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What substrate features allow life? We exhaustively classify all 262,144 outer-totalistic binary cellular automata rules with Moore neighbourhood for self-replication and produce phase diagrams in the $(\lambda, F)$ plane, where $\lambda$…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
The fuel-driven process of replication in living systems generates distributions of copied entities with varying degrees of copying accuracy. Here we introduce a thermodynamically consistent ensemble for investigating universal population…
There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a…
All life, including cells and artificial protocells, must integrate diverse molecules into a single unit in order to reproduce. Despite expected pressure to evolve a simple system with the fastest replication speed, the mechanism by which…
We construct a simple model of a proto-cell that simulates a stochastic dynamics of abstract chemicals on a two-dimensional lattice. We assume that chemicals catalyze their reproduction through interaction with each other, and that between…
Molecular biology explains function of molecules by their geometrical and electronical structures that are mainly determined by utilization of quantum effects in chemistry. However, further quantum effects are not thought to play any…
The evolution of structure in biology is driven by accretion and change. Accretion brings together disparate parts to form bigger wholes. Change provides opportunities for growth and innovation. Here we review patterns and processes that…
For prebiotic chemistry to succeed in producing a starting metastable, autocatalytic and reproducing system subject to evolutionary selection it must satisfy at least two apparently contradictory requirements: Because such systems are rare,…
Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organisms environment, and evolution in changing environments is still poorly…
Biological cells replicate their genomes in a well-planned manner. The DNA replication program of an organism determines the timing at which different genomic regions are replicated, with fundamental consequences for cell homeostasis and…
We use a coarse-grained molecular model to study the self-assembly process of complexes of cationic and neutral lipids with DNA molecules ("lipoplexes") - a promising nonviral carrier of DNA for gene therapy. We identify the resulting…
Deep learning models are gaining popularity and potency in predicting polymer properties. These models can be built using pre-existing data and are useful for the rapid prediction of polymer properties. However, the performance of a deep…
It is a long-standing question in origin-of-life research whether the information content of replicating molecules can be maintained in the presence of replication errors. Extending standard quasispecies models of non-enzymatic replication,…
In growing active matter systems, a large collection of engineered or living autonomous units metabolize free energy and create order at different length scales as they proliferate and migrate collectively. One such example is bacterial…
Large language models show great potential in generating and optimizing code. Widely used sampling methods such as Nucleus Sampling increase the diversity of generation but often produce repeated samples for low temperatures and incoherent…
Modern biological tools have made it possible to unequivocally demonstrate the deep relationship among species in terms of genes and basic molecular mechanisms. In addition, results from genetic, physical and physiological approaches…
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
Assembly theory predicts that a distinguishing signature of life is its ability to produce complex molecules in abundance, opening new possibilities for life detection. Experimental validation of this approach has so far relied on abiotic…