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A key step in the origin of life is the emergence of a primitive metabolism. This requires the formation of a subset of chemical reactions that is both self-sustaining and collectively autocatalytic. A generic theory to study such processes…
We show that in a particular model of catalytic reaction systems, known as the binary polymer model, there is a mathematical invariance between two versions of the model: (1) random catalysis and (2) template-based catalysis. In particular,…
Self-assembly of proteins is a biological phenomenon which gives rise to spontaneous formation of amyloid fibrils or polymers. The starting point of this phase, called nucleation exhibits an important variability among replicated…
Many models for the origin of life have focused on understanding how evolution can drive the refinement of a preexisting enzyme, such as the evolution of efficient replicase activity. Here we present a model for what was, arguably, an even…
Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerisation has been studied theoretically in a number of contexts, often by considering a Markov process in…
We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive…
Polymers are candidate materials for a wide range of sustainability applications such as carbon capture and energy storage. However, computational polymer discovery lacks automated analysis of reaction pathways and stability assessment…
Emergence and maintenance of polymers with complex sequences is a major question in the study of origins of life. To answer this, we studied a model polymerization reaction, where polymers are synthesized by stepwise ligation from two types…
Due to recent advances in synthetic biology and artificial life, the origin of life is currently a hot topic of research. We review the literature and argue that the two traditionally competing "replicator-first" and "metabolism-first"…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
Depolymerization reactions constitute frequent experiments, for instance in biochemistry for the study of amyloid fibrils. The quantities experimentally observed are related to the time dynamics of a quantity averaged over all polymer…
Mathematical models are increasingly being used to understand complex biochemical systems, to analyze experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to…
In this paper, we investigate a stochastic model describing the time evolution of a polymerization process. A polymer is a macro-molecule resulting from the aggregation of several elementary sub-units called monomers. Polymers can grow by…
This is the first report, to our knowledge, on a systematic method for constructing a large scale kinetic metabolic model with incomplete information on kinetic parametersr, and its initial application to the modeling of central metabolism…
Self-replicability is the unique attribute observed in all the living organisms and the question how the life was physically initiated could be equivalent to the question how self-replicating informative polymers were formed in the abiotic…
Template directed replication of nucleic acids is at the essence of all living beings and a major milestone for any origin of life scenario. We here present an idealized model of prebiotic sequence replication, where binary polymers act as…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
We study the ability to maintain information in a population of reacting polymers under the influence of decay, i.e., spontaneous breakdown of large polymers. At a certain decay rate, it becomes impossible to maintain a significant…
Hybrid molecular dynamics/Monte Carlo simulations used to study melts of unentangled, thermoreversibly associating supramolecular polymers. In this first of a series of papers, we describe and validate a model that is effective in…
We derive stationary measures for certain zero-temperature random polymer models, which we believe are new in the case of the zero-temperature limit of the beta random polymer (that has been called the river delta model). To do this, we…