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A universal feature of the biochemistry of any living system is that all the molecules and catalysts that are required for reactions of the system can be built up from an available food source by repeated application of reactions from…
Polymer models are a widely used tool to study the prebiotic formation of metabolism at the origins of life. Counts of the number of reactions in these models are often crucial in probabilistic arguments concerning the emergence of…
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…
All living systems -- from the origin of life to modern cells -- rely on a set of biochemical reactions that are simultaneously self-sustaining and autocatalytic. This notion of an autocatalytic set has been formalized graph-theoretically…
Binary classification models which can assign probabilities to categories such as "the tissue is 75% likely to be tumorous" or "the chemical is 25% likely to be toxic" are well understood statistically, but their utility as an input to…
Self-replicating systems based on information-coding polymers are of crucial importance in biology. They also recently emerged as a paradigm in material design on nano- and micro-scales. We present a general theoretical and numerical…
Advances in algorithms and hardware have enabled computers to design new materials atom-by-atom. However, in order for these computer-generated materials to truly address problems of societal importance, such as clean energy generation, it…
An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…
The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modelling how living systems first arose. It has been known for several decades that such networks will form…
We introduce an autocatalytic aggregation model in which the rate at which two clusters merge to form a cluster is controlled by the presence of a third "catalytic" cluster whose mass must equal to the mass of one of the reaction partners.…
We determine conditions under which a random biochemical system is likely to contain a subsystem that is both autocatalytic and able to survive on some ambient `food' source. Such systems have previously been investigated for their…
We study the equilibrium properties of a model for a binary mixture of catalytically-reactive monomers adsorbed on a two-dimensional substrate decorated by randomly placed catalytic bonds. The interacting $A$ and $B$ monomer species undergo…
An important issue for the origins of life is ensuring the accurate maintenance of information in replicating polymers in the face of inevitable errors. Here, we investigated how this maintenance depends on reaction kinetics by…
Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound).…
Mechanistic understanding of organic reactions can facilitate reaction development, impurity prediction, and in principle, reaction discovery. While several machine learning models have sought to address the task of predicting reaction…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
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…
The ability to reason beyond established knowledge allows Organic Chemists to solve synthetic problems and to invent novel transformations. Here, we propose a model which mimics chemical reasoning and formalises reaction prediction as…
A biological system consists of a variety of polymers that are synthesized from monomers, by catalysis that exists only for some long polymers. It is important to elucidate the emergence and sustenance of such autocatalytic polymerization.…
In small systems, quantitative discrepancies between stochastic and deterministic descriptions of chemical kinetics can be significant, with their magnitude depending on the specific reaction network. Here, we study the Finke-Watzky…