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bioRxiv2018

Investigation of Electrical Stimulation Effect on Intracellular Calcium Dynamics Using Locally Uniform Mesh Refinement

Modeling-based methods are conventionally exploited to simulate and predict the dynamics of a system in various fields of engineering. However, due to the intricacy of biological systems, these methods were rarely utilized in bioengineering until recently. By developing advanced computers with the ability to cope with enormous calculations and extending our knowledge about biological systems, modeling-based approaches have been adopted to manipulate biological systems. While utilizing the models to investigate the behavior of a system has some advantages including lower cost and time consumption, such methods were used for tissue engineering scarcely. Exploiting modeling-based methods to tissue engineering field requires developing and utilizing efficient computational methods to model gene regulation and signaling networks, which determine cell response to environmental changes and cellular fate.\n\nIn the present work, a novel spatio-temporal method was proposed, predicated on locally uniform mesh refinement. A benchmark comparison was performed with the previously used method and the results indicated the better performance of the incipiently adopted method. Besides, the model was utilized to investigate the effect of a popular differentiating stimulator, namely electrical stimulation, on mesenchymal stem cells as a type of stem cells widely used in tissue engineering. The results of the simulations demonstrated the puissance of such computational models in analyzing and predicting the effect of biochemical and biophysical perturbations on the cells and hence, their potential utility in tissue engineering.

systems biology↗

bioRxiv2017

A Biomaterial Screening Approach to Reveal Microenvironmental Mechanisms of Drug Resistance

TOC FigureDrug response screening, gene expression, and kinome signaling were combined across biomaterial platforms to combat adaptive resistance to sorafenib.\n\n\n\nO_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=158 SRC=\"FIGDIR/small/168039_ufig1.gif\" ALT=\"Figure 1\">\nView larger version (60K):\norg.highwire.dtl.DTLVardef@a7af0eorg.highwire.dtl.DTLVardef@d5f2bborg.highwire.dtl.DTLVardef@330bd6org.highwire.dtl.DTLVardef@14e1f1d_HPS_FORMAT_FIGEXP M_FIG C_FIG Insight BoxWe combined biomaterial platforms, drug screening, and systems biology to identify mechanisms of extracellular matrix-mediated adaptive resistance to RTK-targeted cancer therapies. Drug response was significantly varied across biomaterials with altered stiffness, dimensionality, and cell-cell contacts, and kinome reprogramming was responsible for these differences in drug sensitivity. Screening across many platforms and applying a systems biology analysis were necessary to identify MEK phosphorylation as the key factor associated with variation in drug response. This method uncovered the combination therapy of sorafenib with a MEK inhibitor, which decreased viability on and within biomaterials in vitro, but was not captured by screening on tissue culture plastic alone. This combination therapy also reduced tumor burden in vivo, and revealed a promising approach for combating adaptive drug resistance.\n\nAbstractTraditional drug screening methods lack features of the tumor microenvironment that contribute to resistance. Most studies examine cell response in a single biomaterial platform in depth, leaving a gap in understanding how extracellular signals such as stiffness, dimensionality, and cell-cell contacts act independently or are integrated within a cell to affect either drug sensitivity or resistance. This is critically important, as adaptive resistance is mediated, at least in part, by the extracellular matrix (ECM) of the tumor microenvironment. We developed an approach to screen drug responses in cells cultured on 2D and in 3D biomaterial environments to explore how key features of ECM mediate drug response. This approach uncovered that cells on 2D hydrogels and spheroids encapsulated in 3D hydrogels were less responsive to receptor tyrosine kinase (RTK)-targeting drugs sorafenib and lapatinib, but not cytotoxic drugs, compared to single cells in hydrogels and cells on plastic. We found that transcriptomic differences between these in vitro models and tumor xenografts did not reveal mechanisms of ECM-mediated resistance to sorafenib. However, a systems biology analysis of phospho-kinome data uncovered that variation in MEK phosphorylation was associated with RTK-targeted drug resistance. Using sorafenib as a model drug, we found that co-administration with a MEK inhibitor decreased ECM-mediated resistance in vitro and reduced in vivo tumor burden compared to sorafenib alone. In sum, we provide a novel strategy for identifying and overcoming ECM-mediated resistance mechanisms by performing drug screening, phospho-kinome analysis, and systems biology across multiple biomaterial environments.

bioengineering↗

bioRxiv2018

Unifying mutualism diversity for interpretation and prediction

Coarse-grained rules are widely used in chemistry, physics and engineering. In biology, however, such rules are less common and under-appreciated. This gap can be attributed to the difficulty in establishing general rules to encompass the immense diversity and complexity of biological systems. Even when a rule is established, it is often challenging to map it to mechanistic details and to quantify these details. We here address these challenges on a study of mutualism, an essential type of ecological interaction in nature. Using an appropriate level of abstraction, we deduced a general rule that predicts the outcomes of mutualistic systems, including coexistence and productivity. We further developed a standardized calibration procedure to apply the rule to mutualistic systems without the need to fully elucidate or characterize their mechanistic underpinnings. Our approach consistently provides explanatory and predictive power with various simulated and experimental mutualistic systems. Our strategy can pave the way for establishing and implementing other simple rules for biological systems.

systems biology↗

bioRxiv2018

An enriched network motif family regulates multistep cell fate transitions with restricted reversibility

Multistep cell fate transitions with stepwise changes of transcriptional profiles are common to many developmental, regenerative and pathological processes. The multiple intermediate cell lineage states can serve as differentiation checkpoints or branching points for channeling cells to more than one lineages. However, mechanisms underlying these transitions remain elusive. Here, we explored gene regulatory circuits that can generate multiple intermediate cellular states with stepwise modulations of transcription factors. With unbiased searching in the network topology space, we found a motif family containing a large set of networks can give rise to four attractors with the stepwise regulations of transcription factors, which limit the reversibility of three consecutive steps of the lineage transition. We found that there is an enrichment of these motifs in a transcriptional network controlling the early T cell development, and a mathematical model based on this network recapitulates multistep transitions in the early T cell lineage commitment. By calculating the energy landscape and minimum action paths for the T cell model, we quantified the stochastic dynamics of the critical factors in response to the differentiation signal with fluctuations. These results are in good agreement with experimental observations and they suggest the stable characteristics of the intermediate states in the T cell differentiation. These dynamical features may help to direct the cells to correct lineages during development. Our findings provide general design principles for multistep cell linage transitions and new insights into the early T cell development. The network motifs containing a large family of topologies can be useful for analyzing diverse biological systems with multistep transitions.\n\nAuthor summaryThe functions of cells are dynamically controlled in many biological processes including development, regeneration and disease progression. Cell fate transition, or the switch of cellular functions, often involves multiple steps. The intermediate stages of the transition provide the biological systems with the opportunities to regulate the transitions in a precise manner. These transitions are controlled by key regulatory genes of which the expression shows stepwise patterns, but how the interactions of these genes can determine the multistep processes were unclear. Here, we present a comprehensive analysis on the design principles of gene circuits that govern multistep cell fate transition. We found a large network family with common structural features that can generate systems with the ability to control three consecutive steps of the transition. We found that this type of networks is enriched in a gene circuit controlling the development of T lymphocyte, a crucial type of immune cells. We performed mathematical modeling using this gene circuit and we recapitulated the stepwise and irreversible loss of stem cell properties of the developing T lymphocytes. Our findings can be useful to analyze a wide range of gene regulatory networks controlling multistep cell fate transitions.

systems biology↗

bioRxiv2018

Inverse sensitivity analysis of mathematical models avoiding the curse of dimensionality

1Biological systems have evolved a degree of robustness with respect to perturbations in their environment and this capability is essential for their survival. In applications ranging from therapeutics to conservation, it is important to understand not only the sensitivity of biological systems to changes in their environments, but which features of these systems are necessary to achieve a given outcome. Mathematical models are increasingly employed to understand these mechanisms. Sensitivity analyses of such mathematical models provide insight into the responsiveness of the system when experimental manipulation is difficult. One common approach is to seek the probability distribution of the outputs of the system corresponding to a known distribution of inputs. By contrast, inverse sensitivity analysis determines the probability distribution of model inputs which produces a known distribution of outputs. The computational complexity of the methods used to conduct inverse sensitivity analyses for deterministic systems has limited their application to models with relatively few parameters. Here we describe a novel Markov Chain Monte Carlo method we call \"Contour Monte Carlo\", which can be used to invert systems with a large number of parameters. We demonstrate the utility of this method by inverting a range of frequently-used deterministic models of biological systems, including the logistic growth equation, the Michaelis-Menten equation, and an SIR model of disease transmission with nine input parameters. We argue that the simplicity of our approach means it is amenable to a large class of problems of practical significance and, more generally, provides a probabilistic framework for understanding the inversion of deterministic models.\n\n2 Author summaryMathematical models of complex systems are constructed to provide insight into their underlying functioning. Statistical inversion can probe the often unobserved processes underlying biological systems, by proceeding from a given distribution of a models outputs (the aggregate \"effects\") to a distribution over input parameters (the constituent \"causes\"). The process of inversion is well-defined for systems involving randomness and can be described by Bayesian inference. The inversion of a deterministic system, however, cannot be performed by the standard Bayesian approach. We develop a conceptual framework that describes the inversion of deterministic systems with fewer outputs than input parameters. Like Bayesian inference, our approach uses probability distributions to describe the uncertainty over inputs and outputs, and requires a prior input distribution to ensure a unique \"posterior\" probability distribution over inputs. We describe a computational Monte Carlo method that allows efficient sampling from the posterior distribution even as the dimension of the input parameter space grows. This is a two-step process where we first estimate a \"contour volume density\" associated with each output value which is then used to define a sampling algorithm that yields the requisite input distribution asymptotically. Our approach is simple, broadly applicable and could be widely adopted.

systems biology↗

bioRxiv2017

Novel Plasmodium falciparum metabolic network reconstruction identifies shifts associated with clinical antimalarial resistance

BACKGROUNDMalaria remains a major public health burden and resistance has emerged to every antimalarial on the market, including the frontline drug artemisinin. Our limited understanding of Plasmodium biology hinders the elucidation of resistance mechanisms. In this regard, systems biology approaches can facilitate the integration of existing experimental knowledge and further understanding of these mechanisms.\n\nRESULTSHere, we developed a novel genome-scale metabolic network reconstruction, iPfal17, of the asexual blood-stage P. falciparum parasite to expand our understanding of metabolic changes that support resistance. We identified 11 metabolic tasks to evaluate iPfal17 performance. Flux balance analysis and simulation of gene knockouts and enzyme inhibition predict candidate drug targets unique to resistant parasites. Moreover, integration of clinical parasite transcriptomes into the iPfal17 reconstruction reveals patterns associated with antimalarial resistance. These results predict that artemisinin sensitive and resistant parasites differentially utilize scavenging and biosynthetic pathways for multiple essential metabolites including folate and polyamines, and others within the mitochondria. Our findings are consistent with experimental literature, while generating novel hypotheses about artemisinin resistance and parasite biology. We detect evidence that resistance parasites maintain greater metabolic flexibility, perhaps representing an incomplete transition to the metabolic state most appropriate for nutrient-rich blood.\n\nCONCLUSIONUsing this systems biology approach, we identify metabolic shifts that arise with or in support of the resistant phenotype. This perspective allows us to more productively analyze and interpret clinical expression data for the identification of candidate drug targets for the treatment of resistant parasites.

systems biology↗

bioRxiv2016

Dynamic compensation, parameter identifiability, and equivariances

A recent paper by Karin, Swisa, Glaser, Dor, and Alon introduced the mathematical notion of dynamical compensation (DC) in biological circuits, arguing that DC helps explain important features of glucose homeostasis as well as other key physiological regulatory mechanisms. The present paper establishes a connection between DC and two well-known notions in systems biology: system equivalence and parameter (un)identifiability. This recasting leads to effective tests for verifying DC in mathematical models.

systems biology↗

bioRxiv2016

Massively parallel digital transcriptional profiling of single cells

Characterizing the transcriptome of individual cells is fundamental to understanding complex biological systems. We describe a droplet-based system that enables 3' mRNA counting of up to tens of thousands of single cells per sample. Cell encapsulation in droplets takes place in [~]6 minutes, with [~]50% cell capture efficiency, up to 8 samples at a time. The speed and efficiency allow the processing of precious samples while minimizing stress to cells. To demonstrate the system's technical performance and its applications, we collected transcriptome data from [~][1/4] million single cells across 29 samples. First, we validate the sensitivity of the system and its ability to detect rare populations using cell lines and synthetic RNAs. Then, we profile 68k peripheral blood mononuclear cells (PBMCs) to demonstrate the system's ability to characterize large immune populations. Finally, we use sequence variation in the transcriptome data to determine host and donor chimerism at single cell resolution in bone marrow mononuclear cells (BMMCs) of transplant patients. This analysis enables characterization of the complex interplay between donor and host cells and monitoring of treatment response. This high-throughput system is robust and enables characterization of diverse biological systems with single cell mRNA analysis.

Genomics↗

bioRxiv2017

Tellurium Notebooks - An Environment for Dynamical Model Development, Reproducibility, and Reuse

The considerable difficulty encountered in reproducing the results of published dynamical models limits validation, exploration and reuse of this increasingly large biomedical research resource. To address this problem, we have developed Tellurium Notebook, a software system that facilitates building reproducible dynamical models and reusing models by 1) supporting the COMBINE archive format during model development for capturing model information in an exchangeable format and 2) enabling users to easily simulate and edit public COMBINE-compliant models from public repositories to facilitate studying model dynamics, variants and test cases. Tellurium Notebook, a Python-based Jupyter-like environment, is designed to seamlessly inter-operate with these community standards by automating conversion between COMBINE standards formulations and corresponding in-line, human-readable representations. Thus, Tellurium brings to systems biology the strategy used by other literate notebook systems such as Mathematica. These capabilities allow users to edit every aspect of the standards-compliant models and simulations, run the simulations in-line, and re-export to standard formats. We provide several use cases illustrating the advantages of our approach and how it allows development and reuse of models without requiring technical knowledge of standards. Adoption of Tellurium should accelerate model development, reproducibility and reuse.\n\nAuthor summaryThere is considerable value to systems and synthetic biology in creating reproducible models. An essential element of reproducibility is the use of community standards, an often challenging undertaking for modelers. This article describes Tellurium Notebook, a tool for developing dynamical models that provides an intuitive approach to building and reusing models built with community standards. Tellurium automates embedding human-readable representations of COMBINE archives in literate coding notebooks, bringing to systems biology this strategy central to other literate notebook systems such as Mathematica. We show that the ability to easily edit this human-readable representation enables users to test models under a variety of conditions, thereby providing a way to create, reuse, and modify standard-encoded models and simulations, regardless of the users level of technical knowledge of said standards.

systems biology↗

bioRxiv2018

Intrinsic noise modulation in closed oligomerization-type systems

How random fluctuations impact on biological systems and what is their relationship with complexity and energetic cooperativity are challenging questions that are far from being elucidated. Using the stochastic differential equation formalism, we studied analytically the effect of fluctuations on a series of oligomerization processes, in which several molecules of the same or different species interact to form complexes, without interaction with the environment. The conservation of the total number of molecules within the systems imposes constraints on the stochastic quantities, among which the negativity of the covariances and the vanishing of the determinant of the covariance matrix. The intrinsic noise on the number of molecules of each species is represented by the Fano factor, defined as the variance to mean ratio. At the equilibrium steady states, the sum of the Fano factors of all molecular species is equal to the rank of the system, independently of the parameters. The Fano factors of the individual molecular species are, however, parameter dependent. We found that when the free energy cooperativity of the reactions increases, the intrinsic noise on the oligomeric product decreases, and is compensated by a higher noise on the monomeric reactants and/or intermediate states. The noise reduction is moreover more pronounced for higher complexity systems, involving oligomers of higher degrees.

systems biology↗

bioRxiv2018

Improvement of the memory function by negative autoregulation of a mutual repression network in a stochastic environment

BackgroundCellular memory is a ubiquitous function of biological systems. By generating a sustained response to a transient inductive stimulus, often due to bistability, memory is central to the robust control of many important biological processes. However, our understanding of the origins of cellular memory remains incomplete. Stochastic fluctuations that are inherent to most biological systems have been shown to hamper memory function. Yet, how stochasticity changes the behavior of genetic circuits is generally not clear from a deterministic analysis of the network alone. Here, we apply deterministic rate equations, stochastic simulations, and theoretical analyses of Fokker-Planck equations to investigate how intrinsic noise affects the memory function in a mutual repression network.\n\nResultsWe find that the addition of negative autoregulation improves the persistence of memory in a small gene regulatory network by reducing stochastic fluctuations. Our theoretical analyses reveal that this improved memory function stems from an increased stability of the steady states of the system. Moreover, we show how the tuning of critical network parameters can further enhance memory.\n\nConclusionsOur work illuminates the power of stochastic and theoretical approaches to understanding biological circuits, and the importance of considering stochasticity to designing synthetic circuits with memory function.

systems biology↗

bioRxiv2018

Optogenetics enables real-time spatiotemporal control over spiral wave dynamics in an excitable cardiac system

Propagation of non-linear waves is key to the functioning of diverse biological systems. Such waves can organize into spirals, rotating around a core, whose properties determine the overall wave dynamics. Theoretically, manipulation of a spiral wave core should lead to full spatiotemporal control over its dynamics. However, this theory lacks supportive evidence (even at a conceptual level), making it thus a long-standing hypothesis. Here, we propose a new phenomenological concept that involves artificially dragging spiral waves by their cores, to prove the afore-mentioned hypothesis in silico, with subsequent in vitro validation in optogenetically-modified monolayers of rat atrial cardiomyocytes. We thereby connect previously established, but unrelated concepts of spiral wave attraction, anchoring and unpinning to demonstrate that core manipulation, through controlled displacement of heterogeneities in excitable media, allows forced movement of spiral waves along pre-defined trajectories. Consequently, we impose real-time spatiotemporal control over spiral wave dynamics in a biological system.

bioinformatics↗

bioRxiv2015

Prediction of Fine-tuned Promoter Activity from DNA Sequence

The quantitative prediction of transcriptional activity of genes using promoter sequence is fundamental to the engineering of biological systems for industrial purposes and understanding the natural variation in gene expression. To catalyze the development of new algorithms for this purpose, the Dialogue on Reverse Engineering Assessment and Methods (DREAM) organized a community challenge seeking predictive models of promoter activity given normalized promoter activity data for 90 ribosomal protein promoters driving expression of a fluorescent reporter gene. By developing an unbiased modeling approach that performs an iterative search for predictive DNA sequence features using the frequencies of various k-mers, inferred DNA mechanical properties and spatial positions of promoter sequences, we achieved the best performer status in this challenge. The specific predictive features used in the model included the frequency of the nucleotide G, the length of polymeric tracts of T and TA, the frequencies of 6 distinct trinucleotides and 12 tetranucleotides, and the predicted protein deformability of the DNA sequence. Our method accurately predicted the activity of 20 natural variants of ribosomal protein promoters (Spearman correlation r = 0.73) as compared to 33 laboratory-mutated variants of the promoters (r = 0.57) in a test set that was hidden from participants. Notably, our model differed substantially from the rest in 2 main ways: i) it did not explicitly utilize transcription factor binding information implying that subtle DNA sequence features are highly associated with gene expression, and ii) it was entirely based on features extracted exclusively from the 100 bp region upstream from the translational start site demonstrating that this region encodes much of the overall promoter activity. The findings from this study have important implications for the engineering of predictable gene expression systems and the evolution of gene expression in naturally occurring biological systems.\n\nAuthor SummaryGene expression is the first step at which information encoded in DNA is transcribed into RNA. Predicting gene expression from DNA sequence can provide insights into the natural variation of gene expression underlying various phenotypes and direct the engineering of genes of desired activity, for example in industrial processes. While several studies show that gene expression is influenced by DNA sequence. its quantitative prediction from DNA sequence alone remains a challenging problem. Unfortunately, studies aimed at developing quantitative models for gene expression prediction are not directly comparable because most have used distinct data sets for training and evaluation. and many of the methods have not been independently verified. Open innovation challenges in which a problem is posed to a wide community provide a framework for independent verification of the performance of various computational methods using the same benchmark data sets and statistical procedures. Here. we describe the best performing computational model amongst those of 20 other teams in the DREAM6 Gene Expression Prediction challenge. We show that a highly predictive gene expression model can be obtained by an unbiased. data-driven approach that makes little assumption on the role of known mechanisms for gene regulation.

Genomics↗

bioRxiv2017

Conditional Robust Calibration (CRC): a new computational Bayesian methodology for model parameters estimation and identifiability analysis

Computational modeling is a remarkable and common tool to quantitatively describe a biological process. However, most model parameters, such as kinetics parameters, initial conditions and scale factors, are usually unknown because they cannot be directly measured.\n\nTherefore, key issues in Systems Biology are model calibration and identifiability analysis, i.e. estimate parameters from experimental data and assess how well those parameters are determined by the dimension and quality of the data.\n\nCurrently in the Systems Biology and Computational Biology communities, the existing methodologies for parameter estimation are divided in two classes: frequentist methods and Bayesian methods. The first ones are based on the optimization of a cost function while the second ones estimate the posterior distribution of model parameters through different sampling techniques.\n\nIn this work, we present an innovative Bayesian method, called Conditional Robust Calibration (CRC), for model calibration and identifiability analysis. The algorithm is an iterative procedure based on parameter space sampling and on the definition of multiple objective functions related to each output variables. The method estimates step by step the probability density function (pdf) of parameters conditioned to the experimental measures and it returns as output a subset in the parameter space that best reproduce the dataset.\n\nWe apply CRC to six Ordinary Differential Equations (ODE) models with different characteristics and complexity to test its performances compared with profile likelihood (PL) and Approximate Bayesian Computation Sequential Montecarlo (ABC-SMC) approaches. The datasets selected for calibration are time course measurements of different nature: noisy or noiseless, real or in silico.\n\nCompared with PL, our approach finds a more robust solution because parameter identifiability is inferred by conditional pdfs of estimated parameters. Compared with ABC-SMC, we have found a more precise solution with a reduced computational cost.

systems biology↗

bioRxiv2015

Multi -omics and metabolic modelling pipelines: challenges and tools for systems microbiology

Integrated -omics approaches are quickly spreading across microbiology research labs, leading to i) the possibility of detecting previously hidden features of microbial cells like multi-scale spatial organisation and ii) tracing molecular components across multiple cellular functional states. This promises to reduce the knowledge gap between genotype and phenotype and poses new challenges for computational microbiologists. We underline how the capability to unravel the complexity of microbial life will strongly depend on the integration of the huge and diverse amount of information that can be derived today from - omics experiments. In this work, we present opportunities and challenges of multi -omics data integration in current systems biology pipelines. We here discuss which layers of biological information are important for biotechnological and clinical purposes, with a special focus on bacterial metabolism and modelling procedures. A general review of the most recent computational tools for performing large-scale datasets integration is also presented, together with a possible framework to guide the design of systems biology experiments by microbiologists.

Systems Biology↗

bioRxiv2018

Discrete Modeling Dynamical Systems That Determine the Role of Biodiversity in Different Regimes of Using Resources at Different Levels of Organization of Living Matter

The paper aims at mathematical modeling of dynamic systems that determine the role of biodiversity in different modes of resource usage at different levels of the organization of living matter. As a measure of biodiversity, the number of different strategies of the performance of a biological system is used, which differ in ways of usage of the resources by this system. This measure can be supplemented, and in some cases, replaced by the degree of evenness of the intensity of different ways of using resources. As a result of modeling with use of a new class of mathematical models called Discrete Models of Dynamical Systems, the appearance of matrices representing the sets of these strategies corresponding to combinations of values of the systems parameters in columns, strategies observed for the regimes of maximum and limited usage of resources was analyzed. Using the case study related to a local fish population in a pond, it was shown that, in comparison with the regimes of limited use of resources, the regime of maximum usage distinguishes by a larger degree of evenness of the intensities of different ways of using resources by the system. Different size-age groups of the population play the role of resources. A similar result was obtained earlier for different regimes of the performance of the human cardiovascular system; in this case, the heart rate and blood pressure played the role of different ways of resources usage. The similarity of the results obtained for such different biological systems allows us to hope for the prospects of developing universal system approaches to the use of generalized biodiversity parameters for the diagnosis of the state of bioobjects, in particular, with the help of aerospace methods. The necessity of such methods is significantly increasing in the context of global climate change.

systems biology↗

bioRxiv2017

Positive Feedback Between Contractile Ring Myosin and Ring-Directed Cortical Flow Drives Cytokinesis

During cytokinesis, an equatorial actomyosin contractile ring constricts at a relatively constant overall rate despite its progressively decreasing size. Thus, the per-unit-length rate of ring closure increases as ring perimeter decreases. To understand this acceleration, we monitored cortical surface and ring component dynamics during the first division of the C. elegans embryo. We show that the polar cortex expands during ring constriction to provide the cortical surface area required for division. Polar expansion also allows ring myosin to compress cortical surface along the pole-to-pole axis, leading to a continuous flow of cortical surface into the ring. We propose that feedback between ring myosin and compression-driven cortical flow drives an exponential increase in the amount of ring myosin that maintains the high overall closure rate as ring perimeter decreases. We further show that an analytical mathematical formulation of the proposed feedback, called the Compression Feedback model, recapitulates the experimental observations.\n\nIMPACT STATEMENTDuring cytokinesis, positive feedback between myosin motors in the contractile ring and compression-driven cortical flow along the axis perpendicular to the ring drives constriction rate acceleration to ensure timely cell separation.\n\nMAJOR SUBJECT AREASCell biology, Computational and Systems Biology

cell biology↗

bioRxiv2016

A hierarchical Bayesian framework for understanding the spatiotemporal dynamics of the intestinal epithelium

Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cellular migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we develop a probabilistic, hierarchical framework. This framework provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine drawing reliable conclusions - uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. This allows the incorporation of features of both continuum tissue models and discrete cellular models. We perform model checks on both in-sample and out-of-sample datasets and use these checks to illustrate how to test possible model improvements and assess the robustness of our conclusions. This allows us to consider - and ultimately decide against - the need to retain finite-cell-size effects to explain a small misfit appearing in one set of long-time, out-of-sample predictions. Our approach leads us to conclude, for the present set of experiments, that a primarily proliferation-driven model is adequate for predictions over most time-scales. We describe each stage of our framework in detail, and hope that the present work may also serve as a guide for other applications of the hierarchical approach to problems in computational and systems biology more generally.\n\nAuthor SummaryThe intestinal epithelium serves as an important model system for studying the dynamics and regulation of multicellular populations. It is characterised by rapid rates of self-renewal and repair; failure of the regulation of these processes is thought to explain, in part, why many tumours occur in the intestinal and similar epithelial tissues. These features have led to a large amount of work on estimating rate parameters in the intestine. There still remain, however, large gaps between the raw data collected, the experimental interpretation of these data, and speculative mechanistic models for underlying processes. In our view hierarchical statistical modelling provides an ideal, but currently underutilised, method to begin to bridge these gaps. This approach makes essential use of the distinction between measurement, process and parameter models, giving an explicit framework for combining experimental data and mechanistic modelling in the presence of multiple sources of uncertainty. As we illustrate, the hierarchical approach also provides a suitable framework for addressing other methodological questions of broader interest in systems biology: how to systematically relate discrete and continuous mechanistic models; how to formally interpret and visualise statistical evidence; and how to express causal assumptions in terms of conditional independence.

Systems Biology↗