The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately characterise a plethora of biological and chemical processes. However, some mechanisms, such as heterogeneous cellular growth or phenotypic selection at the population level, cannot be represented by the master equation and thus have been tackled separately. In this work, we propose a unifying framework that augments the chemical master equation to capture such auxiliary dynamics, and we develop and analyse a numerical solver that accurately simulates the system dynamics. We showcase these contributions by casting a diverse array of examples from the literature within this framework and applying the solver to both match and extend previous studies. Analytical calculations performed for each example validate our numerical results and benchmark the solver implementation.

Thermodynamics dictates the structure and function of metabolism. Redox reactions drive cellular energy and material flow. Hence, accurately quantifying the thermodynamics of redox reactions should reveal design principles that shape cellular metabolism. However, only few redox potentials have been measured, and mostly with inconsistent experimental setups. Here, we develop a quantum chemistry approach to calculate redox potentials of biochemical reactions and demonstrate our method predicts experimentally measured potentials with unparalleled accuracy. We then calculate the potentials of all redox pairs that can be generated from biochemically relevant compounds and highlight fundamental trends in redox biochemistry. We further address the question of why NAD/NADP are used as primary electron carriers, demonstrating how their physiological potential range fits the reactions of central metabolism and minimizes the concentration of reactive carbonyls. The use of quantum chemistry can revolutionize our understanding of biochemical phenomena by enabling fast and accurate calculation of thermodynamic values.

The study of epithelial morphogenesis is fundamental to increasing our understanding of organ function and disease. Great progress has been made through study of culture systems such as Madin-Darby canine kidney (MDCK) cells, but many aspects of even simple morphogenesis remain unclear. For example, are specific cell actions tightly coupled to the characteristics of the cell's environment or are they more often cell state dependent? How does the single lumen, single cell layer cyst consistently emerge from a variety of cell actions? To improve insight, we instantiated in silico analogues that used hypothesized cell behavior mechanisms to mimic MDCK cystogenesis. We tested them through in vitro experimentation and quantitative validation. We observed novel growth patterns, including a cell behavior shift that began around day five of growth. We created agent-oriented analogues that used the cellular Potts model along with an Iterative Refinement protocol. Following several refinements, we achieved a degree of validation for two separate mechanisms. Both survived falsification and achieved prespecified measures of similarity to cell culture properties. In silico components and mechanisms mapped to in vitro counterparts. In silico, the axis of cell division significantly affects lumen number without changing cell number or cyst size. Reducing the amount of in silico luminal cell death had limited effect on cystogenesis. Simulations provide an observable theory for cystogenesis based on hypothesized, cell-level operating principles.

Chemotactic bacteria form emergent spatial patterns of variable cell density within cultures that are initially spatially uniform. These patterns are the result of chemical gradients that are created from the directed movement and metabolic activity of billions of cells. A recent study on pattern formation in wild bacterial isolates has revealed unique collective behaviors of the bacteria Enterobacter cloacae. As in other bacterial species, Enterobacter cloacae form macroscopic aggregates. Once formed, these bacterial clusters can migrate several millimeters, sometimes resulting in the merging of two or more clusters. To better understand these phenomena, we examine the formation and dynamics of thousands of bacterial clusters that form within a 22 cm square culture dish filled with soft agar over two days. At the macroscale, the aggregates display spatial order at short length scales, and the migration of cell clusters is superdiffusive, with a merging acceleration that is correlated with aggregate size. At the microscale, aggregates are composed of immotile cells surrounded by low density regions of motile cells. The collective movement of the aggregates is the result of an asymmetric flux of bacteria at the boundary. An agent-based model is developed to examine how these phenomena are the result of both chemotactic movement and a change in motility at high cell density. These results identify and characterize a new mechanism for collective bacterial motility driven by a transient, density-dependent change in motility.

Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of cell motion, but whether any of these quantities is physically constrained by the others is poorly understood. Using a combination of theory, simulations, and 3D chemotaxis assays on single metastatic breast cancer cells, we investigate the links among these different aspects of chemotactic performance. In particular, we observe in both experiments and simulations that the chemotactic accuracy, but not the persistence or speed, increases with the gradient strength. We use a random walk model to explain this result and to propose that cells' chemotactic accuracy and persistence are mutually constrained. Our results suggest that key aspects of chemotactic performance are inherently limited regardless of how favorable the environmental conditions are.

Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting behavior of FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data, but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena.

The development of a functional nervous system requires tight control of neurite growth and guidance by extracellular chemical cues. Neurite growth is astonishingly sensitive to shallow concentration gradients, but a widely observed feature of both growth and guidance regulation, with important consequences for development and regeneration, is that both are only elicited over the same relatively narrow range of concentrations. Here we show that all these phenomena can be explained within one theoretical framework. We first test long-standing explanations for the suppression of the trophic effects of nerve growth factor at high concentrations, and find they are contradicted by experiment. Instead we propose a new hypothesis involving inhibitory signalling among the cell bodies, and then extend this hypothesis to show how both growth and guidance can be understood in terms of a common underlying signalling mechanism. This new model for the first time unifies several key features of neurite growth regulation, quantitatively explains many aspects of experimental data, and makes new predictions about unknown details of developmental signalling.

Tumor growth involves a dynamic interplay between cancer cells and host cells, which collectively form a tumor microenvironmental network that either suppresses or promotes tumor growth under different conditions. The transition from tumor suppression to tumor promotion is mediated by a tumor-induced shift in the local immune state, and despite the clinical challenge this shift poses, little is known about how such dysfunctional immune states are initiated. Clinical and experimental observations have indicated that differences in both the composition and spatial distribution of different cell types and/or signaling molecules within the tumor microenvironment can strongly impact tumor pathogenesis and ultimately patient prognosis. How such "functional" and "spatial" heterogeneities confer such effects, however, is not known. To investigate these phenomena at a level currently inaccessible by direct observation, we developed a computational model of a nascent metastatic tumor capturing salient features of known tumor-immune interactions that faithfully recapitulates key features of existing experimental observations. Surprisingly, over a wide range of model formulations, we observed that heterogeneity in both spatial organization and cell phenotype drove the emergence of immunosuppressive network states. We determined that this observation is general and robust to parameter choice by developing a systems-level sensitivity analysis technique, and we extended this analysis to generate other parameter-independent, experimentally testable hypotheses. Lastly, we leveraged this model as an in silico test bed to evaluate potential strategies for engineering cell-based therapies to overcome tumor associated immune dysfunction and thereby identified modes of immune modulation predicted to be most effective. Collectively, this work establishes a new integrated framework for investigating and modulating tumor-immune networks and provides insights into how such interactions may shape early stages of tumor formation.

Competence is a transiently differentiated state that certain bacterial cells reach when faced with a stressful environment. Entrance into competence can be attributed to the excitability of the dynamics governing the genetic circuit that regulates this cellular behavior. Like many biological behaviors, entrance into competence is a stochastic event. In this case cellular noise is responsible for driving the cell from a vegetative state into competence and back. In this work we present a novel numerical method for the analysis of stochastic biochemical events and use it to study the excitable dynamics responsible for competence in Bacillus subtilis. Starting with a Finite State Projection (FSP) solution of the chemical master equation (CME), we develop efficient numerical tools for accurately computing competence probability. Additionally, we propose a new approach for the sensitivity analysis of stochastic events and utilize it to elucidate the robustness properties of the competence regulatory genetic circuit. We also propose and implement a numerical method to calculate the expected time it takes a cell to return from competence. Although this study is focused on an example of cell-differentiation in Bacillus subtilis, our approach can be applied to a wide range of stochastic phenomena in biological systems.

Mechanistic models of biological processes can explain observed phenomena and predict responses to a perturbation. A mathematical model is typically constructed using expert knowledge and informal reasoning to generate a mechanistic explanation for a given observation. Although this approach works well for simple systems with abundant data and well-established principles, quantitative biology is often faced with a dearth of both data and knowledge about a process, thus making it challenging to identify and validate all possible mechanistic hypothesis underlying a system behavior. To overcome these limitations, we introduce a Bayesian multimodel inference (Bayes-MMI) methodology, which quantifies how mechanistic hypotheses can explain a given experimental datasets, and concurrently, how each dataset informs a given model hypothesis, thus enabling hypothesis space exploration in the context of available data. We demonstrate this approach to probe standing questions about heterogeneity, lineage plasticity, and cell-cell interactions in tumor growth mechanisms of small cell lung cancer (SCLC). We integrate three datasets that each formulated different explanations for tumor growth mechanisms in SCLC, apply Bayes-MMI and find that the data supports model predictions for tumor evolution promoted by high lineage plasticity, rather than through expanding rare stem-like populations. In addition, the models predict that in the presence of cells associated with the SCLC-N or SCLC-A2 subtypes, the transition from the SCLC-A subtype to the SCLC-Y subtype through an intermediate is decelerated. Together, these predictions provide a testable hypothesis for observed juxtaposed results in SCLC growth and a mechanistic interpretation for tumor treatment resistance.

Understanding the inherited nature of how biological processes dynamically change over time and exhibit intra- and inter-individual variability, due to the different responses to environmental stimuli and when interacting with other processes, has been a major focus of systems biology. The rise of single-cell fluorescent microscopy has enabled the study of those phenomena. The analysis of single-cell data with mechanistic models offers an invaluable tool to describe dynamic cellular processes and to rationalise cell-to-cell variability within the population. However, extracting mechanistic information from single-cell data has proven difficult. This requires statistical methods to infer unknown model parameters from dynamic, multi-individual data accounting for heterogeneity caused by both intrinsic (e.g. variations in chemical reactions) and extrinsic (e.g. variability in protein concentrations) noise. Although several inference methods exist, the availability of efficient, general and accessible methods that facilitate modelling of single-cell data, remains lacking. Here we present a scalable and flexible framework for Bayesian inference in state-space mixed-effects single-cell models with stochastic dynamic. Our approach infers model parameters when intrinsic noise is modelled by either exact or approximate stochastic simulators, and when extrinsic noise is modelled by either time-varying, or time-constant parameters that vary between cells. We demonstrate the relevance of our approach by studying how cell-to-cell variation in carbon source utilisation affects heterogeneity in the budding yeast Saccharomyces cerevisiae SNF1 nutrient sensing pathway. We identify hexokinase activity as a source of extrinsic noise and deduce that sugar availability dictates cell-to-cell variability.

The rapidly growing amount of publicly available information from biomedical research is readily accessible on the Internet, providing a powerful resource for predictive biomolecular modeling. The accumulated data on experimentally determined structures transformed structure prediction of proteins and protein complexes. Instead of exploring the enormous search space, predictive tools can simply proceed to the solution based on similarity to the existing, previously determined structures. A similar major paradigm shift is emerging due to the rapidly expanding amount of information, other than experimentally determined structures, which still can be used as constraints in biomolecular structure prediction. Automated text mining has been widely used in recreating protein interaction networks, as well as in detecting small ligand binding sites on protein structures. Combining and expanding these two well-developed areas of research, we applied the text mining to structural modeling of protein-protein complexes (protein docking). Protein docking can be significantly improved when constraints on the docking mode are available. We developed a procedure that retrieves published abstracts on a specific protein-protein interaction and extracts information relevant to docking. The procedure was assessed on protein complexes from Dockground (http://dockground.compbio.ku.edu). The results show that correct information on binding residues can be extracted for about half of the complexes. The amount of irrelevant information was reduced by conceptual analysis of a subset of the retrieved abstracts, based on the bag-of-words (features) approach. Support Vector Machine models were trained and validated on the subset. The remaining abstracts were filtered by the best-performing models, which decreased the irrelevant information for ~ 25% complexes in the dataset. The extracted constraints were incorporated in the docking protocol and tested on the Dockground unbound benchmark set, significantly increasing the docking success rate.

Microbiomes are complex ecological systems that play crucial roles in understanding natural phenomena from human disease to climate change. Especially in human gut microbiome studies, where collecting clinical samples can be arduous, the number of taxa considered in any one study often exceeds the number of samples ten to one hundred-fold. This discrepancy decreases the power of studies to identify meaningful differences between samples, increases the likelihood of false positive results, and subsequently limits reproducibility. Despite the vast collections of microbiome data already available, biome-specific patterns of microbial structure are not currently leveraged to inform studies. Here, we derive microbiome-level properties by applying an embedding algorithm to quantify taxon co-occurrence patterns in over 18,000 samples from the American Gut Project (AGP) microbiome crowdsourcing effort. We then compare the predictive power of models trained using properties, normalized taxonomic count data, and another commonly used dimensionality reduction method, Principal Component Analysis in categorizing samples from individuals with inflammatory bowel disease (IBD) and healthy controls. We show that predictive models trained using property data are the most accurate, robust, and generalizable, and that property-based models can be trained on one dataset and deployed on another with positive results. Furthermore, we find that properties correlate significantly with known metabolic pathways. Using these properties, we are able to extract known and new bacterial metabolic pathways associated with inflammatory bowel disease across two completely independent studies. By providing a set of pre-trained embeddings, we allow any V4 16S amplicon study to apply the publicly informed properties to increase the statistical power, reproducibility, and generalizability of analysis.