Cellular automata modelling of biomolecular networks dynamics

Agent-based approaches for biological modeling in oncology: A literature review

CONTEXT

Computational modeling involves the use of computer simulations and models to study and understand real-world phenomena. Its application is particularly relevant in the study of potential interactions between biological elements. It is a promising approach to understand complex biological processes and predict their behavior under various conditions.

METHODOLOGY

This paper is a review of the recent literature on computational modeling of biological systems. Our study focuses on the field of oncology and the use of artificial intelligence (AI) and, in particular, agent-based modeling (ABM), between 2010 and May 2023.

RESULTS

Most of the articles studied focus on improving the diagnosis and understanding the behaviors of biological entities, with metaheuristic algorithms being the models most used. Several challenges are highlighted regarding increasing and structuring knowledge about biological systems, developing holistic models that capture multiple scales and levels of organization, reproducing emergent behaviors of biological systems, validating models with experimental data, improving computational performance of models and algorithms, and ensuring privacy and personal data protection are discussed.

Cellular Automata in Chemistry and Chemical Engineering

We review the modern state of cellular automata (CA) applications for solving practical problems in chemistry and chemical technology. We consider the problems of material structure modeling and prediction of materials' morphology-dependent properties. We review the use of the CA approach for modeling diffusion, crystallization, dissolution, erosion, corrosion, adsorption, and hydration processes. We also consider examples of hybrid CA-based models, which are combinations of various CA with other computational approaches and modeling methods. Finally, we discuss the use of high-performance parallel computing to increase the efficiency of CA.

Mathematical modeling and cellular automata simulation of infectious disease dynamics: Applications to the understanding of herd immunity

The complexity associated with an epidemic defies any quantitatively reliable predictive theoretical scheme. Here, we pursue a generalized mathematical model and cellular automata simulations to study the dynamics of infectious diseases and apply it in the context of the COVID-19 spread. Our model is inspired by the theory of coupled chemical reactions to treat multiple parallel reaction pathways. We essentially ask the question: how hard could the time evolution toward the desired herd immunity (HI) be on the lives of people? We demonstrate that the answer to this question requires the study of two implicit functions, which are determined by several rate constants, which are time-dependent themselves. Implementation of different strategies to counter the spread of the disease requires a certain degree of a quantitative understanding of the time-dependence of the outcome. Here, we compartmentalize the susceptible population into two categories, (i) vulnerables and (ii) resilients (including asymptomatic carriers), and study the dynamical evolution of the disease progression. We obtain the relative fatality of these two sub-categories as a function of the percentages of the vulnerable and resilient population and the complex dependence on the rate of attainment of herd immunity. We attempt to study and quantify possible adverse effects of the progression rate of the epidemic on the recovery rates of vulnerables, in the course of attaining HI. We find the important result that slower attainment of the HI is relatively less fatal. However, slower progress toward HI could be complicated by many intervening factors.

Trends in mathematical modeling of host-pathogen interactions

Pathogenic microorganisms entail enormous problems for humans, livestock, and crop plants. A better understanding of the different infection strategies of the pathogens enables us to derive optimal treatments to mitigate infectious diseases or develop vaccinations preventing the occurrence of infections altogether. In this review, we highlight the current trends in mathematical modeling approaches and related methods used for understanding host-pathogen interactions. Since these interactions can be described on vastly different temporal and spatial scales as well as abstraction levels, a variety of computational and mathematical approaches are presented. Particular emphasis is placed on dynamic optimization, game theory, and spatial modeling, as they are attracting more and more interest in systems biology. Furthermore, these approaches are often combined to illuminate the complexities of the interactions between pathogens and their host. We also discuss the phenomena of molecular mimicry and crypsis as well as the interplay between defense and counter defense. As a conclusion, we provide an overview of method characteristics to assist non-experts in their decision for modeling approaches and interdisciplinary understanding.

Looking "Under the Hood" of Cellular Mechanotransduction with Computational Tools: A Systems Biomechanics Approach across Multiple Scales

Signal modulation has been developed in living cells throughout evolution to promote utilizing the same machinery for multiple cellular functions. Chemical and mechanical modules of signal transmission and transduction are interconnected and necessary for organ development and growth. However, due to the high complexity of the intercommunication of physical intracellular connections with biochemical pathways, there are many missing details in our overall understanding of mechanotransduction processes, i.e., the process by which mechanical signals are converted to biochemical cascades. Cell-matrix adhesions are mechanically coupled to the nucleus through the cytoskeleton. This modulated and tightly integrated network mediates the transmission of mechanochemical signals from the extracellular matrix to the nucleus. Various experimental and computational techniques have been utilized to understand the basic mechanisms of mechanotransduction, yet many aspects have remained elusive. Recently, in silico experiments have made important contributions to the field of mechanobiology. Herein, computational modeling efforts devoted to understanding integrin-mediated mechanotransduction pathways are reviewed, and an outlook is presented for future directions toward using suitable computational approaches and developing novel techniques for addressing important questions in the field of mechanotransduction.

Regulation of RNA-binding proteins affinity to export receptors enables the nuclear basket proteins to distinguish and retain aberrant mRNAs

Export of messenger ribonucleic acids (mRNAs) into the cytoplasm is a fundamental step in gene regulation processes, which is meticulously quality controlled by highly efficient mechanisms in eukaryotic cells. Yet, it remains unclear how the aberrant mRNAs are recognized and retained inside the nucleus. Using a new modelling approach for complex systems, namely the agent-based modelling (ABM) approach, we develop a minimal model of the mRNA quality control (QC) mechanism. Our results demonstrate that regulation of the affinity of RNA-binding proteins (RBPs) to export receptors along with the weak interaction between the nuclear basket protein (Mlp1 or Tpr) and RBPs are the minimum requirements to distinguish and retain aberrant mRNAs. Our results show that the affinity between Tpr and RBPs is optimized to maximize the retention of aberrant mRNAs. In addition, we demonstrate how the length of mRNA affects the QC process. Since longer mRNAs spend more time in the nuclear basket to form a compact conformation and initiate their export, nuclear basket proteins could more easily capture and retain them inside the nucleus.

An agent-based model for mRNA export through the nuclear pore complex

On the basis of previously published biophysical and biochemical parameters of mRNA export, a three-dimensional, coarse-grained, agent-based model is developed for the study and characterization of mRNA nucleocytoplasmic export.

mRNA export from the nucleus is an essential step in the expression of every protein- coding gene in eukaryotes, but many aspects of this process remain poorly understood. The density of export receptors that must bind an mRNA to ensure export, as well as how receptor distribution affects transport dynamics, is not known. It is also unclear whether the rate-limiting step for transport occurs at the nuclear basket, in the central channel, or on the cytoplasmic face of the nuclear pore complex. Using previously published biophysical and biochemical parameters of mRNA export, we implemented a three-dimensional, coarse-grained, agent-based model of mRNA export in the nanosecond regime to gain insight into these issues. On running the model, we observed that mRNA export is sensitive to the number and distribution of transport receptors coating the mRNA and that there is a rate-limiting step in the nuclear basket that is potentially associated with the mRNA reconfiguring itself to thread into the central channel. Of note, our results also suggest that using a single location-monitoring mRNA label may be insufficient to correctly capture the time regime of mRNA threading through the pore and subsequent transport. This has implications for future experimental design to study mRNA transport dynamics.

Higher nucleoporin-Importinβ affinity at the nuclear basket increases nucleocytoplasmic import

Several in vitro studies have shown the presence of an affinity gradient in nuclear pore complex proteins for the import receptor Importinβ, at least partially contributing to nucleocytoplasmic transport, while others have historically argued against the presence of such a gradient. Nonetheless, the existence of an affinity gradient has remained an uncharacterized contributing factor. To shed light on the affinity gradient theory and better characterize how the existence of such an affinity gradient between the nuclear pore and the import receptor may influence the nucleocytoplasmic traffic, we have developed a general-purpose agent based modeling (ABM) framework that features a new method for relating rate constants to molecular binding and unbinding probabilities, and used our ABM approach to quantify the effects of a wide range of forward and reverse nucleoporin-Importinβ affinity gradients. Our results indicate that transport through the nuclear pore complex is maximized with an effective macroscopic affinity gradient of 2000 µM, 200 µM and 10 µM in the cytoplasmic, central channel and nuclear basket respectively. The transport rate at this gradient is approximately 10% higher than the transport rate for a comparable pore lacking any affinity gradient, which has a peak transport rate when all nucleoporins have an affinity of 200 µM for Importinβ. Furthermore, this optimal ratio of affinity gradients is representative of the ratio of affinities reported for the yeast nuclear pore complex – suggesting that the affinity gradient seen in vitro is highly optimized.

Molecular bioelectricity in developmental biology: new tools and recent discoveries: control of cell behavior and pattern formation by transmembrane potential gradients

Significant progress in the molecular investigation of endogenous bioelectric signals during pattern formation in growing tissues has been enabled by recently developed techniques. Ion flows and voltage gradients produced by ion channels and pumps are key regulators of cell proliferation, migration, and differentiation. Now, instructive roles for bioelectrical gradients in embryogenesis, regeneration, and neoplasm are being revealed through the use of fluorescent voltage reporters and functional experiments using well-characterized channel mutants. Transmembrane voltage gradients (V(mem) ) determine anatomical polarity and function as master regulators during appendage regeneration and embryonic left-right patterning. A state-of-the-art recent study reveals that they can also serve as prepatterns for gene expression domains during craniofacial patterning. Continued development of novel tools and better ways to think about physical controls of cell-cell interactions will lead to mastery of the morphogenetic information stored in physiological networks. This will enable fundamental advances in basic understanding of growth and form, as well as transformative biomedical applications in regenerative medicine.

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.

ADAM: analysis of discrete models of biological systems using computer algebra

BACKGROUND

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed.

RESULTS

We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second.

CONCLUSIONS

Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

ADAM: analysis of discrete models of biological systems using computer algebra

Background

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed.

Results

We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second.

Conclusions

Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

Mathematical modelling of the mitochondrial apoptosis pathway

Mitochondria are pivotal for cellular bioenergetics, but are also a core component of the cell death machinery. Hypothesis-driven research approaches have greatly advanced our understanding of the role of mitochondria in cell death and cell survival, but traditionally focus on a single gene or specific signalling pathway at a time. Predictions originating from these approaches become limited when signalling pathways show increased complexity and invariably include redundancies, feedback loops, anisotropies or compartmentalisation. By introducing methods from theoretical chemistry, control theory, and biophysics, computational models have provided new quantitative insights into cell decision processes and have led to an increased understanding of the key regulatory principles of apoptosis. In this review, we describe the currently applied modelling approaches, discuss the suitability of different modelling techniques, and evaluate their contribution to the understanding of the mitochondrial apoptosis pathway. This article is part of a Special Issue entitled Mitochondria: the deadly organelle.

Internet resources for agent-based modelling

The use of agent-based models (ABMs) is steadily increasing in all the disciplines including environmental chemistry and toxicology. This growth is mainly driven by their ability to address problems that conventional modelling techniques cannot, such as the change of scale or the emergence of unanticipated phenomena resulting from interactions between their constitutive goal-directed agents. After a brief introduction on the basic principles of agent-based modelling and the presentation of selected case studies, the main software resources available on the Internet are presented. An attempt is made to estimate the complexity of these tools versus their potentialities and flexibility.