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Modelling biological systems
Modelling biological systems
Modelling biological systems
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Modelling biological systems is a significant task of systems biology and mathematical biology.[a] Computational systems biology[b][1] aims to develop and use efficient algorithms, data structures, visualization and communication tools with the goal of computer modelling of biological systems. It involves the use of computer simulations of biological systems, including cellular subsystems (such as the networks of metabolites and enzymes which comprise metabolism, signal transduction pathways and gene regulatory networks), to both analyze and visualize the complex connections of these cellular processes.[2]

An unexpected emergent property of a complex system may be a result of the interplay of the cause-and-effect among simpler, integrated parts (see biological organisation). Biological systems manifest many important examples of emergent properties in the complex interplay of components. Traditional study of biological systems requires reductive methods in which quantities of data are gathered by category, such as concentration over time in response to a certain stimulus. Computers are critical to analysis and modelling of these data. The goal is to create accurate real-time models of a system's response to environmental and internal stimuli, such as a model of a cancer cell in order to find weaknesses in its signalling pathways, or modelling of ion channel mutations to see effects on cardiomyocytes and in turn, the function of a beating heart.

Standards

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By far the most widely accepted standard format for storing and exchanging models in the field is the Systems Biology Markup Language (SBML).[3] The SBML.org website includes a guide to many important software packages used in computational systems biology. A large number of models encoded in SBML can be retrieved from BioModels. Other markup languages with different emphases include BioPAX, CellML and MorpheusML.[4]

Particular tasks

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Cellular model

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Main article: Cellular model
Part of the cell cycle
Summerhayes and Elton's 1923 food web of Bear Island (Arrows represent an organism being consumed by another organism).
A sample time-series of the Lotka–Volterra model. Note that the two populations exhibit cyclic behaviour.

Creating a cellular model has been a particularly challenging task of systems biology and mathematical biology. It involves the use of computer simulations of the many cellular subsystems such as the networks of metabolites, enzymes which comprise metabolism and transcription, translation, regulation and induction of gene regulatory networks.[5]

The complex network of biochemical reaction/transport processes and their spatial organization make the development of a predictive model of a living cell a grand challenge for the 21st century, listed as such by the National Science Foundation (NSF) in 2006.[6]

A whole cell computational model for the bacterium Mycoplasma genitalium, including all its 525 genes, gene products, and their interactions, was built by scientists from Stanford University and the J. Craig Venter Institute and published on 20 July 2012 in Cell.[7]

A dynamic computer model of intracellular signaling was the basis for Merrimack Pharmaceuticals to discover the target for their cancer medicine MM-111.[8]

Membrane computing is the task of modelling specifically a cell membrane.

Multi-cellular organism simulation

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An open source simulation of C. elegans at the cellular level is being pursued by the OpenWorm community. So far the physics engine Gepetto has been built and models of the neural connectome and a muscle cell have been created in the NeuroML format.[9]

Protein folding

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Main article: Protein folding problem

Protein structure prediction is the prediction of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of a protein's tertiary structure from its primary structure. It is one of the most important goals pursued by bioinformatics and theoretical chemistry. Protein structure prediction is of high importance in medicine (for example, in drug design) and biotechnology (for example, in the design of novel enzymes). Every two years, the performance of current methods is assessed in the CASP experiment.

Human biological systems

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Brain model

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The Blue Brain Project is an attempt to create a synthetic brain by reverse-engineering the mammalian brain down to the molecular level. The aim of this project, founded in May 2005 by the Brain and Mind Institute of the École Polytechnique in Lausanne, Switzerland, is to study the brain's architectural and functional principles. The project is headed by the Institute's director, Henry Markram. Using a Blue Gene supercomputer running Michael Hines's NEURON software, the simulation does not consist simply of an artificial neural network, but involves a partially biologically realistic model of neurons.[10][11] It is hoped by its proponents that it will eventually shed light on the nature of consciousness. There are a number of sub-projects, including the Cajal Blue Brain, coordinated by the Supercomputing and Visualization Center of Madrid (CeSViMa), and others run by universities and independent laboratories in the UK, U.S., and Israel. The Human Brain Project builds on the work of the Blue Brain Project.[12][13] It is one of six pilot projects in the Future Emerging Technologies Research Program of the European Commission,[14] competing for a billion euro funding.

Model of the immune system

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The last decade has seen the emergence of a growing number of simulations of the immune system.[15][16]

Virtual liver

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The Virtual Liver project is a 43 million euro research program funded by the German Government, made up of seventy research group distributed across Germany. The goal is to produce a virtual liver, a dynamic mathematical model that represents human liver physiology, morphology and function.[17]

Tree model

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Main article: Simulated growth of plants

Electronic trees (e-trees) usually use L-systems to simulate growth. L-systems are very important in the field of complexity science and A-life. A universally accepted system for describing changes in plant morphology at the cellular or modular level has yet to be devised.[18] The most widely implemented tree generating algorithms are described in the papers "Creation and Rendering of Realistic Trees" and Real-Time Tree Rendering.

Ecological models

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Main article: Ecosystem model

Ecosystem models are mathematical representations of ecosystems. Typically they simplify complex foodwebs down to their major components or trophic levels, and quantify these as either numbers of organisms, biomass or the inventory/concentration of some pertinent chemical element (for instance, carbon or a nutrient species such as nitrogen or phosphorus).

Models in ecotoxicology

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The purpose of models in ecotoxicology is the understanding, simulation and prediction of effects caused by toxicants in the environment. Most current models describe effects on one of many different levels of biological organization (e.g. organisms or populations). A challenge is the development of models that predict effects across biological scales. Ecotoxicology and models discusses some types of ecotoxicological models and provides links to many others.

Modelling of infectious disease

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Main articles: Mathematical modelling of infectious disease and Epidemic model

It is possible to model the progress of most infectious diseases mathematically to discover the likely outcome of an epidemic or to help manage them by vaccination. This field tries to find parameters for various infectious diseases and to use those parameters to make useful calculations about the effects of a mass vaccination programme.

See also

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Notes

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References

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Sources

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Further reading

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Modelling biological systems

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Modelling biological systems involves the development of mathematical, computational, and conceptual representations to simulate the structure, dynamics, and interactions of biological entities, ranging from molecular networks to entire ecosystems, enabling predictions and insights into complex processes like immune responses or cellular . These models address the inherent complexity of , which are characterized as adaptive entities with nonlinear behaviors, , and multi-scale interconnectivity that traditional reductionist approaches often fail to capture fully. Key methods in biological system modeling include ordinary differential equations (ODEs) for deterministic dynamics, stochastic simulations for handling variability and noise, and agent-based models for individual-level interactions, often integrated through standards like Systems Biology Markup Language (SBML) in software such as COPASI or CellDesigner. Microscopic approaches focus on detailed element-level simulations (e.g., subcellular reactions), while macroscopic models aggregate behaviors at tissue or organ scales, with hybrid techniques combining both to manage computational demands. The modeling process typically encompasses construction of hypotheses, tuning with experimental data, , and validation against observations to ensure reliability. The importance of these models lies in their ability to unify observations across biological scales, test hypotheses non-invasively, and inform applications in , such as predicting drug responses in cancer or progression. Recent advancements incorporate multi-omics data integration, single-cell resolution (e.g., via scRNA-seq), and to enhance and accuracy, as exemplified by whole-cell models of organisms like Mycoplasma genitalium that simulate all known molecular processes. Challenges persist in handling spatial-temporal heterogeneity and ensuring model reproducibility under FAIR principles, driving ongoing efforts in computational .

Fundamentals

Definition and Scope

Modelling biological systems involves the development of mathematical, computational, or conceptual representations to predict, analyze, and simulate biological phenomena ranging from molecular interactions to ecosystem dynamics. These models serve as quantitative frameworks that abstract complex processes into testable structures, enabling researchers to explore system behaviors under various conditions. Biological models can be categorized by their underlying assumptions and structures, including deterministic versus approaches, where deterministic models assume predictable outcomes based on initial conditions, while models incorporate to account for variability in low-copy-number events like . Additionally, continuous models describe gradual changes over time, often using differential equations, in contrast to discrete models that represent state changes at specific points, such as in cellular automata. Reductionist approaches focus on dissecting individual components and their interactions, whereas holistic methods emphasize emergent properties of the entire system, integrating multiple levels for a comprehensive view. The scope of biological modeling spans multiple scales of organization, from molecular levels—such as protein interactions and —to cellular processes, organismal , , and interactions. This multi-scale applicability allows models to bridge micro- and macro-level phenomena, facilitating the study of how local events influence global outcomes. Such modeling plays a crucial role in integrating diverse experimental data from sources like and , enabling testing through simulations that reveal causal relationships otherwise difficult to observe. It also supports predictions in unobservable scenarios, such as progression or responses to perturbations, thereby guiding experimental design and therapeutic interventions. Core principles include to simplify reality while retaining essential features, parameterization derived from empirical data to quantify relationships, validation against independent experimental results to ensure reliability, and iterative refinement to improve accuracy as new data emerges.

Historical Development

The modeling of biological systems traces its origins to the late , when Thomas Malthus introduced one of the earliest mathematical frameworks for in his 1798 essay An Essay on the Principle of Population. Malthus proposed that populations grow exponentially in the absence of constraints, while resources increase only linearly, leading to inevitable checks on growth such as or . This conceptual model laid foundational ideas for later ecological simulations, emphasizing limits to unchecked biological expansion. Building on such empirical observations, the early saw the development of differential equation-based models for interacting populations. In the 1920s, and independently formulated the predator-prey equations, which describe oscillatory dynamics between two species through coupled ordinary differential equations capturing growth, predation, and mortality rates. Lotka's work appeared in his 1925 book Elements of Physical Biology, while Volterra's 1926 paper analyzed fluctuations in Adriatic Sea fisheries, marking a shift toward predictive modeling of ecological interactions. Mid-20th-century advances introduced biophysical realism to biological modeling, integrating experimental data with mathematical descriptions of cellular processes. In 1952, and published their seminal model of the , using voltage-clamp experiments to derive equations for ionic currents that quantitatively reproduced impulses; this work earned them the 1963 Nobel Prize in or . That same year, Alan Turing's paper "The Chemical Basis of Morphogenesis" proposed reaction-diffusion equations to explain in developing embryos, demonstrating how chemical gradients could generate spatial structures like animal stripes without genetic pre-specification. Extending these ideas to excitable tissues, developed the first comprehensive ionic model of the in 1962, adapting Hodgkin-Huxley principles to simulate pacemaker activity and contraction in heart cells based on voltage-dependent currents. These models transitioned biological inquiry from descriptive to mechanistic simulations of physiological events. The late 20th and early 21st centuries heralded the emergence of as a data-integrated , fueled by genomic advancements. The completion of the in 2003 provided a complete reference sequence of human DNA, enabling large-scale network models that incorporate gene expression, protein interactions, and regulatory dynamics across cellular systems. Pioneers like advanced this field by co-founding the Institute for Systems Biology in 2000 and promoting integrative approaches that combine high-throughput with computational predictions to uncover emergent properties in complex biological networks. Post-2010, the integration of marked a pivotal shift toward data-driven modeling; DeepMind's 2, released in 2021, achieved near-atomic accuracy in protein structure prediction using deep learning on evolutionary and structural databases, revolutionizing simulations of molecular interactions and accelerating drug design. Building on this, AlphaFold 3 was released in May 2024, extending predictions to the structures and interactions of protein complexes with DNA, RNA, ligands, and ions, with model code and weights open-sourced for academic use in November 2024, further enhancing applications in drug discovery and molecular biology. This evolution from empirical equations to AI-enhanced paradigms has enabled holistic representations of biological systems, bridging scales from molecules to organisms.

Modeling Methods

Mathematical and Analytical Techniques

Mathematical and analytical techniques form the foundational backbone of modeling biological systems, providing exact solutions and insights into without relying on numerical approximations. These methods leverage differential equations, linear algebra, and stochastic processes to capture time-dependent, spatial, and probabilistic behaviors in biological phenomena, such as , reaction-diffusion patterns, and network stability. By deriving analytical expressions and analyzing stability, researchers can identify critical parameters that govern qualitative changes in system behavior, enabling predictions of tipping points or steady states in simpler models before extending to more complex simulations. Ordinary differential equations (ODEs) are widely used to model time-dependent processes in , assuming well-mixed systems where spatial variations are negligible. A classic example is the exponential growth model for unconstrained , given by the ODE dNdt=rN,\frac{dN}{dt} = rN, where N(t)N(t) is the population size at time tt, and r>0r > 0 is the intrinsic growth rate. To solve this, separate variables: dNN=r dt\frac{dN}{N} = r \, dt, integrate both sides to obtain ln⁡N=rt+C\ln N = rt + C, and exponentiate to yield N(t)=N0ertN(t) = N_0 e^{rt}, where N0=eCN_0 = e^C is the initial population. This derivation reveals unbounded growth, but stability analysis shows the equilibrium N=0N=0 is unstable, as small perturbations grow exponentially; for the linearized system around N=0N=0, the eigenvalue is r>0r > 0, confirming instability via the sign of the real part. Such models underpin analyses of microbial growth and spread in early phases. Partial differential equations (PDEs) extend ODEs to incorporate spatial dynamics, essential for modeling and in biological tissues or populations. A seminal application is the reaction-diffusion equation, exemplified by for the propagation of an advantageous in a : ∂u∂t=D∂2u∂x2+ru(1−u),\frac{\partial u}{\partial t} = D \frac{\partial^2 u}{\partial x^2} + r u (1 - u), where u(x,t)u(x,t) is the gene frequency, D>0D > 0 is the diffusion coefficient, and r>0r > 0 is the growth rate. Fisher derived traveling wave solutions by assuming u(x,t)=f(x−ct)u(x,t) = f(x - ct) for wave speed c≥2rDc \geq 2\sqrt{rD}
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