This year we celebrate the 150th anniversary of the law of mass action. This law is often assumed to have been “there” forever, but it has its own history, background, and a definite starting point. The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate. It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases. The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes.
Global constraint principle for microbial growth laws | PNAS
Understanding complex living systems requires identifying universal phenomenological laws that are independent of species and molecular-biological ...
An attempt to explain category theory to biologists in 15 minutes | David Spivak
A Drive to Survive
Since 2005, Karl Friston's proposal that the principle of free energy minimization underpins the purposive behavior of living agents has evolved through thou...
Claude discovers a novel enzyme system
In early results from our new life sciences research lab, Claude agents found an enzyme system whose function is still unknown.
The lost art of mathematical modelling
We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities – (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data – inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of a pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls – universalism, creating models of models, etc. – that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.
Are biological systems poised at criticality?
Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts and memories. Physicists have long hoped that these collective behaviors could be described using the ideas and methods of statistical mechanics. In the past few years, new, larger scale experiments have made it possible to construct statistical mechanics models of biological systems directly from real data. We review the surprising successes of this "inverse" approach, using examples form families of proteins, networks of neurons, and flocks of birds. Remarkably, in all these cases the models that emerge from the data are poised at a very special point in their parameter space--a critical point. This suggests there may be some deeper theoretical principle behind the behavior of these diverse systems.
Design in The Age of Biology: Shifting From a Mechanical-Object Ethos to an Organic-Systems Ethos
In the early twentieth century, our understanding of physics changed rapidly; now, our understanding of biology is undergoing a similar rapid change.
Complexity Explorables
A collection of interactive explorable explanations of complex systems in biology, physics, mathematics, social sciences, epidemiology, ecology and other fields....
How AI Can Advance Mathematical Biology: Opportunities, Challenges, and Future Directions
Mathematical biology has long relied on mechanistic models, including ordinary and partial differential equations, stochastic systems, and agent-based models, to study biological processes across scales. These approaches remain central because they provide structure, interpretability, and biological insight. However, modern biological and biomedical data, including longitudinal clinical records, medical imaging, and multi-omics measurements, are often high-dimensional, noisy, heterogeneous, and incomplete. These features make model calibration, simulation, and uncertainty quantification increasingly difficult. As a result, artificial intelligence (AI) and machine learning (ML) are playing a growing role in mathematical biology, not as replacements for mechanistic modeling, but as complementary tools that can support prediction, hybrid modeling, inference, and control. In this review, we organize these uses of AI from a mathematical biology perspective and examine how data-driven and mechanistic approaches interact across different modeling tasks. The selected examples span biomedical, epidemiological, ecological, evolutionary, biochemical, and population-level systems, while the review is intended to be representative rather than exhaustive. We emphasize recurring challenges that strongly affect biological credibility and practical usefulness, including interpretability, identifiability, generalization, and uncertainty quantification. Our goal is to clarify the roles AI can play in mathematical biology and to highlight the opportunities and limitations that arise when flexible learning methods are integrated with biologically grounded modeling.
Biohub releases a world model of protein biology
Open AI models used for a wide range of scientific applications, including accelerating the design of therapeutic molecules.
Growth, metabolic partitioning, and the size of microorganisms
Population growth rate is a fundamental ecological and evolutionary characteristic of living organisms, but individuals must balance the metabolism devoted to biosynthesis and reproduction against the maintenance of existing structure and other functionality. Here we present a mathematical model that relates metabolic partitioning to the form of growth. The model captures the observed growth trajectory of single cells and individuals for a variety of species and taxa spanning prokaryotes, unicellular eukaryotes, and small multicellular eukaryotes. Our analysis suggests that the per-unit costs of biosynthesis and maintenance are conserved across prokaryotes and eukaryotes. However, the relative metabolic expenditure on growth and maintenance of whole organisms clearly differentiates taxa: prokaryotes spend an increasing fraction of their entire metabolism on growth with increasing cell size, whereas eukaryotes devote a diminishing fraction. These differences allow us to predict the minimum and maximum size for each taxonomic group, anticipating observed evolutionary life-history transitions. The framework provides energetic insights into taxonomic tradeoffs related to growth and metabolism and constrains traits that are important for size-structured modeling of microbial communities and their ecological and biogeochemical effects.
GEMOT: Towards Mechanistic World Models for Biology
Scientific discovery seeks mechanisms that explain observations and predict beyond the measurements that produced them. Whereas large language models (LLMs) encode knowledge implicitly, mechanistic world models organise it as a parsimonious set of explicit, modular, reusable mechanisms whose predictions can be scored against data.
Agentic systems are adept at solving well-scoped, verifiable problems in computational biology
We introduce CompBioBench, a benchmark of 100 diverse tasks for evaluating agentic systems in computational biology. Unlike mathematics and programming, which more readily admit systematic verification, biological data are inherently noisy and open to interpretation.
Maximum power in evolution, ecology and economics
Ludwig Boltzmann suggested that natural selection was fundamentally a struggle among organisms for available energy. Alfred Lotka argued that organisms that capture and use more energy than their competition will have a selective advantage in the evolutionary process, i.e. the Darwinian notion of evolution was based on a fundamental, generalized energy principle. He extended this general principle from the energetics of a single organism or species to the energetics of entire energy pathways through ecosystems. Howard Odum and Richard Pinkerton, building on Lotka, extended this concept to ‘The maximum power principle’ and applied it to many biological and physical systems including human economies. We examine this history and how these ideas relate to concepts from other disciplines including philosophy. But there has been considerable confusion in understanding and applying these concepts which we attempt to resolve while providing various examples from routine life and discussing some unresolved issues. This article is part of the theme issue ‘Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)’.
Import AI 459: AI oversight is difficult; scaling laws for protein folding models; and pricing the extinction risk of AI systems
Do you feel as though you are living in a revolution?
