Agent-Based Modeling of Intracellular Transport

We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of vesicles follows a log-normal distribution that changes over time due to fusion processes, their spatial distribution gives rise to distinct patterns. Their occurrence depends on the concentration of proteins which are synthesized based on the transcriptional activities of some genes. Hence, differences in these spatio-temporal vesicle patterns allow indirect conclusions about the (unknown) impact of these genes. By means of agent-based computer simulations we are able to reproduce such patterns on real temporal and spatial scales. Our modeling approach is based on Brownian agents with an internal degree of freedom, $\theta$, that represents the different modes of motion. Conditions inside the cell are modeled by an effective potential that differs for agents dependent on their value $\theta$. Agent's motion in this effective potential is modeled by an overdampted Langevin equation, changes of $\theta$ are modeled as stochastic transitions with values obtained from experiments, and fusion events are modeled as space-dependent stochastic transitions. Our results for the spatio-temporal vesicle patterns can be used for a statistical comparison with experiments. We also derive hypotheses of how the silencing of some genes may affect the intracellular transport, and point to generalizations of the model

Agent-based modeling of intracellular transport

We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of vesicles follows a log-normal distribution that changes over time due to fusion processes, their spatial distribution gives rise to distinct patterns. Their occurrence depends on the concentration of proteins which are synthesized based on the transcriptional activities of some genes. Hence, differences in these spatio-temporal vesicle patterns allow indirect conclusions about the (unknown) impact of these genes. By means of agent-based computer simulations we are able to reproduce such patterns on real temporal and spatial scales. Our modeling approach is based on Brownian agents with an internal degree of freedom, θ, that represents the different modes of motion. Conditions inside the cell are modeled by an effective potential that differs for agents dependent on their value θ. Agent's motion in this effective potential is modeled by an overdampted Langevin equation, changes of θ are modeled as stochastic transitions with values obtained from experiments, and fusion events are modeled as space-dependent stochastic transitions. Our results for the spatio-temporal vesicle patterns can be used for a statistical comparison with experiments. We also derive hypotheses of how the silencing of some genes may affect the intracellular transport, and point to generalizations of the mode

Multi-Scale Modeling and Simulation of Cell Signaling and Transport in Renal Collecting Duct Principal Cells

The response of cells to their environment is driven by a variety of proteins and messenger molecules. In eukaryotes, their distribution and location in the cell is regulated by the vesicular transport system. The transport of aquaporin 2 between membrane and storage region is a crucial part of the water reabsorption in renal principal cells, and its malfunction can lead to Diabetes insipidus. To understand the regulation of this system, I aggregated pathways and mechanisms from literature and derived models in a hypothesis-driven approach. Furthermore, I combined the models to a single multi-scale model to gain insight into key regulatory mechanisms of aquaporin 2 recycling. To achieve this, I developed a computational framework for the modeling and simulation of cellular signaling systems. The framework integrates reaction and difusion of biochemical entities on a microscopic scale with mobile vesicles, membranes, and compartments on a cellular level. The simulation uses an adaptive step-width approach that e ciently regulates the agent-based simulation of macroscopic components with the numerical integration of mass action kinetics and grid-based nite diference methods. A reaction network generation algorithm was designed, that, in combination with a highly-modular modeling approach, allows for fast model prototyping. The analysis of the aquaporin 2 model system rationalizes that the compartmentalization of cAMP in renal principal cells is a result of the protein kinase A signalosome and can only occur if speci c cellular components are observed in conjunction. Endocytotic and exocytotic processes are inherently connected and can be regulated by the same protein kinase A signal.:Abstract 1. Introduction 1.1. Eukaryotic Signaling 1.2. Modeling and Simulation of Cellular Processes 1.3. Aquaporin 2 recycling 1.4. Motivation and Aims 1.5. Outline I. Background 2. Modeling and Simulation of Complex Signaling Pathways 2.1. Multi-scale Modeling 2.1.1. Approaches to Multi-scale Modeling 2.1.2. Reduction of Computational Complexity 2.2. Models of Chemical Reaction Networks 2.2.1. Reactions and Reaction Rates 2.2.2. Numerical Solutions 2.2.3. Reaction Network Generation 2.3. Models of Intracellular Transport 2.3.1. Undirected Transport 2.3.2. Directed Transport 3. Aquaporin 2 Recycling in Renal Principal Cells 3.1. The Physiology of Water Homeostasis 3.2. Molecular Mechanisms of the Vasopressin Response 3.2.1. The Vasopressin Receptor 3.2.2. cAMP Regulation of Protein Kinase A 3.2.3. Endo- and Exocytosis 3.3. Models of Water Transport in Renal Principal Cells II. Results & Discussion 4. Multi-scale Simulation of Cellular Signaling Pathways 4.1. Scale Separation and Bridging 4.2. Micro-scale Simulation Approach 4.2.1. Difusion and Discretization of the Simulation Space 4.2.2. Reaction Kinetics 4.3. Rule-based Reaction Network Generation 4.3.1. Definition of the Data Model 4.3.2. Design of Rule Based Reactions 4.3.3. Automated Generation of Reaction Networks 4.4. Macro-scale Simulation Approach 4.4.1. Agent-based Simulation of Discrete Entities 4.4.2. Modules for Displacement-based Behavior 4.5. Modularization and Error Estimation 4.5.1. Determination of the Numerical Error 4.5.2. Modularization of Concentration-based Events 4.5.3. Determination of the Displacement-based Error 5. Aquaporin 2 Recycling Model and Simulation 5.1. Model of Allosteric PKA Phosphorylation 5.1.1. Model Design 5.1.2. Simulation Results and Discussion 5.1.3. Conclusions 5.2. cAMP Compartmentalization in the Vesicle Storage Region 5.2.1. Model Design 5.2.2. Simulation Results and Discussion 5.2.3. Conclusions 5.3. Clathrin-mediated Endocytosis 5.3.1. Model Design 5.3.2. Simulation Results and Discussion 5.3.3. Conclusions 5.4. Intracellular Transport and Recycling 5.4.1. Model Design 5.4.2. Simulation Results and Discussion 6. Conclusion 6.1. Modeling and simulation approach 6.2. Insights into the AQP2 recycling model III. Appendix A. Code Availability B. Module Overview Bibliograph

Investigating biocomplexity through the agent-based paradigm.

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Agent-based computational modeling of wounded epithelial cell monolayers

Computational modeling of biological systems, or ‘in silico biology’ is an emerging tool for understanding structure and order in biological tissues. Computational models of the behavior of epithelial cells in monolayer cell culture have been developed and used to predict the healing characteristics of scratch wounds made to urothelial cell cultures maintained in low and physiological [Ca2+] environments. Both computational models and in vitro experiments demonstrated that in low exogenous [Ca2+], the closure of 500mm scratch wounds was achieved primarily by cell migration into the denuded area. The wound healing rate in low (0.09mM) [Ca2+] was approximately twice as rapid as in physiological (2mM) [Ca2+]. Computational modeling predicted that in cell cultures that are actively proliferating, no increase in the fraction of cells in S-phase would be expected, and this conclusion was supported experimentally in vitro by BrdU incorporation assay. We have demonstrated that a simple rule-based model of cell behavior, incorporating rules relating to contact inhibition of proliferation and migration, is sufficient to qualitatively predict the calcium-dependent pattern of wound closure observed in vitro. Differences between the in vitro and in silico models suggest a role for wound-induced signaling events in urothelial cell cultures