Related papers: Simplifying Biochemical Models With Intermediate S…

Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…

A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes,…

Model selection methods are used in different scientific contexts to represent a characteristic data set in terms of a reduced number of parameters. Apparently, these methods have not found their way into the literature on multibody systems…

Modeling social-ecological systems is difficult due to the complexity of ecosystems and of individual and collective human behavior. Key components of the social-ecological system are often over-simplified or omitted. Generalized modeling…

Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…

A simple mathematical model of the aging process for long-lived organisms is considered. The key point in this model is the assumption that the body does not have internal clocks that count out the chronological time at scales of decades.…

Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…

Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…

Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…

Molecular line emission is a powerful probe of the physical conditions of astrophysical objects but can be complex to model, and it is often unclear which transitions would be the best targets for observers who wish to constrain a given…

The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…

Many cellular processes involve information processing and decision making. We can probe these processes at increasing molecular detail. The analysis of heterogeneous data remains a challenge that requires new ways of thinking about cells…

A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…

Nonequilibrium steady state of isothermal biochemical cycle kinetics has been extensively studied, but much less investigated under non-isothermal conditions. However, once the heat exchange between subsystems is rather slow, the isothermal…

Machine learning models of vastly different modalities and architectures are being trained to predict the behavior of molecules, materials, and proteins. However, it remains unclear whether they learn similar internal representations of…

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

We advocate the use of qualitative models in the analysis of large biological systems. We show how qualitative models are linked to theoretical differential models and practical graphical models of biological networks. A new technique for…

Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…

Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…

A molecular understanding of how protein function is related to protein structure will require an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy…