Assembly theory is used to map molecular and gene assembly pathways exploring evolutionary trajectories looking for novelty.

Explaining the origin of life requires us to elucidate how self-replication arises. To be specific, how can a self-replicating entity develop spontaneously from a chemical reaction system in which no reaction is self-replicating? Previously proposed mathematical models either supply an explicit framework for a minimal living system or consider only catalyzed reactions, and thus fail to provide a comprehensive theory. Here, we set up a general mathematical model for chemical reaction systems that properly accounts for energetics, kinetics, and the conservation law. We found that 1) some systems are collectively catalytic, a mode whereby reactants are transformed into end products with the assistance of intermediates (as in the citric acid cycle), whereas some others are self-replicating, that is, different parts replicate each other and the system self-replicates as a whole (as in the formose reaction, in which sugar is replicated from formaldehyde); 2) side reactions do not always inhibit such systems; 3) randomly chosen chemical universes (namely random artificial chemistries) often contain one or more such systems; 4) it is possible to construct a self-replicating system in which the entropy of some parts spontaneously decreases, in a manner similar to that discussed by Schrödinger; and 5) complex self-replicating molecules can emerge spontaneously and relatively easily from simple chemical reaction systems through a sequence of transitions. Together, these results start to explain the origins of prebiotic evolution.

Antimicrobial peptides (AMPs) are valuable alternatives to traditional antibiotics, possess a variety of potent biological activities and exhibit immunomodulatory effects that alleviate difficult-to-treat infections. Clarifying the structure-activity relationships of AMPs can direct the synthesis of desirable peptide therapeutics. In this study, the lipopolysaccharide-binding domain (LBD) was identified through machine learning-guided directed evolution, which acts as a functional domain of the anti-lipopolysaccharide factor family of AMPs identified from Marsupenaeus japonicus. LBD_A-D was identified as an output of this algorithm, in which the original LBD_Mj sequence was the input, and the three-dimensional solution structure of LBD_B was determined using nuclear magnetic resonance. Furthermore, our study involved a comprehensive series of experiments, including morphological studies and in vitro and in vivo antibacterial tests. The NMR solution structure showed that LBD_B possesses a circular extended structure with a disulfide crosslink at the terminus and two 3₁₀-helices and exhibits a broad antimicrobial spectrum. In addition, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) showed that LBD_B induced the formation of a cluster of bacteria wrapped in a flexible coating that ruptured and consequently killed the bacteria. Finally, coinjection of LBD_B, Vibrio alginolyticus and Staphylococcus aureus in vivo improved the survival of M. japonicus, demonstrating the promising therapeutic role of LBD_B for treating infectious disease. The findings of this study pave the way for the rational drug design of activity-enhanced peptide antibiotics.

The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory and exobiology. Many measures of these quantities are either difficult to compute, rely on the statistical notion of information, or can only be applied to strings. Based on assembly theory, we propose the notion of a ladderpath, which describes how an object can be decomposed into hierarchical structures using repetitive elements. From the ladderpath, two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath approach can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and the origin of life. The ladderpath approach provides an alternative characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.

Community ecosystems at very different levels of biological organization often have similar properties. Coexistence of multiple species, cross-feeding, biodiversity and fluctuating population dynamics are just a few of the properties that arise in a range of ecological settings. Here we develop a bottom-up model of consumer–resource interactions, in the form of an artificial ecosystem ‘number soup’, which reflects basic properties of many bacterial and other community ecologies. We demonstrate four key properties of the number soup model: (i) communities self-organize so that all available resources are fully consumed; (ii) reciprocal cross-feeding is a common evolutionary outcome, which evolves in a number of stages, and many transitional species are involved; (iii) the evolved ecosystems are often ‘robust yet fragile’, with keystone species required to prevent the whole system from collapsing; (iv) non-equilibrium dynamics and chaotic patterns are general properties, readily generating rich biodiversity. These properties have been observed in empirical ecosystems, ranging from bacteria to rainforests. Establishing similar properties in an evolutionary model as simple as the number soup suggests that these four properties are ubiquitous features of all community ecosystems, and raises questions about how we interpret ecosystem structure in the context of natural selection.

The golden ratio, ϕ = 1.61803…, has often been found in connection with biological phenomena, ranging from spirals in sunflowers to gene frequency. One example where the golden ratio often arises is in self-replication, having its mathematical origins in Fibonacci’s sequence for “rabbit reproduction”. Recently, it has been claimed that ϕ determines the ratio between the number of different nucleobases in human genome. Such empirical examples continue to give credence to the idea that the golden ratio is a universal constant, not only in mathematics but also for biology. In this paper, we employ a general framework for chemically realistic self-replicating reaction systems and investigate whether the ratio of chemical species population follows “universal constants”. We find that many self-replicating systems can be characterised by an algebraic number, which, in some cases, is the golden ratio. However, many other algebraic numbers arise from these systems, and some of them—such as and 1.22074… which is also known as the 3rd lower golden ratio—arise more frequently in self-replicating systems than the golden ratio. The “universal constants” in these systems arise as roots of a limited number of distinct characteristic equations. In addition, these “universal constants” are transient behaviours of self-replicating systems, corresponding to the scenario that the resource inside the system is infinite, which is not always the case in practice. Therefore, we argue that the golden ratio should not be considered as a special universal constant in self-replicating systems, and that the ratios between different chemical species only go to certain numbers under some idealised scenarios.