Accounting for Diffusion in Agent Based Models of Reaction-Diffusion Systems with Application to Cytoskeletal Diffusion

Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the diffusion of molecules and macromolecules in three-dimensional solutions using agent based modeling. This method allows for realistic modeling of a system of particles with different properties such as size, diffusion coefficients, and affinity as well as the environment properties such as viscosity and geometry. Simulations using these movement probabilities yield behavior that mimics natural diffusion. Using this modeling framework, we simulate the effects of molecular crowding on effective diffusion and have validated the results of our model using Langevin dynamics simulations and note that they are in good agreement with previous experimental data. Furthermore, we investigate an extension of this framework where single discrete cells can contain multiple particles of varying size in an effort to highlight errors that can arise from discretization that lead to the unnatural behavior of particles undergoing diffusion. Subsequently, we explore various algorithms that differ in how they handle the movement of multiple particles per cell and suggest an algorithm that properly accommodates multiple particles of various sizes per cell that can replicate the natural behavior of these particles diffusing. Finally, we use the present modeling framework to investigate the effect of structural geometry on the directionality of diffusion in the cell cytoskeleton with the observation that parallel orientation in the structural geometry of actin filaments of filopodia and the branched structure of lamellipodia can give directionality to diffusion at the filopodia-lamellipodia interface

An Agent-Based Model of Cryoprotectant Equilibration in Secondary Stage Preantral Ovarian Follicles

Young cancer patients have limited options for fertility treatment when facing gonadotoxic treatment. One promising fertility treatment for young cancer patients is the cryopreservation of immature ovarian follicles followed by maturation and subsequent reimplantation. However, preantral ovarian follicles currently have lower post-thaw success rates compared to mature oocytes and embryos. Previous research suggests that damage to vital intercellular connections, Transzonal Projections (TZPs), occurs during the cryopreservation process and may account for the observed lower post-thaw success rate in this tissue. It is likely that cryoprotective agent (CPA) equilibration is the cryopreservation step during which TZP damage occurs. Constructing a biologically relevant model of CPA equilibration and the associated damage may allow for improved protocols as measured by increased post-thaw success rates. Agent-based models are a promising technique to capture steps in the cryopreservation process, such as CPA equilibration. In this thesis, I conducted a series of experiments with typical CPAs and nonpermeating solutes at different temperatures using preantral ovarian follicles from a non-human primate (Rhesus monkeys) to measure TZP damage. In these experiments, I also estimated relevant permeability parameters within the tissue. I found that the majority of TZP damage was likely the result of mechanical forces that occurred during the cell volume reduction phase of CPA equilibration. Furthermore, through these experiments, I demonstrate that for this tissue type, parameters collected either during monolayer or single-cell experiments can be used to construct full tissue models. Using the derived experimental parameters and available literature values, I constructed and validated a 3-D agent-based model to capture CPA equilibration in preantral ovarian follicles. My agent-based model utilizes parallel computing on an average desktop computer and allows for the rapid design and testing of CPA equilibration protocols. The model I constructed can account for both mechanical and toxic damage. Importantly, my model accurately captures the experimental damage to TZPs in the majority of simulations. Lastly, I propose several theoretically improved cryopreservation protocols for preantral ovarian follicles. The research presented in this thesis demonstrates that agent-based models can be utilized to capture steps in the cryopreservation in silico and represents a non-invasive, less costly means to test and improve CPA equilibration protocols

Rule Derivation for Agent-Based Models of Complex Systems: Nuclear Waste Management and Road Networks Case Studies

This thesis explores the relation between equation-based models (EBMs) and agent-based models (ABMs), in particular, the derivation of agent rules from equations such that agent collective behavior produces results that match or are close to those from EBMs. This allows studying phenomena using both approaches and obtaining an understanding of the aggregate behavior as well as the individual mechanisms that produce them. The use of ABMs allows the inclusion of more realistic features that would not be possible (or would be difficult to include) using EBMs. The first part of the thesis studies the derivation of molecule displacement probabilities from the diffusion equation using cellular automata. The derivation is extended to include reaction and advection terms. This procedure is later applied to estimate lifetimes of nuclear waste containers for various scenarios of interest and the inclusion of uncertainty. The second part is concerned with the derivation of a Bayesian state algorithm that consolidates collective real-time information about the state of a given system and outputs a probability density function of state domain, from which the most probable state can be computed at any given time. This estimation is provided to agents so that they can choose the best option for them. The algorithm includes a diffusion or diffusion-like term to account for the deterioration of information as time goes on. This algorithm is applied to a couple of road networks where drivers, prior to selecting a route, have access to current information about the traffic and are able to decide which path to follow. Both problems are complex due to heterogeneous components, nonlinearities, and stochastic behavior; which make them difficult to describe using classical equation models such as the diffusion equation or optimization models. The use of ABMs allowed for the inclusion of such complex features in the study of their respective systems

Transfer of Antibiotic Resistance in Enterococcus faecalis. Modeling and Computational Study

Bacteria of the genus Enterococcus, commonly found in the intestinal tract, are the main cause of antibiotic-resistant infections that are acquired in hospitals[1], [2]. Donor cells that contain plasmid pCF10 have the ability to resist to antibiotics and are capable of transferring this plasmid to recipient cells. This transfer occurs via a rapid horizontal inducible conjugation regulated by peptide-mediated cell-cell signaling molecules (quorum sensing), known as cCF10 and iCF10. This quorum sensing system functions by producing low levels of an inducing substance that accumulates in the environments until a threshold is reached, at which point there is a change in cellular behavior. Cells of this type can either exist in the free floating form or in biofilms, which are composed of cells attached on biotic and abiotic surfaces. Complexity of the biofilm structure hinders and affects the exposures of cells to antibiotics and hence reduces treatment efficacy. Successful models of this mechanism can lead to useful techniques/methods in controlling or interfering with the plasmid transfer. Several efforts to model this phenomenon have been initiated and developed by our group in recent years. Recently, the collaborative experimental group in University of Minnesota has discovered new mechanisms that are associated with the system. This discover invalidates previous assumptions and hence requires modifications on both reactions and modeling assumptions. Moreover, various variables in the system have shown stiff behaviors that are much more challenging to work with. Explicit SDE, used in previous system, can be no longer capable of obtaining accurate solutions. For these reasons, this thesis presents new updated strategies to capture the drug resistance transfer in both Planktonic and biofilm environments. Since the two systems are inherently different in structure and physics, usage of varied modeling formulations for each environment is inevitable. Deterministic models are very simple and can be used to acquire a rough prediction of Planktonic environment. However, their simplicity also limits their capability of capturing large complex systems such as biofilms and other highly heterogeneous systems. Unfortunately, stochastic models can also carry a huge burden on CPU time. Therefore, another part of this thesis is dedicated to illustrate techniques, which can be used to reduce stochastic simulation time without losing accuracy. Successfully solving these two major problems together can potentially serve as a tool to gain knowledge about the system and eventually develop methods to treat/control this phenomenon

Mathematical models of cellular signaling and supramolecular self-assembly

Synthetic biologists endeavor to predict how the increasing complexity of multi-step signaling cascades impacts the fidelity of molecular signaling, whereby cellular state information is often transmitted with proteins diffusing by a pseudo-one-dimensional stochastic process. We address this problem by using a one-dimensional drift-diffusion model to derive an approximate lower bound on the degree of facilitation needed to achieve single-bit informational efficiency in signaling cascades as a function of their length. We find that a universal curve of the Shannon-Hartley form describes the information transmitted by a signaling chain of arbitrary length and depends upon only a small number of physically measurable parameters. This enables our model to be used in conjunction with experimental measurements to aid in the selective design of biomolecular systems. Another important concept in the cellular world is molecular self-assembly. As manipulating the self-assembly of supramolecular and nanoscale constructs at the single-molecule level increasingly becomes the norm, new theoretical scaffolds must be erected to replace the classical thermodynamic and kinetics-based models. The models we propose use state probabilities as its fundamental objects and directly model the transition probabilities between the initial and final states of a trajectory. We leverage these probabilities in the context of molecular self-assembly to compute the overall likelihood that a specified experimental condition leads to a desired structural outcome. We also investigated a larger complex self-assembly system, the heterotypic interactions between amyloid-beta and fatty acids by an independent ensemble kinetic simulation using an underlying differential equation-based system which was validated by biophysical experiments

Multicellular Systems Biology of Development

Embryonic development depends on the precise coordination of cell fate specification, patterning and morphogenesis. Although great strides have been made in the molecular understanding of each of these processes, how their interplay governs the formation of complex tissues remains poorly understood. New techniques for experimental manipulation and image quantification enable the study of development in unprecedented detail, resulting in new hypotheses on the interactions between known components. By expressing these hypotheses in terms of rules and equations, computational modeling and simulation allows one to test their consistency against experimental data. However, new computational methods are required to represent and integrate the network of interactions between gene regulation, signaling and biomechanics that extend over the molecular, cellular and tissue scales. In this thesis, I present a framework that facilitates computational modeling of multiscale multicellular systems and apply it to investigate pancreatic development and the formation of vascular networks. This framework is based on the integration of discrete cell-based models with continuous models for intracellular regulation and intercellular signaling. Specifically, gene regulatory networks are represented by differential equations to analyze cell fate regulation; interactions and distributions of signaling molecules are modeled by reaction-diffusion systems to study pattern formation; and cell-cell interactions are represented in cell-based models to investigate morphogenetic processes. A cell-centered approach is adopted that facilitates the integration of processes across the scales and simultaneously constrains model complexity. The computational methods that are required for this modeling framework have been implemented in the software platform Morpheus. This modeling and simulation environment enables the development, execution and analysis of multi-scale models of multicellular systems. These models are represented in a new domain-specific markup language that separates the biological model from the computational methods and facilitates model storage and exchange. Together with a user-friendly graphical interface, Morpheus enables computational modeling of complex developmental processes without programming and thereby widens its accessibility for biologists. To demonstrate the applicability of the framework to problems in developmental biology, two case studies are presented that address different aspects of the interplay between cell fate specification, patterning and morphogenesis. In the first, I focus on the interplay between cell fate stability and intercellular signaling. Specifically, two studies are presented that investigate how mechanisms of cell-cell communication affect cell fate regulation and spatial patterning in the pancreatic epithelium. Using bifurcation analysis and simulations of spatially coupled differential equations, it is shown that intercellular communication results in a multistability of gene expression states that can explain the scattered spatial distribution and low cell type ratio of nascent islet cells. Moreover, model analysis shows that disruption of intercellular communication induces a transition between gene expression states that can explain observations of in vitro transdifferentiation from adult acinar cells into new islet cells. These results emphasize the role of the multicellular context in cell fate regulation during development and may be used to optimize protocols for cellular reprogramming. The second case study focuses on the feedback between patterning and morphogenesis in the context of the formation of vascular networks. Integrating a cell-based model of endothelial chemotaxis with a reaction-diffusion model representing signaling molecules and extracellular matrix, it is shown that vascular network patterns with realistic morphometry can arise when signaling factors are retained by cell-modified matrix molecules. Through the validation of this model using in vitro assays, quantitative estimates are obtained for kinetic parameters that, when used in quantitative model simulations, confirm the formation of vascular networks under measured biophysical conditions. These results demonstrate the key role of the extracellular matrix in providing spatial guidance cues, a fact that may be exploited to enhance vascularization of engineered tissues. Together, the modeling framework, software platform and case studies presented in this thesis demonstrate how cell-centered computational modeling of multi-scale and multicellular systems provide powerful tools to help disentangle the complex interplay between cell fate specification, patterning and morphogenesis during embryonic development

Simulations and Modelling for Biological Invasions

Biological invasions are characterized by the movement of organisms from their native geographic region to new, distinct regions in which they may have significant impacts. Biological invasions pose one of the most serious threats to global biodiversity, and hence significant resources are invested in predicting, preventing, and managing them. Biological systems and processes are typically large, complex, and inherently difficult to study naturally because of their immense scale and complexity. Hence, computational modelling and simulation approaches can be taken to study them. In this dissertation, I applied computer simulations to address two important problems in invasion biology. First, in invasion biology, the impact of genetic diversity of introduced populations on their establishment success is unknown. We took an individual-based modelling approach to explore this, leveraging an ecosystem simulation called EcoSim to simulate biological invasions. We conducted reciprocal transplants of prey individuals across two simulated environments, over a gradient of genetic diversity. Our simulation results demonstrated that a harsh environment with low and spatially-varying resource abundance mediated a relationship between genetic diversity and short-term establishment success of introduced populations rather than the degree of difference between native and introduced ranges. We also found that reducing Allee effects by maintaining compactness, a measure of spatial density, was key to the establishment success of prey individuals in EcoSim, which were sexually reproducing. Further, we found evidence of a more complex relationship between genetic diversity and long-term establishment success, assuming multiple introductions were occurring. Low-diversity populations seemed to benefit more strongly from multiple introductions than high-diversity populations. Our results also corroborated the evolutionary imbalance hypothesis: the environment that yielded greater diversity produced better invaders and itself was less invasible. Finally, our study corroborated a mechanical explanation for the evolutionary imbalance hypothesis – the populations evolved in a more intense competitive environment produced better invaders. Secondly, an important advancement in invasion biology is the use of genetic barcoding or metabarcoding, in conjunction with next-generation sequencing, as a potential means of early detection of aquatic introduced species. Barcoding and metabarcoding invariably requires some amount of computational DNA sequence processing. Unfortunately, optimal processing parameters are not known in advance and the consequences of suboptimal parameter selection are poorly understood. We aimed to determine the optimal parameterization of a common sequence processing pipeline for both early detection of aquatic nonindigenous species and conducting species richness assessments. We then aimed to determine the performance of optimized pipelines in a simulated inoculation of sequences into community samples. We found that early detection requires relatively lenient processing parameters. Further, optimality depended on the research goal – what was optimal for early detection was suboptimal for estimating species richness and vice-versa. Finally, with optimal parameter selection, fewer than 11 target sequences were required in order to detect 90% of nonindigenous species