The emergence of novel respiratory pathogens can challenge the capacity of key health care resources, such as intensive care units, that are constrained to serve only specific geographical populations. An ability to predict the magnitude and timing of peak incidence at the scale of a single large population would help to accurately assess the value of interventions designed to reduce that peak. However, current disease-dynamic theory does not provide a clear understanding of the relationship between: epidemic trajectories at the scale of interest (e.g. city); population mobility; and higher resolution spatial effects . Here, we used a spatially-explicit stochastic meta-population model of arbitrary spatial resolution to determine the effect of resolution on model-derived epidemic trajectories. We simulated an influenza-like pathogen spreading across theoretical and actual population densities and varied our assumptions about mobility using Latin-Hypercube sampling. Even though, by design, cumulative attack rates were the same for all resolutions and mobilities, peak incidences were different. Clear thresholds existed for all tested populations, such that models with resolutions lower than the threshold substantially overestimated population-wide peak incidence. The effect of resolution was most important in populations which were of lower density and lower mobility. With the expectation of accurate spatial incidence datasets in the near future, our objective was to provide a framework for how to use these data correctly in a spatial meta-population model. Our results suggest that there is a fundamental spatial resolution for any pathogen-population pair. If underlying interactions between pathogens and spatially heterogeneous populations are represented at this resolution or higher, accurate predictions of peak incidence for city-scale epidemics are feasible. Fundamental spatial processes such as individuals' interactions and movement are not sufficiently well understood and yet they define the transmission of infectious diseases through populations. Spatial models of epidemics represent the region of interest (such as a city or country) as a collection of spatial units. To anticipate the magnitude and timing of peak incidence and to predict demand on health care resources in the region a clear understanding is needed of the relationship between the resolution of the representation (number and size of the pixels), the population interactions and the epidemic trajectories. We used a spatially explicit meta-population model of disease transmission to demonstrate that thresholds existed such that models with too low a resolution overestimated peak incidence, implying that ill-defined models may result in incorrect predictions. However, the results suggest that if population interactions are represented in sufficient detail, accurate estimates of peak demands on key health care resources are feasible. Novel respiratory pathogens continue to pose substantial public health challenges, not least because of the risk that large epidemics may overwhelm key health care resources such as vaccination stockpiles and intensive care facilities. Recent epidemics of concern include: SARS Spatially explicit transmission models are used frequently to increase understanding of the spread of epidemics caused by pathogens which transmit between individuals close in space. For example: influenza It is known that heterogeneity both in population density and typical mixing behaviour heavily influence disease spread. Both of these are defined according to the resolution of the population representation, where resolution defines the number and size of the pixels making up the “image” of the population within the model. A pixel is the smallest single component of an image. A high resolution representation will divide the region into many small pixels; a lower resolution uses fewer, larger pixels . The resThe concepts in our paper require precise definitions of the terms: scale, resolution and pixel. The literature using these three words is somewhat ambiguous with the terms resolution and scale sometimes used interchangeably. Therefore, for clarity, we have included explicit definitions at first use of the words (above) and in We implemented a generic metapopulation model with arbitrary spatial resolution see  varying  upwards . We genel region , simulatThe within-pixel contact rate was fixed for all pixels. Mobility between pixels was represented by a kernel with an offset power function. A kernel defines the relative probability of travelling between two pixels. The offset power function is an adaptation of the gravity model. The gravity model states that an individual's probability of mixing in a pixel different to their home pixel is inversely proportional to the distance apart of the pixels, to some power. The offset power function adds in an offset distance parameter, which means that pixels closer together than this distance mix fully. See Initially we considered three different kernels: we used an offset of 2 km and three different powers giving low, medium and high contact between pixels  for our model was independent of the mobility kernel and the model resolution . This waFor the theoretical population density, the existence of a fundamental spatial resolution was apparent: at resolutions lower than this threshold, system-wide peak incidence was substantially over-estimated, obtaining a high peak incidence and fast spread similar to that obtained in a fully mixed model (the lowest resolution). However, at the fundamental resolution and above, consistent estimates of the peak attack rate were obtained . This waIncreased mobility reduced the effect of resolution on the epidemic trajectory. At medium mobility, peak incidence increased with decreasing resolution but there was no distinct threshold. At the highest mobility, peak incidence was unaffected by resolution: the high level of contact between pixels facilitated the quick spread of the epidemic, indicated by a short epidemic duration and a high peak incidence at every resolution .2 (30″ by 30″) in size. The effect of resolution was most evident when mobility was more restricted, as with the theoretical population. In Guangzhou, Rio and New York, changing the spatial resolution had a significant effect on the peak incidence when mobility was at a low to medium level, though the effect was less clear in Delhi  for four regions selected from LandScan data in Delhi . The Delin Delhi . TherefoWe used Latin Hypercube Sampling (LHS) Recently it has been suggested that the movement of individuals depends not only on the source and destination cities, but also on the population density of the surrounding area When managing epidemics it is desirable to know the size and duration of the epidemic and the magnitude and timing of the peak incidence over the spatial scale of interest We have shown how the representation of population interactions can impact model estimates of key epidemic outcomes. We examined the effect of the resolution of the population density on the model predictions of epidemic spread over the scale of interest. We refer to resolution as defining the number and size of the individual pixels dividing the region; higher resolution representations use a higher number of smaller pixels. Our results imply that for plausible population densities and mobility patterns, fundamental resolutions exist for specific pathogens such that the detail of the population and their interactions must be represented faithfully if accurate epidemic trajectories are to be estimated.The impact of model resolution was clear in models of less mobile populations: our results indicate that at lower mobility, low resolution representations overestimated the peak incidence, obtaining a high peak incidence and fast spread similar to that obtained in a fully mixed model. However, sufficiently high resolution representations gave lower and later peak incidences because of the delaying effect of multiple small pixels. Indeed at low mobility, clear thresholds existed for the resolution of the theoretical population density, such that models with resolutions below the threshold over-estimated the system-wide peak incidence. Similar thresholds existed for real population densities: Guangzhou, Rio, New York and Delhi. Increased mobility reduced the effect of resolution on the epidemic.The kernels which were most affected by resolution were those which gave a lower mobility than that identified by commuting data . GeneralAlthough we have considered age effects implicitly by including lower mobility levels than are reported for commuting data , the expWe have chosen to represent the real biological process by a high resolution metapopulation model. Although we have not been able to push the model to resolutions higher than 1 km by 1 km, we suggest it is reasonable to assume, for the mobility kernels considered here, that the thresholds observed for peak incidence would not change substantially were we to approach the resolution of an individual-based model.The model used here was intended specifically to test only the changing resolution of the disease transmission process. By design we did not want to assume that transmissibility was intrinsically higher or lower in different parts of the population. In future work, we hope to calibrate this model structure using actual disease incidence data and (after a minor modification to the definition of the force of infection) test for the possibility that population density affects transmissibility.Although it is somewhat reassuring that estimates of peak incidence are biased upwards if resolution is too low, the epidemic duration is underestimated. In order to avoid the effects of incorrect model specification, where possible, spatial resolution should be treated in a similar manner to temporal resolution in fixed-time-step models: neither the doubling nor halving of spatial resolution should have a substantive effect on key model outputs.We defined a spatially explicit meta-population model as follows whereFigure S1A simple example to illustrate how the resolution of the population is changed by aggregating multiple smaller units into larger units. The raster package in R is used to manipulate the population data. A: The population at its finest spatial resolution, 36 squares total. B: Four (2×2) of the smallest units from the population in A are combined into one pixel. C: Nine (3×3) of the smallest units (from A) are combined to make one pixel. D: The whole region is considered as one pixel. Note that the populations of the aggregated units are summed to find the total number of individuals in the new pixels.(EPS)Click here for additional data file.Figure S2The kernel function,  against the distances, , for the three different mobilities that we consider in the main results. The kernel is an offset power law function, (EPS)Click here for additional data file.Figure S3Details of the regions used in the main analysis. Histograms of the population densities of the four regions: Guangzhou, Rio, Delhi and New York and unprojected spatial maps of the populations. The central point is marked by a red dot and the area where the epidemic was seeded is marked in orange.(EPS)Click here for additional data file.Figure S4The kernels for the 50 parameter sets used in the Latin Hypercube Analysis of the model. The kernel is an offset power law function defined in the main text. The parameter sets vary (EPS)Click here for additional data file.Figure S5The impact of resolution on peak incidence for a range of parameter sets chosen by Latin Hypercube Sampling. The results are for four regions: Guangzhou, Rio, Delhi and New York. SLU are the Smallest Landscan Units (30″ by 30″ or approximately (EPS)Click here for additional data file.Movie S1The spatial spread of the epidemic in a theoretical population for the three mobility scenarios considered in the main text. From top to bottom is most restrictive ((PDF)Click here for additional data file.Supporting Information S1The spatial resolution of epidemic peaks.Text S1: Simplification of the next generation matrix. Text S2: Final epidemic size.(PDF)Click here for additional data file.Table S1A review of current data and studies on mobility patterns in humans. There is a lack of empirical data detailing why people travel, mode and distance travelled, divided by age and gender.(PDF)Click here for additional data file.Table S2Details of the 4 regions used in the main paper. All regions are 49×29 cells in size , area varies according to latitude and longitude. Rio has a large number of zero regions because it is on the coast. Delhi has the highest population density but also the highest variance in population sizes. The map in (PDF)Click here for additional data file.


Understanding the mechanisms of gene transcriptional regulation through analysis of high-throughput postgenomic data is one of the central problems of computational systems biology. Various approaches have been proposed, but most of them fail to address at least one of the following objectives: (1) allow for the fact that transcription factors are potentially subject to posttranscriptional regulation; (2) allow for the fact that transcription factors cooperate as a functional complex in regulating gene expression, and (3) provide a model and a learning algorithm with manageable computational complexity. The objective of the present study is to propose and test a method that addresses these three issues. The model we employ is a mixture of factor analyzers, in which the latent variables correspond to different transcription factors, grouped into complexes or modules. We pursue inference in a Bayesian framework, using the Variational Bayesian Expectation Maximization (VBEM) algorithm for approximate inference of the posterior distributions of the model parameters, and estimation of a lower bound on the marginal likelihood for model selection. We have evaluated the performance of the proposed method on three criteria: activity profile reconstruction, gene clustering, and network inference. Transcriptional gene regulation is a complex process that utilizes a network of interactions. This process is primarily controlled by diverse regulatory proteins called transcription factors (TFs), which bind to specific DNA sequences and thereby repress or initiate gene expression. Transcriptional regulatory networks control the expression levels of thousands of genes as part of diverse biological processes such as the cell cycle, embryogenesis, host-pathogen interactions, and circadian rhythms. Determining accurate models for TF-genes regulatory interactions is thus an important challenge of computational systems biology. Most recent studies of transcriptional regulation can be placed broadly in one of three categories.Approaches in the first class attempt to build quantitative models to associate gene expression levels, as typically obtained from microarray experiments, with putative binding motifs on the gene promoter sequences. Bussemaker et al.  and ConlA shortcoming of the methods in the first class is that the activities of the TFs are not included in the model. This limitation is addressed by models in the second class, which predict gene expression levels from both binding motifs on promoter sequences and the expression levels of putative regulators. Middendorf et al. , 7 approactivities, that is the concentration of the TF subpopulation capable of DNA binding. The methods in the second class approximate the activities of TFs by their gene expression levels. However, TFs are frequently subject to post-translational modifications, which may affect their DNA binding capability. Consequently, gene expression levels of TFs contain only limited information about their actual activities. The methods in the third class address this shortcoming by treating TFs as latent or hidden components. The regulatory system is modelled as a bipartite network, as shown in Figure Transcriptional regulation is influenced by TF Contrary to the methods in the first two classes, the methods in the third class do not incorporate interaction effects between TFs, though. This is a major limitation, since especially in higher eukaryotes transcription factors cooperate as a functional complex in regulating gene expression , 21. Boudata. This appears methodologically more consistent than the approach in Sanguinetti et al. [prior knowledge. Our paper is organized as follows. In Section 2 we review Bayesian factor analysis applied to modelling transcriptional regulation. In Section 3 we discuss how TF complexes and interaction effects among TFs can be modelled with a mixture of factor analyzers. The data used for the evaluation of the method are described in Section 4. Section 5 provides three types of results related to the reconstruction of the unknown TF activity profiles are discussed in Section 5.1, gene clustering is discussed in Section 5.2, and the reconstruction of the transcriptional regulatory network is discussed in Section 5.3. We conclude our paper in Section 6 with a summary and a brief outlook on future work.In the present paper we aim to combine the advantages of the methods in the three classes summarized above. Like the approaches in the third class, our method is a latent variable model that allows for the fact that owing to post-translational modifications the true TF activities are unknown. Similar to the approaches of the first two classes, our model explicitly incorporates interactions among TFs. Inspired by Boulesteix and Strimmer , we aim i et al.  and Sabai et al. , where TIn this section, we will briefly review the application of Bayesian factor analysis to transcriptional regulation. To keep the notation simple, we use the same letter Given the expression levels of where d Hinton . Note th Nielsen ) that  and (A.25) The likelihood of the data One can then, in principle, estimate the parameters d Hinton  and Nield Hinton . HoweverWernisch  deal wit Nielsen , Ghahram Nielsen  and Beal Nielsen , is a seand a conjugate prior on the hyperparameters i et al.  and Sabai et al. , based oi et al. . The modwhere The prior probability on the matrix of auxiliary variables where the values of The objective of Bayesian inference is to learn the posterior distribution of the model parameters and latent variables. Since this distribution does not have a closed form, approximate procedures have to be adopted. Sabatti and James  follow ai et al.  follow aThe Bayesian FA models discussed in the previous section aim to explain changes in gene expression levels from the activities of TFs, modelled as the hidden factors or latent variables omplexes , and thaomplexes . We usedomplexes  and Bealomplexes . Each coomplexes , with thwhere As discussed in Section 2, (10) offers a way to relax the linearity constraint of FA by means of tiling the data manifold. One approach would be for in which For (3) we now get: which completes the definition of (10). Recall that in (A.3), the loading matrix nd James , is affeIn practice, gene expression and TF binding profiles will usually be differently distributed. The former tend to be approximately log-normally distributed, while for the latter we tend to get r et al. ). -valueand the hyperparameters: where Here is an alternative interpretation of our model, which is based on the assumption that a variation of gene expression is brought about by different TFs binding in different proportions to the promoter. In the ideal case, genes with the same TFs binding in identical proportions to the promoter should have identical gene expression profiles; this is expressed in our model by To complete the specification of the model, we need to define prior distributions for the various parameter groups. In the present paper we follow Beal  and impo in Beal  and treawith gamma distributions for the precision hyperparameters A Gaussian prior with mean where The objective of Bayesian inference is to estimate the posterior distribution of the parameters and the marginal posterior probability of the model . The two principled approaches to this end are MCMC and VBEM. A sampling-based approach based on MCMC has been proposed in Fokoué and Titterington . A VBEM ing Beal , we assuwhere  in Beal . A summaThe final issue to address is model selection, that is, selecting the number of mixture components ing Beal , we have in Beal . This sc in Beal . Via a b in Beal . Note tha et al. .Saccharomyces cerevisiae. Although S. cerevisiae has been widely used as a model organism in computational biology, we still lack any reliable gold standard for the underlying regulatory network, and therefore need to use alternative evaluation criteria, based on out-of-sample performance. We will describe the data sets in the present section, and discuss the evaluation criteria together with the results in Section 5.We tested the performance of the proposed method on both simulated and real gene expression and TF binding data. The first approach has the advantage that the regulatory network structure and the activities of the TF complexes are known, which allows us to assess the prediction performance of the model against a known gold standard. However, the data generation mechanism is an idealized simplification of real biological processes. We therefore also tested the model on gene expression data and TF binding profiles from We generated synthetic data to simulate both the processes of transcriptional regulation as well as noisy data acquisition. We started from the activities of the TF protein complexes that regulate the genes by binding to their promoters. Note that owing to post-translational modifications these activities are usually not amenable to microarray experiments and therefore remain hidden. The advantage of the synthetic data is that we can assess to what extent these activities can be reconstructed from the gene expression profiles of the regulated genes.gene expression profile we mean the vector of log gene expression ratios with respect to a control) Figure where ed from 2 are showHere we have assumed that each gene is regulated by a single TF complex. Note, however, that an individual TF can be involved in more than one TF module and therefore contribute to the regulation of different subsets of genes, as illustrated in Figure To group the TFs into modules when designing the synthetic TF binding set, we followed Guelzim et al.  and modeIn the real world, TF binding data—whether obtained from gene upstream sequences via a motif search or from immunoprecipitation experiments—are not free of errors, and we therefore modelled two noise scenarios for two different data formats. In the first TF binding set, the non-binding elements were sampled from the beta distribution Saccharomyces cerevisiae (baker's yeast). For the clustering experiments, we combined ChIP-chip binding data of 113 TFs from Lee et al. [S. cerevisiae, and is publicly available from http://www.yeastract.com/. Our combined data set thus included the expression levels of 5464 genes under 214 experimental conditions and binary TF binding patterns associating these genes with 169 TFs. For evaluating the inference of transcriptional regulation in real organisms, we chose gene expression and TF binding data from the widely used model organism e et al.  with twoe et al. , the expe et al. , the expe et al.  and the e et al. . YeastTrWe have evaluated the performance of the proposed method on three criteria: activity profile reconstruction, gene clustering, and network inference. The objective of the first criterion, discussed in Section 5.1, is to assess whether the activity profiles of the transcriptional regulatory modules can be reconstructed from the gene expression data. The second criterion, discussed in Section 5.2, tests whether the method can discover biologically meaningful groupings of genes. The third criterion, discussed in Section 5.3, addresses the question of whether the proposed scheme can make a useful contribution to computational systems biology, where one is interested in the reconstruction of regulatory networks from diverse sources of postgenomic data. We have compared the proposed MFA-VBEM approach with various alternative methods: the partial least squares approach proposed of Boulesteix and Strimmer , maximumg et al. . These rSince TF activity profiles are not available for real data, we used the synthetic data of Section 4.1 to evaluate the profile reconstruction performance of the model. We have compared the proposed MFA-VBEM model with the partial least-squares (PLS) approach of Boulesteix and Strimmer , and witThe PLS approach of Boulesteix and Strimmer  is formaStrimmer , using tThe BFA-Gibbs method of Sabatti and James  correspond James , using tnd James  to test nd James .For the proposed MFA-VBEM model, the activity profile of the Table A comparison between BFA-Gibbs and MFA-VBEM shows that BFA-Gibbs tends to outperform MFA-VBEM when the expression profiles are short (length L1) or when the noise level is high (N3). This could be a consequence of the different inference schemes ("VBEM" versus "Gibbs"). Short expression profiles and high noise levels lead to diffuse posterior distributions of the parameters. Variational learning—as opposed to Gibbs sampling—is known to lead to a systematic underestimation of the posterior variation , which cFollowing up on the seminal work of Eisen et al. , there hS. cerevisiae, described in Section 4.2. For comparison, we also applied two standard clustering algorithms: K-means and hierarchical agglomerative average linkage clustering . We usee et al.  as a morustering  in our chttp://www.yeastgenome.org/. We assessed the enrichment for annotated GO terms in a given gene cluster with the program Ontologizer [specific GO terms, as generic and non-biologically informative GO terms often tend to show a statistically significant enrichment. Following a recommendation made by one of the referees, we defined GO terms that were four or less levels from the roots of the hierarchy defined in the gene ontology  as generic, and discarded them from the subsequent analysis.In order to evaluate the predicted clusters with respect to their biological plausibility, we tested them for significant enrichment of gene ontology (GO) annotations. To this end, we used the GO terms from the Saccharomyces genome database (SGD), which are publicly available from ologizer , using tThe results are shown in Table Interestingly, COSA shows a particularly poor performance on the combined gene expression and TF binding data. This can be explained as follows. The TF binding profiles extracted from YeastTract  are binaIt is also interesting to observe that the inclusion of binding data occasionally deteriorates the performance of K-means and hierarchical agglomerative clustering. This deterioration is a consequence of the different nature of the TF binding and gene expression profiles. While the former are binary and hence nonnegative, the log gene expression ratios my vary in sign. This renders the approach of combining them in a monolithic block suboptimal, as coregulated genes may have anticorrelated expression profiles and positively correlated TF binding patterns. Avoiding this potential conflict by taking the modulus of the expression profiles is no solution, as the resulting information loss was found to lead to a deterioration of the clustering results. The proposed MFA-VBEM model, on the other hand, uses the extra flexibility that the model provides via the factor loading vector A topic of interest in computational systems biology is the reconstruction of transcriptional regulatory networks, and it is this question that most of the methods reviewed in the Introduction section ultimately aim to address. Note that in the current setting the regulatory network has the form of a bipartite graph between TFs and potentially regulated genes. The successful solution of the reconstruction task therefore requires us to infer for each TF the correct binding profile, that is, the set of genes that it potentially binds to and regulates. For the synthetic data of Section 4.1, this is a straightforward task as the true regulatory network is known. For real data, however, the true regulatory network is unknown, rendering the assessment more difficult. We approached this problem from two different angles: noise reduction and test-set performance. In the first assessment scheme, we trained  the different statistical models on noisy complete data—containing both gene expression profiles and TF binding affinities—and investigated whether the method succeeded in reducing the noise in the TF binding profiles, that is, whether it could predict a curated transcriptional regulatory network. In the second assessment scheme, the models were trained on 80% of the original data, and then evaluated on 20% of held-out test data, from which the binding profiles had been removed. We refer to these two network reconstructions tasks as network curation and network prediction, respectively. We compared the proposed MFA-VBEM scheme of Section 3 with the BFA Gibbs sampling approach of Sabatti and James  and withFor reconstructing the transcriptional regulatory network with MFA-VBEM, we estimated the vector where where We carried out maximum likelihood FA with the EM algorithm, using the software implementation of Ghahramani and Hinton , and a sThe network reconstruction with BFA-Gibbs was carried out as described in Sabatti and James . For theS. cerevisiae data when the number of nonzero entries in S. cerevisiae genes were not affected by this intervention, as the number of TF binding connections reported in Teixeira et al. [The practical application of BFA-Gibbs faces a computational hurdle. Within the Gibbs sampling procedure the vectors of binary latent variables (Wernisch ) are samnd James , which wa et al.  is well a et al.  were incFigures Interestingly, for the low noise in the TF binding data, from which the prior connectivity matrix a et al.  has founa et al. .A comparison of the original TF-binding data in Figure Table For the network curation task, 10% false-positive interactions were added to the TF binding data of Teixeira et al. . All thrBFA with Gibbs sampling recovered a very accurate but sparse connectivity matrix. Most of the predicted connections were correct according to the chosen criterion . HoweveS. cerevisiae genes, and used an independent test set containing a randomly chosen subset of 20% of the genes to estimate the out-of-sample network prediction accuracy. Note that for the genes in the test set, only the expression profiles were made available, while the corresponding TF binding connections were held back. The task was to predict these TF binding connections from the gene expression data, using the (average) TF activity profiles inferred from the training set. A more comprehensive description of the evaluation is provided in the appendix.For the network prediction task, we trained the models on only 80% of the The results are shown in the right panel of Figure S. cerevisiae genes, then sorted the TFs according to the numbers of connections between them and the selected genes. The most densely connected 12 TFs were chosen. Then all 5464 genes were sorted according to the numbers of their connections to the chosen TFs, and the most densely connected 2000 genes were chosen. These sorting steps were iterated until convergence. We thus obtained a 12 TFs by 2000 genes connectivity matrix with dense connections for evaluating the different network reconstruction methods. This procedure, and the reduction in the number of TFs, allowed the application of BFA-Gibbs with an uninformative prior connectivity matrix, and hence ensured a fair comparison with the proposed MFA-VBEM method.While the previous study has pointed to a performance improvement of MFA-VBEM over BFA-Gibbs, this improvement is a combination of two effects: the actual model performance, and the computational complexity. In order to focus on the first effect and distinguish it from the latter, we repeated the analysis on the same data in a slightly different manner. Recall that the proper evaluation of the out-of-sample network prediction accuracy according to (A.35) requires an uninformative prior connectivity matrix S. cerevisiae genes, and used an independent test set containing the remaining 60%, 40% or 20% of the genes to estimate the out-of-sample network prediction accuracy. As before, for the genes in the test set only the expression profiles were made available, while the corresponding TF binding connections were held back. The task was to predict these TF binding connections from the gene expression data, using the (average) TF activity profiles inferred from the training set. The results are shown in the subfigures of Figure For the network prediction task, we trained the models on randomly selected 40%, 60% or 80% of the Of particular interest is that among the 12 TFs of the yeast set, there is a well established TF complex (module) composed of TFs Ste12 and Tec1 . This TFThe measured TF-gene binding patterns of these two TFs show a modest correlation (correlation coefficient = 0.60). When MFA-VBEM is applied to the network reconstruction task by integrating gene expression profiles, the predicted binding patterns of the two TFs involved in the complex show an increased correlation (correlation coefficient = 0.74). However, the cooperation of TFs was not detected by the BFA or the FA methods. Here, the corresponding correlation coefficients between the TF binding patterns predicted with BFA and FA are low, 0.15 and 0.14, respectively. Hence, BFA and FA fail to identify this TF complex.We have investigated the application of Bayesian mixtures of factor analyzers (MFA-VBEM) to modelling transcriptional regulation in cells. Like recent approaches based on Bayesian factor analysis applied to the same problem , 17, MFAS. cerevisiae, MFA-VBEM found biologically more plausible gene clusters than K-means, hierarchical agglomerative average linkage clustering and COSA [S. cerevisiae and a synthetic simulation. The better performance over the Gibbs sampling approach of Sabatti and James [S. cerevisiae was partly a consequence of the computational complexity of the latter approach; this highlights the practical advantage of the proposed scheme in scaling up to complex postgenomic data sets.We have evaluated the proposed MFA-VBEM on three performance criteria: transcriptional activity profile reconstruction, gene clustering, and regulatory network inference. Using a synthetic data set, we found that MFA-VBEM reconstructed the hidden activity profiles of the TF complexes more accurately than PLS  and Bayeand COSA , as indind James  on S. ceWe have pursued a variational approach to Bayesian inferences, by which a lower bound on the marginal likelihood is obtained and used for model selection. This allows us to estimate the number ale-free , meaningale-free . This noale-free . The appThis section provides a concise review of variational inference. For a more comprehensive tutorial, we refer the reader to Bishop . ConsideIt is easy to show that which is the difference of the log marginal likelihood and the Kullback-Leibler divergence between the model distribution From information theory it is known that the Kullback-Leibler divergence, which is a measure of the difference between two distributions, is non-negative; see, for instance, Papoulis . This imTo apply the concept of variational learning to Bayesian FA, the model distribution is assumed to factorize into separate contributions from the parameters and latent variables: where where which has the closed form solution Again,  Nielsen  and Beal Nielsen . For dis Nielsen . In anal(i) variational E-step: given the distribution of the parameters (ii) variational M-step: given the distribution of the latent variables This procedure, called the Variational Bayesian Expectation Maximization (VBEM) algorithm, is repeated until a stationary point of We briefly describe the VBEM algorithm for the MFA model discussed in Section 3, which is derived from 22) by applying the variational calculus outlined in Section A.1. A complete derivation of the update equations can be found in Beal . We here2 by applin which where is a multivariate Gaussian distribution: in which with where The variational posterior for the hidden factor in which where The variational posterior distribution for the indicator variables Here, Recall from Section 3 and Figure Here, The hyperparameters where  in Beal . Note tha et al. . A MATLAa et al. .Network Reconstruction with The Proposed Mfa-Vbem SchemeMathematically, the TF binding profile predicted from the training data where The integral in (A.27) is analytically intractable. In an MCMC setting, it would be approximated by a sum over parameters, hyperparameters and latent variables sampled from a Markov chain. In the variational approach, the posterior distribution is approximated by where expressions for the variational distributions where For the out-of-sample network prediction, we want to compute the conditional expectation value of the binding profile from an expression profile where Having described how to approach the tasks of network curation and prediction with the proposed MFA-VBEM model, we will now briefly outline how to address these problems with the factor analysis models of Sabatti and James  and GhahNetwork Reconstruction with Maximum Likelihood Factor AnalysisRecall the definition of the FA model in (A.3) and (A.25). The EM approach proposed in Ghahramani and Hinton  consistsWernisch  and minirotation ; this prFor the practical application, we applied the EM algorithm as reported in Ghahramani and Hinton , using tgraphs.)  to assiga et al.  was miniNetwork Reconstruction with Bayesian Factor Analysis and Gibbs SamplingThe Bayesian factor analysis model of Sabatti and James  was discwhich is straightforwardly affected with the Gibbs sampling procedure described in Sabatti and James . Recall The practical application would require us to re-run the Gibbs sampling algorithm of Sabatti and James  on an auWhen expression profiles of new genes This approach corresponds to running the Gibbs sampling algorithm of Sabatti and James  with the


Cell proliferation is critical to the outgrowth of biological structures including the face and limbs. This cellular process has traditionally been studied via sequential histological sampling of these tissues. The length and tedium of traditional sampling is a major impediment to analyzing the large datasets required to accurately model cellular processes. Computerized cell localization and quantification is critical for high-throughput morphometric analysis of developing embryonic tissues. We have developed the Incremental Cell Search (ICS), a novel software tool that expedites the analysis of relationships between morphological outgrowth and cell proliferation in embryonic tissues. Based on an estimated average cell size and stain color, ICS rapidly indicates the approximate location and amount of cells in histological images of labeled embryonic tissue and provides estimates of cell counts in regions with saturated fluorescence and blurred cell boundaries. This capacity opens the door to high-throughput 3D and 4D quantitative analyses of developmental patterns. In many areas of biomedical research including clinical pathology, cell counts obtained from images are crucial data for diagnosing patients or for addressing hypotheses about developmental or pathological processes. Manual cell counting is challenging in that it typically requires a specialist such as a biologist or a pathologist to identify and characterize different cell types. Even then, manual cell counts are subjective. To date, several stereological tissue analysis methods have been developed with the aim of accurately estimating cell counts in a given tissue , 2. HoweRecent technological advances in microscopy now enable high-throughput imaging of thousands of cells in a short time –5. FurthA common challenge for computerized cell counting methods arises from the great variation in the morphology and size of cells , compounImages of developing embryonic tissue, which is of particular interest to developmental biologists, can be difficult to process using edge detection methods, particularly when the density of the cells in the tissue is high and blurring, or if the boundaries between cells disappear entirely. An example of this occurs in fluorescence microscopy, when excess saturation in the brightness signal seeps into a cell from adjacent cells labeled with fluorescent dye. The blue-saturated regions of the sample shown in An alternative approach to obtain cell count estimates that are not based on edge detection is texture analysis, where image segmentation is followed by cell quantification using a measure of the average cell size , 17. MalWe have developed software for cell identification and localization in images depicting the roughly spherical proliferating cells commonly present in embryonic tissue. sic) and an estimate of the minimum distance between the nuclei, a value set by default at half the width. From this information, ITCN provides total cell counts for an image or a region of interest and an output image that shows the cell locations.We have compared our software with the Image-Based Tool for Counting Nuclei (ITCN) , 15, a cOur cell identification algorithm is inspired by Mould's progressive stippling , a technMany graphics applications rely on the production of Poisson-Disk (PD) distributions , and stiTo find cells using ICS, the user indicates the color or grayscale intensity of the target cells (resp.), a margin of tolerance that defines the amount of acceptable variation with respect to the base color, and an average cell diameter. After user input is complete, ICS first runs the input image through color filtering . Color fTo help the user visualize the selected region resulting from the user-provided base color and margin of tolerance values, the user can run ICS's graphical interface to obtain a color-filtered version of the input image before execution of the whole algorithm. Alternatively, the user can run the freely available GNU Image Manipulation Program (GIMP) . GIMP's Regardless of whether ICS or GIMP is used to select the values of the base color and its margin of tolerance, the user does not need to compute the margin of tolerance that defines the amount of acceptable variation with respect to the base color for each color channel. ICS calculates whether the color of each pixel in the image falls within the user-provided margin of tolerance by computing the Euclidean distance between the base color's RGB triplet and each pixel's own RGB triplet. If (and only if) this distance is less than the margin of tolerance, the color is considered to be within the acceptable range of variation. After color filtering, and once the diffuse edge detection buffer has been obtained see , a searcThe initial seed is used as the starting point for an expansion operation performed using Dijkstra's shortest path search algorithm , 21 Fig. For illAn essential feature of Dijkstra's shortest-path search is that every edge in the graph has an associated cost that contributes to the total cost of a given path. In ICS, the cost for traveling from one node to the next  is the sum of the cost stored in the source node and the computed cost of the target node. Three elements contribute to the cost of a target node: the distance to the seed from the target, whether the color  of the underlying pixel matches the target cell color (within the user-provided range), and the intensity of the gradient at the location of the node.s, ysx) and the neighboring target pixel ,First, we calculate the base cost of a target node as the distance between the source pixel . DAPI stain makes nuclei appear as bright blue spots under UV light . ProlifeWe compared the counts obtained using ICS and ITCN , 15 agaiThe statistical validation aimed to quantify both measurement bias and measurement error for cell counts on the DAB (proliferating cells only) and DAPI  sections, as well as for cell proliferation. Cell proliferation is the ratio of DAB-positive cells to the total number of DAPI-stained cell nuclei. We assume the average manual count to be the gold standard for comparison. Since each individual counter made a separate count of each section, we average the values produced by these two individual counters to obtain the average manual count. Bias is then quantified as the average difference between the cell counts obtained using the computer-based methods and the average manual count. ANOVA was used to determine the statistical significance of bias. Measurement error is quantified as the variation between measurements of the cell counts of the two automated methods with respect to the average manual count. To quantify measurement error for the two methods, we obtained the coefficient of variation (CV) for the deviations from the average manual count for each method. We used the CV, which is defined as the ratio of the standard deviation to the mean, rather than the variance, since the CV is a normalized measure of variation which allows direct comparison of the three variables examined. Statistical comparisons of the variances about the mean deviations for each method were based on Levene's test, which is robust to deviations from normality . To asseThe performance of ICS for handling images at multiple resolutions was tested using the same dataset previously described. To produce copies of this set at multiple resolutions, the original set of images was digitally resized. Four additional sets of images were generated using this procedure, corresponding to magnifications 400x, 100x, 50x, and 12.5x each. The base value for the average cell diameter was 23 pixels, so the method was tested against the corresponding average cell diameter values of 34.4, 16.2, 11.5, and 5.75 pixels. The changes in the resolution of the additional sets correspond to a 100% increase (400x) and a decrease to 50%, 25%, and 6.25% of the surface covered by a cell from the original dataset. Unlike our method, in the case of ITCN, it was not possible to obtain consistent counts at multiple resolutions by only changing the value of the input cell diameter according to the resolution of the corresponding set. Instead, it was also necessary to adjust the threshold value for each set, so that the method could still detect the relevant cells. In this regard, ICS can be more generally applied than ITCN see . P < .001). ICS is less biased overall than ITCN. However, the reason for the lower correlations of cell proliferation (P = .286) and a marginally significant difference for DAPI (P = .045). feration  using ICThe counts provided by ICS and the average of the counts made by manual counters were highly correlated (0.88). Overall, ICS produces less biased counts of cells using both imaging techniques than ITCN with comparable measurement error. This result suggests that ICS is more accurate than ITCN for estimating cell counts overall. However, due to the fact that the smaller biases present for ICS work in opposite directions for the two image types, the accuracy of the cell proliferation estimate is lower for ICS than ITCN. The precision of the cell count and cell proliferation estimates is comparable for both automated methods and for manual counting. For samples such as the one shown in Whereas ITCN can only be used to analyze images that have been converted to 8-bit grayscale (thereby losing color information), ICS can be used to count cells that have been stained to show different coloration under the same source. This means that the user can take a single image of a sample and obtain two or more cell counts, one for each of the two stains if both are visible on the slide. Further, the current implementation of ICS, also done in Java, can be executed from a command-line interface. This makes it possible to process large batches of images in parallel, provided they have uniform color intensities. Finally, in addition to producing an output image highlighting the detected cells, ICS provides a list of the cell locations in a convenient text file format. This information is used in the creation of a 3D point cloud of cell locations obtained by accumulating the data from a stack of sequential tissue samples. This facilitates further analysis of cell proliferation data in a way that not only considers the amount of cells in a sample, but also the location of these cells within a 3D volume, which is essential for morphometric analysis. An inherent limitation of ICS is that it is appropriate for use only when the cells that are being analyzed can be characterized as having a certain average radius. Since cell types vary widely, the reader must double-check that this assumption can be made prior to using this method. ICS was tested for images produced at 200x magnification but has been designed to adapt to varying degrees of magnification. It is important to consider that when the intercellular distance is reduced to four pixels or less, which might happen at lower magnifications, the algorithm is bound to lose precision, as the traversal costs are computed on a per-pixel basis. To avoid this, we advise that the images given to ICS be taken at the highest resolution available in the microscope or scanner used. Since the color filter used by ICS is based on a user-provided color range, ICS depends on the application of a consistent illumination setting across samples. This can become a limitation if several samples are produced under inconsistent illumination settings or when illumination of the subject is inconsistent across the image. The images used in the study have some degree of variation in the intensity see , which aAs previously mentioned, an advantage of ICS is that it can be used to estimate cell counts in high-density regions of an input image where it is hard to assess the cell counts using standard edge detection-based algorithms. On the other hand, standard edge detection and segmentation-based algorithms  In addition, ICS can complement texture analysis methods for cell counting  by We have developed Incremental Cell Search (ICS), a novel cell identification and counting algorithm used for histomorphometric analysis of embryonic tissue samples. ICS distributes markers in regions of interest that represent cells based on progressive algorithms used in image sampling and nonphotorealistic rendering. The regions of interest are defined by the user, who specifies the color range that identifies potential cells in the tissue and the estimated average cell diameter. The algorithm also contributes to finding cell location markers in regions with saturated fluorescence, although this feature has not been extensively validated. ICS use is appropriate when the cells or nuclei being identified are similar in size and can be approximated using round regions, as is the case in our application. Our results show that quick and consistent estimates of cell counts can be done using ICS on a variety of input images matching these criteria. The authors declare that they have no conflict of interests.O. E. Meruvia-pastor, J. Soh, E. J. Schmidt, J. C. Boughner, M. Xiao, H. A. Jamniczky, B. Hallgrímsson and C. W. Sensen participated in the writing of the paper and in the design of the validation. E. J. Schmidt prepared the specimens for sampling, E. J. Schmidt and H. A. Jamniczky obtained the images, and E. J. Schmidt and J. C. Boughner performed the manual counts. O. E. Meruvia-Pastor wrote the method description and produced the counts using the automated software tools. B. Hallgrímsson and O. E. Meruvia-Pastor analyzed the results. B. Hallgrímsson and C. W. Sensen directed the research. The research was carried out at the University of Calgary, as well as most of the paper edition. All authors read and approved the final version of the paper.


Gyejibongnyeong-hwan (GJBNH) is one of the most popular Korean medicine formulas for menstrual pain of dysmenorrhea. The concept of blood stagnation in Korean medicine is considered the main factor of causing abdominal pain, or cramps, during menstrual periods. To treat the symptoms, GJBNH is used to fluidify the stagnated blood and induce the blood flow to be smooth, reducing pain as the result. The purpose of this trial is to identify the efficacy of GJBNH in dysmenorrhea caused by blood stagnation.rd, 4th and 5th menstrual cycles. From the screening (Visit 1) through the second follow-up (Visit 6) the entire process will take 25 weeks.This study is a multi-centre, randomised, double-blind, controlled trial with two parallel arms: the group taking GJBNH and the group taking placebo. 100 patients (women from age 18 to 35) will be enrolled to the trial. Through randomization 50 patients will be in experiment arm, and the other 50 patients will be in control arm. At the second visit (baseline), all participants who were already screened that they fulfil both the inclusion and the exclusion criteria will be randomised into two groups. Each group will take the intervention three times per day during two menstrual cycles. After the treatment for two cycles, each patient will be followed up during their 3This trial will provide evidence for the effectiveness of GJBNH in treating periodical pain due to dysmenorrhea that is caused by blood stagnation. The primary outcome between the two groups will be measured by changes in the Visual Analogue Score (VAS) of pain. The secondary outcome will be measured by the Blood Stagnation Scale, the Short-form McGill questionnaire and the COX menstrual symptom scale. Analysis of covariance (ANCOVA) and repeated measured ANOVA will be used to analyze the data analysis.ISRCTN30426947Current Controlled Trials:  Dysmenorrhea is a very common medical condition in women worldwide. The prevalence varies from 45% to 95% of all women depending on its definition . In KoreThe most prominent physiological cause of dysmenorrhea in allopathic medicine is the production of uterine prostaglandins. Endometrial cells release prostaglandins when they are deciduous. The released prostaglandins stimulate myometrial contractions and cause ischemia. This results in abdominal pain, which has been the source of difficulties that women have to cope with in their daily lives.But the explanation for the pain is different in Traditional Korean Medicine. In Traditional Korean Medicine, the causes of sicknesses are classified according to symptoms and signs. Traditional Korean Medical specialists diagnose the cause of the sickness by symptoms and signs and prescribe the appropriate remedy.qi and blood inside the both is smooth, the body is healthy without any diseases. But if the flow is interrupted, it causes pain. This can be applicable to qi and blood. Blood stagnation means obstructed blood flow, and a woman experiencing dysmenorrhea can be explained by blood stagnation in her body. The signs of blood stagnation are getting bruised easily, tender abdominal pain, etc.The most common factor causing dysmenorrhea in Traditional Korean Medicine is blood stagnation in the uterus. 'Flow' is a very important concept in Traditional Korean Medicine. If the flow of The first treatment of dysmenorrhea in allopathic medicine is an over-the-counter drug, especially non-steroidal anti-inflammatory drugs (NSAIDs) such as Ibuprofen, Naproxen, Mefenamic, etc. ,4. TheseGyejibongnyeong-hwan (GJBNH) is one of the most popular Korean medicine formulas for periodical pain due to dysmenorrhea. GJBNH fluidifies blood to induce smooth blood flow and reduce pain . HoweverThe purpose of this trial is to identify the efficacy of GJBNH in dysmenorrhea caused by blood stagnation.1) Clinically significant improvement in the severity of pain caused by dysmenorrhea2) Correlation between blood stagnation level and pain severityThe hypothesis is that GJBNH will reduce menstrual pain more effectively than placebo after taking the intervention--GJBNH or the placebo--for two menstrual cycles.nd follow-up) can vary according to the participant's period. Figure This trial is a randomized, double-blind, parallel group, placebo-controlled phase IV trial. There are three investigational sites: Oriental Medicine Obstetrics and Gynecology Clinic of Kyung Hee Medical Center in Seoul, Obstetrics and Gynecology Clinic of Won Kwang Oriental Hospital in Gunpo, and Obstetrics and Gynecology Clinic of Kyung Won Gil Oriental Medical Hospital of Kyung Won University in Incheon, Korea. Participants will be treated as outpatients in these sites. Before the beginning of the trial, the protocol of the trial has been approved by the Institutional Review Board (IRB). All participants will take GJBNH or placebo for two menstrual cycles (about eight weeks). They will be followed up during three menstrual cycles. It takes five menstrual cycles (about 20 weeks) from baseline to finish. The total span from screening visit 1) to finish  is a Traditional Korean Medicine formula. It consists of Ten pain killer pills will be given during each treatment cycle as rescue medication. If the participant can not endure the pain, she can take the rescue medication. But all participants should not take any pain-killer except given by the investigator. If the participant takes any other drug than what is given from the trial, it should be described in the case-report form (CRF). Any participant taking drugs that can influence the outcome such as NSAIDs or oral contraceptive pills will be excluded from the trial.The primary outcome in this study is the change in the Visual Analogue Scale (VAS) of average menstrual pain between the baseline (Visit 2) and after the treatment (Visit 4). A 100 mm VAS will be used to assess average level of pain during the menstrual period.The secondary outcome measures include the VAS , the Blood Stagnation Scale, the Short Form McGill Pain Questionnaire , and theAll participants will report any adverse event she had while taking the intervention at every visit. Every adverse event will be described in the CRF. If the adverse event is severe and associates with the trial, the participant will be withdrawn from the trial and appropriate treatment will be given to her. For safety assessment, a liver function test, blood cell count test, physical examination, and urine analysis will be carried out at Visit 4.The primary outcome in this trial is the change of the Visual Analogue Score (VAS) of average pain in the menstrual period between the baseline (Visit 2) and after treatment (Visit 4). The hypothesis isΔ1: The change of VAS score between Visit 4 and baseline in GJBNH groupΔ2: The change of VAS score between Visit 4 and baseline in placebo controlAs a reference, we have chosen the study of Choi et. al.  and Yeh http://mrcc.snuh.org) and input patient's number and birthday, and confirm that the patient fulfil the inclusion and the exclusion criteria. Then, a random number is generated. No one except the researcher at the MRCC can know whether the number indicates treatment group or placebo group, and all participants, investigators, and monitors are blinded.Participants will be given a random number at Visit 2. When a participant makes the second visit to the trial site, the investigator will connect to the Medical Research Collaboration Center (MRCC) web site run by Seoul National University Hospital which is commissioned for the allocation process in this trial. To randomize, the investigator will connect to the MRCC website  and PP  data sets. To compare the differences of the average changes of the VAS between the experimental arm and the control arm, the Short Form McGill Pain Questionnaire score, the blood stagnation score, the Cox menstrual score from the baseline (Visit 2) to after the treatment (Visit 4) between two groups, and analysis of covariance (ANCOVA) using the baseline score as a covariate will be used.For the variables which measure the autonomic nerve system , similar methods described above or their corresponding non-parametric analysis will be performed as appropriate.For ITT analysis, missing data will be imputed by MI (Multiple Imputation) method using SAS/MI procedure.The safety data set will include the participants who take the intervention at least once. For safety analysis, physical examination and self-reported adverse event will be compared by the chi-square test. In addition, the results of liver function tests, blood cell count and urine analysis will be analyzed using the same methods as described in efficacy analysis after classifying these results into normal or abnormal according to their respective normal ranges. The chi-square test will be used to compare the differences between the groups.The Center for Clinical Research and Genomics  is responsible for monitoring. Monitoring will begin after the first participant completes the whole process of this study. Every institution where the trial is being conducted will be monitored while this trial is in process using the Standard Operation Procedure (SOP)s.The trial is conducted to the Declaration of Helsinki 2008 and/or the regulations of the "Good Clinical Practice" principles in the Korea Food & Drug Administration.th of Aug 2008), WONSBHB IRB 2009-02  and 09-101 . Prior to undertaking any study-related procedures, all participants will provide written informed consent.The Institutional Review Board (IRB) has approved of this clinical trial at all institution before the participant recruitment. The reference numbers are KOMC IRB 2008-07 (IRB of Kyung Hee Oriental Medical Center, approved on 18It is not a facile task to design a trial to identify the efficacy of Traditional Korean herbal formula, because the sickness has to be diagnosed according to various symptoms and signs, and in Traditional Korean Medicine herbal formula has to be decided according to different diagnosis. The symptoms and signs are critical, not the name of the disease--this led the inclusion and exclusion criteria to be as diverse and thorough as the subjects of the trial.qi deficiency and weak constitution of liver and kidney [Dysmenorrhea has typical symptoms and characteristics and thus can be categorized into types based on certain symptoms. The types vary according to diseases, and in this case dysmenorrhea can be defined to four types of causes: blood stagnation, coldness in the uterus, blood and d kidney . The remDetermining the sample size is another challenge. There are few references, so we used two reference papers to calculate the sample size.Gyejibongnyeong-hwan as one of Traditional Korean Medicine formula has been widely used for thousands of years. But, the evidence supporting this formula is rare. We are hoping that this trial will provide high quality evidence and that the protocol for this trial will be a reference in design further clinical trials.The authors declare that they have no competing interests.JSP, SJP, CHC and BHJ have written the first manuscript for this trial and calculated the sample size. They will monitor this trial. YCS, HYG, SHS and SGK have edited the first manuscript. SGK has conducted all the procedures for this protocol. All authors read and approved the final manuscript.


A Z-plasty is a critical and reliable technique that is useful for scar revisions and correction of free margin distortion. A Z-plasty can help lengthen a contracted scar, change the direction of a scar so that it is better aligned with the relaxed skin tension lines, or interrupt and break a scar for better camouflage. This article will review the technique of a basic Z-plasty as well as provide case examples of its use in free margin distortion and scar revision. In order to achieve optimal aesthetic and functional results, there is no substitute for careful planning and meticulous surgical technique. Yet even in the most competent hands, surgical complications are an inevitable fact of life. In particular, areas of the face that border free margins, such as the eyes, nose, and lips, present a special challenge to the dermatologic surgeon. These areas offer little resistance to any tension created by surgical movement of nearby tissue and are not very forgiving. Any abnormality in the natural contours of these visually critical structures focuses the attention to the disruption or distortion itself. Often the distortion not only leads to an unacceptable cosmetic result but may also have functional consequences. A Z-plasty  is a criAs with all surgical reconstruction, it is essential to carefully plan, measure, and draw out the Z-plasty. Ideally this is done before any local anesthesia is injected to prevent tissue distortion. The fundamental unit of a Z-plasty is a triangular double transposition flap. However, as with most lifting flaps, there are also elements of rotation and advancement. In a classic Z-plasty three incisions of equal length create two equilateral triangular flaps . After undermining, one triangular flap is transposed about its pivotal point in a clockwise direction and the other in a counterclockwise direction to create the Z-plasty. In most cases, one does not need a lot of buried interrupted sutures and must be fairly gentle with the tips of the Z-plasty to avoid vascular compromise of these small flaps .The degree of scar directional change and lengthening is determined by the angles of the flap: the larger the angle, the greater the lengthening and the greater the change in direction of the original scar, the smaller the angle, the less the lengthening and change in the direction of the original scar . AlthougThe limb lengths of the Z-plasty also influence the length gained: the longer the limbs, the greater the gain in scar length. Yet these limbs of the Z-plasty have some practical limitations in terms of their length. Although the broken line scar created by a Z-plasty allows for an overall less perceptible scar, this advantage diminishes with longer limbs as they will eventually create more obvious scar lines . Usually 6 to 10 millimeters is as long as any segment of the Z-plasty should be designed, particularly if the segment does not lie in a favorable direction or at the junction of two cosmetic units. In order to decrease the formation of a noticeable Z-shaped scar and overcome the practical limb lengths, a longer scar can be broken up by using multiple Z-plasties . FinallyFinally one should also consider the relaxed skin tension lines of the face when planning the Z-plasty such that the amount of directional change  can be most similar to the RSTLs. For each particular scar or central limb, there are always two choices for the alignment of the peripheral arms, these being mirror images of one another . Both opLike other transposition flaps, a Z-plasties can create trapdoor or pincushion effect. Wide undermining to create an even scar contraction plate may help decrease this risk. Post-operative intralesional steroids may also help diminish such an effect should it occur.


Its implementation requires the use of all available knowledge of a given product, including the parameters that affect its quality, for the design, optimization and control of the manufacturing process. The goal is to ensure that quality is built into the product at every stage of the manufacturing process. Most licensed monoclonal antibodies (mAbs) are based on the immunoglobulin G isotype and contain a consensus N-linked glycosylation site on the Cγ2 domains of their heavy chains. Studies have found that the oligosaccharides attached to this site dramatically influence the efficacy of mAbs as therapeutics either by reducing their serum half-life or by directly affecting the mechanisms they trigger in vivo,2, thus in vivo. To our sm,glc) from the cell culture model; the outlet of NSDs from the cells was associated to the product secretion rate.Several reports have shown that glycosylation is directly affected by the intracellular availability of nucleotide sugar donors (NSDs)  which arIn order to estimate the unknown parameters of the combined model, experimental data from Kochanowski and collaborators  was usedFigure sm,glc). Furthermore, it is the first model to relate cell culture variables with intracellular NSD concentrations and the results show that it is capable of reproducing experimental data accurately. However, in order to achieve better reproduction of experimental data and obtain higher confidence in the estimated parameters, additional experimental data is needed. Specifically, the concentration profiles of GDP-Fuc and CMP-Neu5Ac throughout cell culture would lead to improved reproduction of experimental data and predictive capabilities of the model. Furthermore, fed-batch cultures are also necessary to validate the model and its parameters.To our knowledge, the model presented in this work is the first to link cell culture variables with intracellular metabolic processes through the glucose maintenance energy term (built in glycosylation-associated quality as proposed under the QbD paradigm.Once validated with additional data, our mathematical model for NSD metabolism, can be coupled to a model for Golgi N-linked glycosylation. This combined model would generate a direct link between extracellular glucose concentration, which is a readily measurable process variable, and protein glycosylation. Such a combined model has great potential for the design, control and optimization of manufacturing processes that produce mAbs with


Multiple sclerosis (MS) is a disease of central nervous system that causes the removal of fatty myelin sheath from axons of the brain and spinal cord. Autoimmunity plays an important role in this pathology outcome and body's own immune system attacks on the myelin sheath causing the damage. The etiology of the disease is partially understood and the response to treatment cannot easily be predicted.We presented the results obtained using 8 genetically predisposed randomly chosen individuals reproducing both the absence and presence of malfunctions of the Teff-Treg cross-balancing mechanisms at a local level. For simulating the absence of a local malfunction we supposed that both Teff and Treg populations had similar maximum duplication rates. Results presented here suggest that presence of a genetic predisposition is not always a sufficient condition for developing the disease. Other conditions such as a breakdown of the mechanisms that regulate and allow peripheral tolerance should be involved.The presented model allows to capture the essential dynamics of relapsing-remitting MS despite its simplicity. It gave useful insights that support the hypothesis of a breakdown of Teff-Treg cross balancing mechanisms. Multiple sclerosis (MS) is a disease of central nervous system. The disease causes the removal of fatty myelin sheath from axons of the brain and spinal cord resulting reduced communication among nerve cells. Autoimmunity plays an important role in the disease outcome and body's own immune system attacks on the myelin sheath causing the damage. Several genetic factors including HLA-DR15, HLA-A*02 and HLA-DRB1*1501 , where hlife (Δ(t)-1) represents the mean half life of involved agents. The life counter is usually decremented by 1 at every time-step for all agents. All agents can move and interact during the simulation at every time-step. Movement and interaction rules are described in the next sections. We used a Von Neumann neighborhood  and , respectively. We took, as outcome of the experiments, the total damage at the end of the simulations for both the scenarios. Median values of the final total damage were 77268 for the hill sample and 5357 for the healty sample. Non parametric Kolmogorov-Smirnov two samples goodness-of-fit test gave as result a maximum difference between the cumulative distributions D = 0.7500 with a corresponding p-value of: 0.000, thus suggesting that the two samples are unlikely to be drawn from the same distribution .We also tested the model by simulating 100 randomly chosen virtual patients (data not shown) in both the hill and the healthy scenarios by setting [In Figure In Figure We also observed that (data not shown), in some cases (for some seeds) a decrease in the Teff or an increase Treg proliferation does not always entitle less severe relapses and, as a matter of fact, it could produce more severe relapses. This is mainly due to the stochasticity of the model. It may happen that the stochastic injection of new resting Teff may be not shortly followed by an equivalent injection of Treg, thus creating a temporary disequilibrium between the two populations which would entitle some neural damage even in potential healthy patients.Results presented here suggest that presence of a genetic predisposition is not always a sufficient condition for developing the disease. Other conditions such as a breakdown of the mechanisms that regulate and allow peripheral tolerance should be involved. This has also been observed in . In our Moreover we observed that in the simulations of hill patients relapses mainly occur in the first half of the simulation rather than in the second half (see, for example, Figure In this work, we presented the first simple model of MS using agent based modeling approach. It shows the main behavior of this neural disease i.e., the relapse-remitting one. Compared to the real biological scenario, the model is naive, but takes into account the main entities involved at cellular level in the pathogenesis of MS. It allows to grasp how the role of regulatory vs effectors cells and their internal dynamics are crucial in the understanding the evolution of neural damage in the progression of the pathology. We will continue working with this model to integrate the damage done by demyelination and role of Treg cells in a quantitative way to correlate the disfunction of Treg cells and demyelinated area as shown in a recent study .MS is a disease that involves practically all the immune system machinery, both at cellular, molecular and sub-molecular level. A detailed model would require a specialized framework and for this reason would be computationally expensive. The current version of Netlogo is probably not suitable to this purpose. We are working in this direction using a general framework for the immune system developed by us for other pathologies. Progress in this direction will be published in due course.The authors declare that they have no competing interests.MP: designed the model, analyzed data, developed the Netlogo model, performed numerical simulations, wrote the manuscript. AMR: designed the model, analyzed data, developed the Netlogo Model, gave biological knowledge, wrote the manuscript. LT: gave useful insights and wrote the manuscript. FP: conceived the application of an agent based simulator to MS, supervised the whole project and drafted the manuscript.


In order to manage the outdoor thermal environment with regard to human health and the environmental impact of waste heat, quantitative evaluations are indispensable. It is necessary to use a thermal environment evaluation index. The purpose of this paper is to clarify the relationship between the psychological thermal responses of the human body and winter outdoor thermal environment variables. Subjective experiments were conducted in the winter outdoor environment. Environmental factors and human psychological responses were measured. The relationship between the psychological thermal responses of the human body and the outdoor thermal environment index ETFe (enhanced conduction-corrected modified effective temperature) in winter was shown. The variables which influence the thermal sensation vote of the human body are air temperature, long-wave thermal radiation and short-wave solar radiation. The variables that influence the thermal comfort vote of the human body are air temperature, humidity, short-wave solar radiation, long-wave thermal radiation, and heat conduction. Short-wave solar radiation, and heat conduction are among the winter outdoor thermal environment variables that affect psychological responses to heat. The use of thermal environment evaluation indices that comprise short-wave solar radiation and heat conduction in winter outdoor spaces is a valid approach. Much research relating to the control of air conditioning systems for living environments and office spaces has been performed but that on outdoor spaces is incomplete. It has been shown that, in addition to physical and physiological environmental factors, psychological environmental stimuli are also important for the determination of thermal comfort. In contrast to indoor spaces, it is not just the thermal environment stimuli but also the environmental complex consisting of visual and auditory stimuli that has an influence on comfort. Adaptation to the thermal environment according to cultural background, experience of being in hot/cold thermal environments and the like, sense of expectation of the thermal environment, behavioural thermal regulation, and the effect of thermal environment history such as the time spent exposed to it are strongly apparent –8. AlthoThe hot and cold that humans sense is typically investigated by means of air temperature. In a summer outdoor space, however, strong solar radiation from the sun gives a hot feeling, a strong wind gives a cool feeling, high humidity gives a muggy feeling, and a heated road surface feels so hot that it cannot be touched. Accordingly, it is necessary to include not only air temperature but also the environmental elements of thermal radiation, convection, humidity, and heat conduction in assessment of the thermal sense of humans. That is to say, it is necessary to make an explicit relationship between the thermal sense of the human body and the thermal environment evaluation indices that support the heat balance of the human body. Givoni et al. , OliveirEnhanced conduction-corrected modified effective temperature (ETFe)  and univAccordingly, this research shows the relationship between the outdoor thermal environmental evaluation index for winter and the psychological response of the human body by using ETFe to temperature-convert the effect of air temperature and air velocity, long-wave thermal radiation in outdoor space, short-wave solar radiation, contact member's surface temperature, and humidity and arrange them on the same evaluation axis. It goes on to investigate the individual environmental factors that should be incorporated as evaluation factors for an outdoor thermal environment. The thermal environment evaluation index for an outdoor space ETFe was developed by Kurazumi et al. . It was hta); radiant heat transfer area combined effective radiation field concerning long-wave thermal radiation in an outdoor space for long-wave thermal radiation in an outdoor space (ERFhtaL); radiant heat transfer area combined effective radiation field concerning short-wave solar radiation in an outdoor space for solar radiation (ERFhtaS); conductive heat transfer area combined effective conductive field for the contact member's surface temperature (ECFhta); and effective humid field in enhanced conduction-corrected modified effective temperature in humidity ETFe for humidity (EHFETFe). The addition of each temperature-converted factor is also possible, and quantifying the composite effect on sensation in the outdoor space as well as the discrete effect of each meteorological element is possible on the same evaluation axis.The effect of these five environmental factors on the heat balance of the human body can be expressed by a newly defined thermal environment evaluation index as follows: convective heat transfer area combined thermal velocity field for air velocity . Ground surface temperature in the vicinity of the human body was measured by a radiation thermometer . The sky factor was measured by a photograph of the sky taken 1.2 m above the ground at the observation point with a fisheye lens with an orthographical projection format (Nikon: OP Fisheye Nikkor 10 mm f/5.6) and a 35 mm digital SLR camera. The proportion of the solid angle of components of greenery, water, and so forth comprising the solid angle of the total celestial sphere was measured by a photograph of the sky taken 1.2 m above the ground at the observation point with a fisheye lens with an equisolid angle projection format (Olympus: Fisheye Zuiko 8 mm f/2.8) and a 35 mm digital SLR camera. The albedo, sky temperature, and ground surface temperature were calculated from each directional component of the short-wave solar radiation and the long-wave thermal radiation. Furthermore, since the ground surface temperature in the vicinity of the human body is essential for the calculation of transmission heat quantity, values measured by radiation thermometer were used. Also, the values calculated by long- and short-wave solar radiometers were used as the average surface temperature and average sky temperature for the calculation of long-wave thermal radiation. In order to maintain consistency with the measurements Kurazumi et al.  carried 2), response time 200 ms, T type thermocouple measurement range −50~230°C, one side painted black). The temperature of skin exposed to the air velocity was measured at the seven positions of the head, trunk, arm, hand, thigh, lower leg, and foot. The sole of the foot was measured for the temperature of the contact part skin. The subjects chose clothing suitable for the weather on the measurement day. The clothing quantity of the subjects was sought by the clo value by layering the clothing reported by the subjects [With regard to the physiological conditions of the human body, the skin temperature of the part exposed to the air velocity was measured by a thermistor thermometer , and the skin temperature of contact parts was measured by a heat flux temperature sensor  and the whole-body thermal comfort (comfortable-uncomfortable) on a linear scale , 30. Onlμm or more was used for the emissivity of the human body. Hendler et al.'s [μm or less was used for the solar radiation absorption factor of the human body. The heat transfer of short-wave solar radiation is affected by the solar radiation absorption factor. According to VDI3787-2 [ETFe is an outdoor thermal environment evaluation index based on the heat balance of the human body. Accordingly, a weighting factor that takes into account the convection area of heat transfer surface was used for the calculation of the average skin temperature used to calculate the heat balance of the human body . Then, tet al.'s  and Elamet al.'s  value ofDI3787-2 , the absDI3787-2  showed, DI3787-2  were useThe measurement data for the observation points are shown in Ta and air velocity, which are components of ETFe  TVFhta, long-wave thermal radiation ERFhtaL, heat conduction ECFhta, humidity EHFETFe, and short-wave solar radiation ERFhtaS as explanatory variables. The results are shown in In order to predict the thermal sensation votes for the human body, multiple linear regression analysis was performed with air temperature hta had a different symbol from other environmental factors. The convection heat exchange because of air velocity  TVFhta functions as a heat loss for the human body, but heat exchange owed to other environmental factors functions as a heat gain for the human body. Accordingly, air velocity controls the direction of increase or decrease of thermal sensation vote owed to other environmental factors, and so all environmental factors were employed as explanatory variables in the multiple regression formula. Being negative, the partial regression constant for air velocity  TVFP < 0.01 as a result of analysis of variance on the multiple regression formula proved that the formula was valid.A laboratory experiment is an environment in which it is easy to control environmental stimuli and human body conditions. Office spaces permit a wider range of thermal environments than laboratory space controlled by a supervisor. In turn, the living space in which a broader range of behaviour is available to the individual permits a wider range of thermal environment than does the office space. Finally, outdoor space which may be thermally uncomfortable but in which one's selection of location or point of attention may be changed at will permits a broader range of thermal environment than living space. That is, there is a significant dispersion in the psychological response of the human body in outdoor space. The coefficient of determination for the multiple regression formula depends on the experimental judgement of the analyst. The coefficient of determination for the multiple regression formula found in this study was 0.48, and the multiple regression formula was considered to be quite good. Furthermore, t-testing the components of ETFe, it was found that the thermal sensation vote for outdoors in winter is strongly influenced by and varies according to air temperature Ta, long-wave thermal radiation ERFhtaL, and short-wave solar radiation ERFhtaS. As stated in the previous results previous, the air velocity was comparatively gentle at about 3 m/s throughout all observations, and it is possible that the difference in convection heat exchange had little influence on sensational and physiological temperature. Also, in winter, footwear with thick soles and excellent heat insulation is generally worn in order to protect against the cold. Accordingly, it can be said that the heat acquisition of the human body because of heat conduction did not influence thermal sensation votes even though the ground surface temperature was low because of the effect of insulation. As a standard for selection of explanatory variables in order to derive multiple linear regression analysis results that are more useful in practice, the objective significance probability was sometimes made 20–30%. Given that the psychological quantity for the human body in an outdoor environment differed from the case of an indoor environment and the results showed a lot of noise and dispersion, investigations were carried out with a significance probability of 25%. As a result of Dealing with the relationship between outdoor environmental elements and thermal sensation votes, Givoni et al. , OliveirTa and air velocity, which are components of ETFe  TVFhta, long-wave thermal radiation ERFhtaL, heat conduction ECFhta, humidity EHFETFe, and short-wave solar radiation ERFhtaS as explanatory variables. The results of the multiple linear regression analysis for the thermal comfort votes, which were the objective parameters, are shown in In order to predict the thermal comfort votes for the human body, multiple linear regression analysis was performed with air temperature hta differed from other environmental factors inasmuch that it was negative. Air velocity  TVFhta controls the direction of increase or decrease of thermal comfort vote, however, because of other environmental factors, and so all environmental factors were employed as explanatory variables in the multiple regression formula.Similarly to the relationship between the above components of ETFe and thermal sensation votes, the partial regression constant for air velocity  TVFP < 0.01 resulting from analysis of variance on the multiple regression formula. The poor analytical accuracy may have been influenced by environmental factors other than thermal environment stimuli. In this research, the experiment was carried out after the subjects had been informed that comfort is specific to heat. It was, however, implied that there is a psychological tendency to perform a nonspecific and comprehensive evaluation of the entire space including visual and auditory stimuli, when one is outdoors [The coefficient of determination for the multiple regression formula was 0.29. Although the analysis of the multiple regression formula cannot be said to be accurate, the multiple regression formula was shown to be valid, with outdoors –14. t-testing the components of ETFe, it was shown that the thermal comfort vote for outdoors in winter is easily influenced by air temperature Ta, humidity EHFETFe, short-wave solar radiation ERFhtaS, long-wave thermal radiation ERFhtaL, and heat conduction ECFhta. Considering that the air velocity was comparatively gentle at about 3 m/s throughout all observations, it is conjectured that the thermal comfort vote for outdoors in winter is influenced by all environmental factors addressed in this research. Accordingly, it may be necessary to treat short-wave solar radiation and heat conduction in the thermal environment evaluation of an outdoor space. Ishii et al. [As a result of i et al.  demonstri et al.  demonstrAlthough it is physically possible to handle environmental stimuli, it is difficult to handle the human body effect on the environmental stimuli independently. For example, in the case of a hot environment in summer where the temperature is higher than skin temperature, the heat balance of the human body dropping as the air velocity increases can promote a sense of discomfort. In addition, in the case of a cooling winter environment of a temperature lower than the air temperature because of radiative cooling, the heat balance of the human body as the air velocity increases can show a thermal stimulus close to the air temperature. In the above, the response of the thermal sense to the environmental stimuli is subsidiary, but when the rate at which the environment stimuli contribute to thermal sense is investigated, it is appropriate to consider the following. In the evaluation of a winter outdoor environment, it has been demonstrated that it is essential to incorporate short-wave solar radiation and heat conduction as evaluation factors in addition to air temperature and air velocity, humidity, and long-wave thermal radiation. Given the results of Ishii et al.  for air An experiment on test subjects was performed to clarify the effect that the thermal environment stimuli in a winter outdoor space have on the human body, and the relationship between outdoor environmental factors and the psychological response of the human body was demonstrated. In addition to air temperature and humidity, air velocity, and long-wave thermal radiation, it was found that short-wave solar radiation and heat conduction are among the influential factors which affect the thermal sensation vote and thermal comfort vote of the human body in a winter outdoor thermal environment. The validity of using a thermal environment evaluation index that incorporates these environmental factors for an outdoor space was demonstrated.