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Key enzymatic processes in biology use the nonequilibrium error correction mechanism called kinetic proofreading to enhance their specificity. Kinetic proofreading typically requires several dedicated structural features in the enzyme, such…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as…
A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies,…
Many biological systems, such as metabolic pathways, exhibit bistability behavior: these biological systems exhibit two distinct stable states with switching between the two stable states controlled by certain conditions. Since…
Bistability is considered wide-spread among bacteria and eukaryotic cells, useful e.g. for enzyme induction, bet hedging, and epigenetic switching. However, this phenomenon has mostly been described with deterministic dynamic or well-mixed…
Many enzymes appear to diffuse faster in the presence of substrate and to drift either up or down a concentration gradient of their substrate. Observations of these phenomena, termed enhanced enzyme diffusion (EED) and enzyme chemotaxis,…
Bipartite networks are widely used to encode the ecological interactions. Being able to compare the organization of bipartite networks is a first step toward a better understanding of how environmental factors shape community structure and…
Living cells exhibit a complex organization comprising numerous compartments, among which are RNA- and protein-rich membraneless, liquid-like organelles known as biomolecular condensates. Energy-consuming processes regulate their formation…
The evolution and emergence of antibiotic resistance is a major public health concern. The understanding of the within-host microbial dynamics combining mutational processes, horizontal gene transfer and resource consumption, is one of the…
We study a notion of robustness of a Markov kernel that describes a system of several input random variables and one output random variable. Robustness requires that the behaviour of the system does not change if one or several of the input…
The formation of condensates is now considered as a major organization principle of eukaryotic cells. Several studies have recently shown that the properties of these condensates are affected by enzymatic reactions. We propose here a simple…
Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species.…
Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult,…
In multiplex networks with a large number of layers, the nodes can have different activities, indicating the total number of layers in which the nodes are present. Here we model multiplex networks with heterogeneous activity of the nodes…
Multilayer networked systems are ubiquitous in nature and engineering, and the robustness of these systems against failures is of great interest. A main line of theoretical pursuit has been percolation induced cascading failures, where…
Adhesion interactions mediated by multiple bond types are relevant for many biological and soft matter systems, including the adhesion of biological cells and functionalized colloidal particles to various substrates. To elucidate advantages…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of the steady-state system…
We demonstrate a modeling and computational framework that allows for rapid screening of thousands of potential network designs for particular dynamic behavior. To illustrate this capability we consider the problem of hysteresis, a…