first construct a PHMM. Then using a MSA, we model the similarity emission (SE) matrix for consideration of the similarity information and generalize the Baum-Welch algorithm. We finally compare the results of applying the similarity emission to the Baum-Welch algorithm with the results of the commonly used emission for sequence alignment. For this purpose we use real data from the top twenty protein families in the Pfam database The profile hidden Markov model (PHMM) is a useful method to determine distantly related proteins by sequence comparison Following Durbin The sequences appearing in the final multiple sequence alignment are written based on their similarity S: a set of lattice pointss: a lattice point, Emissions Hidden states Transition probabilities on the lattice: a matrix Emission probabilities on the lattice: a matrix Emission probabilities on the lattice based on the above position: a matrix Initial value: the probability of starting state at The likelihood of the parameters , we choose just ten samples. Therefore, each time we have selected 200 sequences. In total 2000 sequences are randomly removed. Then we estimate the transition matrix In this paper, due to computational challenges and round-off errors in estimating probabilities of  matrix  . The res