Computational modeling of the EGF-receptor system: a paradigm for systems biology

Computational models have rarely been used as tools by biologists but, when models provide experimentally testable predictions, they can be extremely useful. The epidermal growth factor receptor (EGFR) is probably the best-understood receptor system, and computational models have played a significant part in its elucidation. For many years, models have been used to analyze EGFR dynamics and to interpret mutational studies, and are now being used to understand processes including signal transduction, autocrine loops and developmental patterning. The success of EGFR modeling can be a guide to combining models and experiments productively to understand complex biological processes as integrated systems.     

Multiscale modeling of twitch contractions in cardiac trabeculae

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca²⁺ transient, thin-filament activation, and the myosin–actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca²⁺ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length–tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.     

Studies of folding and misfolding using simplified models

Computer simulations are as vital to our studies of biological systems as experiments. They bridge and rationalize experimental observations, extend the experimental "field of view", which is often limited to a specific time or length scale, and, most importantly, provide novel insights into biological systems, offering hypotheses about yet-to-be uncovered phenomena. These hypotheses spur further experimental discoveries. Simplified molecular models have a special place in the field of computational biology. Branded as less accurate than all-atom protein models, they have offered what all-atom molecular dynamics simulations could not--the resolution of the length and time scales of biological phenomena. Not only have simplified models proven to be accurate in explaining or reproducing several biological phenomena, they have also offered a novel multiscale computational strategy for accessing a broad range of time and length scales upon integration with traditional all-atom simulations. Recent computer simulations of simplified models have shaken or advanced the established understanding of biological phenomena. It was demonstrated that simplified models can be as accurate as traditional molecular dynamics approaches in identifying native conformations of proteins. Their application to protein structure prediction yielded phenomenal accuracy in recapitulating native protein conformations. New studies that utilize the synergy of simplified protein models with all-atom models and experiments yielded novel insights into complex biological processes, such as protein folding, aggregation and the formation of large protein complexes.     

Spreading dynamics on complex networks: a general stochastic approach

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.     

Verification, validation and sensitivity studies in computational biomechanics

Computational techniques and software for the analysis of problems in mechanics have naturally moved from their origins in the traditional engineering disciplines to the study of cell, tissue and organ biomechanics. Increasingly complex models have been developed to describe and predict the mechanical behavior of such biological systems. While the availability of advanced computational tools has led to exciting research advances in the field, the utility of these models is often the subject of criticism due to inadequate model verification and validation (V&V). The objective of this review is to present the concepts of verification, validation and sensitivity studies with regard to the construction, analysis and interpretation of models in computational biomechanics. Specific examples from the field are discussed. It is hoped that this review will serve as a guide to the use of V&V principles in the field of computational biomechanics, thereby improving the peer acceptance of studies that use computational modeling techniques.     

Multi-scale computational modelling in biology and physiology

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.     

Analysis and Simulation of Division- and Label-Structured Population Models

In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models only consider the size of the overall populations, others take division numbers and labeling of the cells into account. In this work, we present a modeling and computational framework for proliferating cell populations undergoing symmetric cell division, which incorporates both the discrete division number and continuous label dynamics. Thus, it allows for the consideration of division number-dependent parameters as well as the direct comparison of the model prediction with labeling experiments, e.g., performed with Carboxyfluorescein succinimidyl ester (CFSE), and can be shown to be a generalization of most existing models used to describe these data. We prove that under mild assumptions the resulting system of coupled partial differential equations (PDEs) can be decomposed into a system of ordinary differential equations (ODEs) and a set of decoupled PDEs, which drastically reduces the computational effort for simulating the model. Furthermore, the PDEs are solved analytically and the ODE system is truncated, which allows for the prediction of the label distribution of complex systems using a low-dimensional system of ODEs. In addition to modeling the label dynamics, we link the label-induced fluorescence to the measure fluorescence which includes autofluorescence. Furthermore, we provide an analytical approximation for the resulting numerically challenging convolution integral. This is illustrated by modeling and simulating a proliferating population with division number-dependent proliferation rate.     

Structural modification of phenylpropanoid-derived compounds and the effects on their participation in redox processes

Oxidation and reduction processes are fundamental to many of the proposed mechanisms by which dietary phytochemicals are thought to exert protective effects against cardiovascular disease and some cancers. An understanding of the redox chemistry of these compounds is essential in assessing their potential to participate in these processes. Phenylpropanoid-derived compounds were selected and synthesised where required to represent many of the structural features found in this important group of compounds. Using electron paramagnetic resonance spectroscopy and computational chemistry a structure-redox activity relationship was obtained. Good correlation of computational and experimental results was observed for the mono-hydroxylated compounds. This demonstrated the value of computational chemistry in obtaining information about compounds, not readily available and the effect of electron delocalisation on parent radical stability. For compounds containing more than one hydroxyl, the relationship was found to be more complex. The importance of quinone formation in compounds containing more than one hydroxyl substituent was highlighted, as this was found to have a significant effect on stabilisation and therefore, their participation in redox processes.     

OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany

Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. However, reliably inferring the epidemical dynamics by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address this problem with a novel combination of epidemiological modeling with specialized neural networks. Our approach entails two computational phases: In an initial training phase, a mathematical model describing the epidemic is used as a coach for a neural network, which acquires global knowledge about the full range of possible disease dynamics. In the subsequent inference phase, the trained neural network processes the observed data of an actual outbreak and infers the parameters of the model in order to realistically reproduce the observed dynamics and reliably predict future progression. With its flexible framework, our simulation-based approach is applicable to a variety of epidemiological models. Moreover, since our method is fully Bayesian, it is designed to incorporate all available prior knowledge about plausible parameter values and returns complete joint posterior distributions over these parameters. Application of our method to the early Covid-19 outbreak phase in Germany demonstrates that we are able to obtain reliable probabilistic estimates for important disease characteristics, such as generation time, fraction of undetected infections, likelihood of transmission before symptom onset, and reporting delays using a very moderate amount of real-world observations.     

Modelling and simulation techniques for membrane biology

One of the most important aspects of Computational Cell Biology is the understanding of the complicated dynamical processes that take place on plasma membranes. These processes are often so complicated that purely temporal models cannot always adequately capture the dynamics. On the other hand, spatial models can have large computational overheads. In this article, we review some of these issues with respect to chemistry, membrane microdomains and anomalous diffusion and discuss how to select appropriate modelling and simulation paradigms based on some or all the following aspects: discrete, continuous, stochastic, delayed and complex spatial processes.     

Quantitative cell biology with the Virtual Cell

Cell biological processes are controlled by an interacting set of biochemical and electrophysiological events that are distributed within complex cellular structures. Computational models, comprising quantitative data on the interacting molecular participants in these events, provide a means for applying the scientific method to these complex systems. The Virtual Cell is a computational environment designed for cell biologists, to facilitate the construction of models and the generation of predictive simulations from them. This review summarizes how a Virtual Cell model is assembled and describes the physical principles underlying the calculations that are performed. Applications to problems in nucleocytoplasmic transport and intracellular calcium dynamics will illustrate the power of this paradigm for elucidating cell biology.     

Inference for nonlinear epidemiological models using genealogies and time series

Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.     

基于智能体模型的土地利用动态模拟研究进展

土地利用动态变化是全球变化和可持续发展研究的基础,对区域水循环、大气循环、环境质量、气候变化及陆地生态系统生产力等具有重要影响,也是造成生物多样性衰减的最主要原因.目前,建立于复杂性科学基础上的的智能体模型(ABM)成为土地利用动态模拟的重要方法.智能体模型能模拟个体或群体的行为及决策模式,从而能将政府、城市规划、房地产开发商、住户等社会群体及个人对土地利用产生的影响进行模拟,同时能对不同社会经济政策对土地动态影响进行模拟.智能体模型在元胞自动机基础上,加入了人为因素的智能体概念,从而能更好地模拟土地动态.在分析总结了智能体模型的相关概念和组织结构,并分析了其在土地利用动态、城市动态模拟及生态过程模拟等方面的应用与元胞自动机的关系,比较了常用的智能体模型的主要软件,最后概括了智能体模型优点、发展趋势及存在的主要问题.     

A cure for the plague of parameters: constraining models of complex population dynamics with allometries

A major goal of ecology is to discover how dynamics and structure of multi-trophic ecological communities are related. This is difficult, because whole-community data are limited and typically comprise only a snapshot of a community instead of a time series of dynamics, and mathematical models of complex system dynamics have a large number of unmeasured parameters and therefore have been only tenuously related to real systems. These are related problems, because long time-series, if they were commonly available, would enable inference of parameters. The resulting ‘plague of parameters’ means most studies of multi-species population dynamics have been very theoretical. Dynamical models parametrized using physiological allometries may offer a partial cure for the plague of parameters, and these models are increasingly used in theoretical studies. However, physiological allometries cannot determine all parameters, and the models have also rarely been directly tested against data. We confronted a model of community dynamics with data from a lake community. Many important empirical patterns were reproducible as outcomes of dynamics, and were not reproducible when parameters did not follow physiological allometries. Results validate the usefulness, when parameters follow physiological allometries, of classic differential-equation models for understanding whole-community dynamics and the structure–dynamics relationship.     

PSysCal: a parallel tool for calibration of ecosystem models

The methods used for ecosystem modelling are generally based on differential equations. Nowadays, new computational models based on concurrent processing of multiple agents (multi-agents) or the simulation of biological processes with the Population Dynamic P-System models (PDPs) are gaining importance. These models have significant advantages over traditional models, such as high computational efficiency, modularity and its ability to model the interaction between different biological processes which operate concurrently. By this, they are becoming useful for simulating complex dynamic ecosystems, untreatable with classical techniques. On the other hand, the main counterpart of P-System models is the need for calibration. The model parameters represent the field measurements taken by experts. However, the exact values of some of these parameters are unknown and experts define a numerical interval of possible values. Therefore, it is necessary to perform a calibration process to fit the best value of each interval. When the number of unknown parameters increases, the calibration process becomes computationally complex and storage requirements increase significantly. In this paper, we present a parallel tool (PSysCal) for calibrating next generation PDP models. The results shown that the calibration time is reduced exponentially with the amount of computational resources. However, the complexity of the calibration process and a limitation in the number of available computational resources make the calibration process intractable for large models. To solve this, we propose a heuristic technique (PSysCal+H). The results show that this technique significantly reduces the computational cost, it being practical for solving large model instances even with limited computational resources.     

gauseR: Simple methods for fitting Lotka‐Volterra models describing Gause’s “Struggle for Existence”

Point 1: The ecological models of Alfred J. Lotka and Vito Volterra have had an enormous impact on ecology over the past century. Some of the earliest—and clearest—experimental tests of these models were famously conducted by Georgy Gause in the 1930s. Although well known, the data from these experiments are not widely available and are often difficult to analyze using standard statistical and computational tools.Point 2: Here, we introduce the gauseR package, a collection of tools for fitting Lotka‐Volterra models to time series data of one or more species. The package includes several methods for parameter estimation and optimization, and includes 42 datasets from Gause''s species interaction experiments and related work. Additionally, we include with this paper a short blog post discussing the historical importance of these data and models, and an R vignette with a walk‐through introducing the package methods. The package is available for download at github.com/adamtclark/gauseR.Point 3: To demonstrate the package, we apply it to several classic experimental studies from Gause, as well as two other well‐known datasets on multi‐trophic dynamics on Isle Royale, and in spatially structured mite populations. In almost all cases, models fit observations closely and fitted parameter values make ecological sense.Point 4: Taken together, we hope that the methods, data, and analyses that we present here provide a simple and user‐friendly way to interact with complex ecological data. We are optimistic that these methods will be especially useful to students and educators who are studying ecological dynamics, as well as researchers who would like a fast tool for basic analyses.     

Insights into the dynamic interactions at chemokine-receptor interfaces and mechanistic models of chemokine binding

Chemokine receptors are the central signaling hubs of several processes such as cell migration, chemotaxis and cell positioning. In this graphical review, we provide an overview of the structural and mechanistic principles governing chemokine recognition that are currently emerging. Structural models of chemokine-receptor co-complexes with endogenous chemokines, viral chemokines and therapeutics have been resolved that highlight multiple interaction sites, termed as CRS1, CRS1.5 etc. The first site of interaction has been shown to be the N-terminal domain of the receptors (CRS1 site). A large structural flexibility of the N-terminal domain has been reported that was supported by both experimental and simulation studies. Upon chemokine binding, the N-terminal domain appears to show constricted dynamics and opens up to interact with the chemokine via a large interface. The subsequent sites such as CRS1.5 and CRS2 sites have been structurally well resolved although differences arise such as the localization of the N-terminus of the ligand to a major or minor pocket of the orthosteric binding site. Several computational studies have highlighted the dynamic protein-protein interface at the CRS1 site that seemingly appears to resolve the differences in NMR and mutagenesis studies. Interestingly, the differential dynamics at the CRS1 site suggests a mixed model of binding with complex signatures of both conformational selection and induced fit models. Integrative experimental and computational approaches could help unravel the structural basis of promiscuity and specificity in chemokine-receptor binding and open up new avenues of therapeutic design.     

Modelling Southern Ocean ecosystems: krill, the food-web, and the impacts of harvesting

The ecosystem approach to fisheries recognises the interdependence between harvested species and other ecosystem components. It aims to account for the propagation of the effects of harvesting through the food-web. The formulation and evaluation of ecosystem-based management strategies requires reliable models of ecosystem dynamics to predict these effects. The krill-based system in the Southern Ocean was the focus of some of the earliest models exploring such effects. It is also a suitable example for the development of models to support the ecosystem approach to fisheries because it has a relatively simple food-web structure and progress has been made in developing models of the key species and interactions, some of which has been motivated by the need to develop ecosystem-based management. Antarctic krill, Euphausia superba, is the main target species for the fishery and the main prey of many top predators. It is therefore critical to capture the processes affecting the dynamics and distribution of krill in ecosystem dynamics models. These processes include environmental influences on recruitment and the spatially variable influence of advection. Models must also capture the interactions between krill and its consumers, which are mediated by the spatial structure of the environment. Various models have explored predator-prey population dynamics with simplistic representations of these interactions, while others have focused on specific details of the interactions. There is now a pressing need to develop plausible and practical models of ecosystem dynamics that link processes occurring at these different scales. Many studies have highlighted uncertainties in our understanding of the system, which indicates future priorities in terms of both data collection and developing methods to evaluate the effects of these uncertainties on model predictions. We propose a modelling approach that focuses on harvested species and their monitored consumers and that evaluates model uncertainty by using alternative structures and functional forms in a Monte Carlo framework.