Complexity Thoughts: Issue #50
Unraveling complexity: building knowledge, one paper at a time
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Foundations of network science and complex systems
Anderson Localization of Walking Droplets
Understanding the ability of particles to maneuver through disordered environments is a central problem in innumerable settings, from active matter and biology to electronics. Macroscopic particles ultimately exhibit diffusive motion when their energy exceeds the characteristic potential barrier of the random landscape. In stark contrast, wave-particle duality causes electrons in disordered media to come to rest even when the potential is weak—a remarkable phenomenon known as Anderson localization. Here, we present a hydrodynamic active system with wave-particle features, a millimetric droplet self-guided by its own wave field over a submerged random topography, whose dynamics exhibits localized statistics analogous to those of electronic systems. Consideration of an ensemble of particle trajectories reveals a suppression of diffusion when the guiding wave field extends over the disordered topography. We rationalize mechanistically the emergent statistics by virtue of the wave-mediated resonant coupling between the droplet and topography, which produces an attractive wave potential about the localization region. This hydrodynamic analog, which demonstrates how a classical particle may localize like a wave, suggests new directions for future research in various areas, including active matter, wave localization, many-body localization, and topological matter.
Incorporating Heterogeneous Interactions for Ecological Biodiversity
Understanding the behaviors of ecological systems is challenging given their multifaceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical mean-field theory to provide insights into underlying principles such as how biodiversity and stability depend on the randomness in interaction strength. Yet the fully connected structures assumed in these previous studies are not realistic, as revealed by a vast amount of empirical data. We derive a generic formula for the abundance distribution under an arbitrary distribution of degree, the number of interacting neighbors, which leads to degree-dependent abundance patterns of species. Notably, in contrast to the fully interacting systems, the number of surviving species can be reduced as the community becomes cooperative in heterogeneous interaction structures. Our study, therefore, demonstrates that properly taking into account heterogeneity in the interspecific interaction structure is indispensable to understanding the diversity in large ecosystems, and our general theoretical framework can apply to a much wider range of interacting many-body systems.
Evolution and Origin of Life
Evolution of Sensory Receptors
Sensory systems enable organisms to perceive environmental stimuli crucial for survival, functioning through molecular receptors that transduce external signals into biochemical and neural responses to guide behavior. The evolutionary adaptation of sensory receptors is fundamental for species to occupy specific ecological niches, making them a model for studying genotype-phenotype links and the molecular basis of adaptation.
Recent studies have explored the evolutionary dynamics of sensory receptors across various taxa, highlighting trends in lineage-specific expansions, contractions, and functional innovations. A comprehensive comparative analysis across animal phylogenies reveals conserved and novel patterns in sensory receptor evolution, driven by shared stimuli such as light, chemicals, and temperature. Key innovations in early animal evolution, including nervous systems and multicellularity, have facilitated the development of intricate sensory systems that support complex behaviors and ecological roles.
This beautiful review synthesizes data on receptor family gains and losses, repertoire sizes, and molecular adaptations across major clades, emphasizing the role of sensory receptors in natural selection, reproductive isolation, and adaptive radiations, shedding light on their contribution to biodiversity and evolutionary innovation.
Sensory receptors are at the interface between an organism and its environment and thus represent key sites for biological innovation. Here, we survey major sensory receptor families to uncover emerging evolutionary patterns. Receptors for touch, temperature, and light constitute part of the ancestral sensory toolkit of animals, often predating the evolution of multicellularity and the nervous system. In contrast, chemoreceptors exhibit a dynamic history of lineage-specific expansions and contractions correlated with the disparate complexity of chemical environments. A recurring theme includes independent transitions from neurotransmitter receptors to sensory receptors of diverse stimuli from the outside world. We then provide an overview of the evolutionary mechanisms underlying sensory receptor diversification and highlight examples where signatures of natural selection are used to identify novel sensory adaptations. Finally, we discuss sensory receptors as evolutionary hotspots driving reproductive isolation and speciation, thereby contributing to the stunning diversity of animals.
Thresholds in Origin of Life Scenarios
Thresholds are widespread in origin of life scenarios, from the emergence of chirality, to the appearance of vesicles, of autocatalysis, all the way up to Darwinian evolution. Here, we analyze the “error threshold,” which poses a condition for sustaining polymer replication, and generalize the threshold approach to other properties of prebiotic systems. Thresholds provide theoretical predictions, prescribe experimental tests, and integrate interdisciplinary knowledge. The coupling between systems and their environment determines how thresholds can be crossed, leading to different categories of prebiotic transitions. Articulating multiple thresholds reveals evolutionary properties in prebiotic scenarios. Overall, thresholds indicate how to assess, revise, and compare origin of life scenarios.
A synthetic approach to abiogenesis
Synthetic biology seeks to probe fundamental aspects of biological form and function by construction (resynthesis) rather than deconstruction (analysis). Here we discuss how such an approach could be applied to assemble synthetic quasibiological systems able to replicate and evolve, illuminating universal properties of life and the search for its origins.
All life is organized as cells. Physical compartmentation from the environment and self–organization of self–contained redox reactions are the most conserved attributes of living things, hence inorganic matter with such attributes would be life's most likely forebear. We propose that life evolved in structured iron monosulphide precipitates in a seepage site hydrothermal mound at a redox, pH and temperature gradient between sulphide–rich hydrothermal fluid and iron(II)–containing waters of the Hadean ocean floor. The naturally arising, three–dimensional compartmentation observed within fossilized seepage–site metal sulphide precipitates indicates that these inorganic compartments were the precursors of cell walls and membranes found in free–living prokaryotes. The known capability of FeS and NiS to catalyse the synthesis of the acetyl–methylsulphide from carbon monoxide and methylsulphide, constituents of hydrothermal fluid, indicates that pre–biotic syntheses occurred at the inner surfaces of these metal–sulphide–walled compartments, which furthermore restrained reacted products from diffusion into the ocean, providing sufficient concentrations of reactants to forge the transition from geochemistry to biochemistry. The chemistry of what is known as the RNA–world could have taken place within these naturally forming, catalyticwalled compartments to give rise to replicating systems. Sufficient concentrations of precursors to support replication would have been synthesized in situ geochemically and biogeochemically, with FeS (and NiS) centres playing the central catalytic role. The universal ancestor we infer was not a free–living cell, but rather was confined to the naturally chemiosmotic, FeS compartments within which the synthesis of its constituents occurred. The first free–living cells are suggested to have been eubacterial and archaebacterial chemoautotrophs that emerged more than 3.8 Gyr ago from their inorganic confines. We propose that the emergence of these prokaryotic lineages from inorganic confines occurred independently, facilitated by the independent origins of membrane–lipid biosynthesis: isoprenoid ether membranes in the archaebacterial and fatty acid ester membranes in the eubacterial lineage. The eukaryotes, all of which are ancestrally heterotrophs and possess eubacterial lipids, are suggested to have arisen ca. 2 Gyr ago through symbiosis involving an autotrophic archaebacterial host and a heterotrophic eubacterial symbiont, the common ancestor of mitochondria and hydrogenosomes. The attributes shared by all prokaryotes are viewed as inheritances from their confined universal ancestor. The attributes that distinguish eubacteria and archaebacteria, yet are uniform within the groups, are viewed as relics of their phase of differentiation after divergence from the non–free–living universal ancestor and before the origin of the free–living chemoautotrophic lifestyle. The attributes shared by eukaryotes with eubacteria and archaebacteria, respectively, are viewed as inheritances via symbiosis. The attributes unique to eukaryotes are viewed as inventions specific to their lineage. The origin of the eukaryotic endomembrane system and nuclear membrane are suggested to be the fortuitous result of the expression of genes for eubacterial membrane lipid synthesis by an archaebacterial genetic apparatus in a compartment that was not fully prepared to accommodate such compounds, resulting in vesicles of eubacterial lipids that accumulated in the cytosol around their site of synthesis. Under these premises, the most ancient divide in the living world is that between eubacteria and archaebacteria, yet the steepest evolutionary grade is that between prokaryotes and eukaryotes.
The origin of life is a spatially localized stochastic transition
Life depends on biopolymer sequences as catalysts and as genetic material. A key step in the Origin of Life is the emergence of an autocatalytic system of biopolymers. Here we study computational models that address the way a living autocatalytic system could have emerged from a non-living chemical system, as envisaged in the RNA World hypothesis.
We consider (i) a chemical reaction system describing RNA polymerization, and (ii) a simple model of catalytic replicators that we call the Two’s Company model. Both systems have two stable states: a non-living state, characterized by a slow spontaneous rate of RNA synthesis, and a living state, characterized by rapid autocatalytic RNA synthesis. The origin of life is a transition between these two stable states. The transition is driven by stochastic concentration fluctuations involving relatively small numbers of molecules in a localized region of space. These models are simulated on a two-dimensional lattice in which reactions occur locally on single sites and diffusion occurs by hopping of molecules to neighbouring sites.
If diffusion is very rapid, the system is well-mixed. The transition to life becomes increasingly difficult as the lattice size is increased because the concentration fluctuations that drive the transition become relatively smaller when larger numbers of molecules are involved. In contrast, when diffusion occurs at a finite rate, concentration fluctuations are local. The transition to life occurs in one local region and then spreads across the rest of the surface. The transition becomes easier with larger lattice sizes because there are more independent regions in which it could occur. The key observations that apply to our models and to the real world are that the origin of life is a rare stochastic event that is localized in one region of space due to the limited rate of diffusion of the molecules involved and that the subsequent spread across the surface is deterministic. It is likely that the time required for the deterministic spread is much shorter than the waiting time for the origin, in which case life evolves only once on a planet, and then rapidly occupies the whole surface.
The concept of cellular evolution
A central evolutionary question is whether the eucaryotic cytoplasm represents a line of descent that is separate from the typical bacterial line. It is argued on the basis of differences between their respective translation mechanisms that the two lines do represent separate phylogenetic trees in the sense that each line of descent independently evolved to a level of organization that could be called procaryotic. The two lines of descent, nevertheless shared a common ancestor, that was far simpler than the procaryote. This primitive entity is called a progenote, to recognize the possibility that it had not yet completed evolving the link between genotype and phenotype. This concept changes considerably the view one takes toward cellular evolution.
A genetic annealing model for the universal ancestor of all extant life is presented; the name of the model derives from its resemblance to physical annealing. The scenario pictured starts when “genetic temperatures” were very high, cellular entities (progenotes) were very simple, and information processing systems were inaccurate. Initially, both mutation rate and lateral gene transfer levels were elevated. The latter was pandemic and pervasive to the extent that it, not vertical inheritance, defined the evolutionary dynamic. As increasingly complex and precise biological structures and processes evolved, both the mutation rate and the scope and level of lateral gene transfer, i.e., evolutionary temperature, dropped, and the evolutionary dynamic gradually became that characteristic of modern cells. The various subsystems of the cell “crystallized,” i.e., became refractory to lateral gene transfer, at different stages of “cooling,” with the translation apparatus probably crystallizing first. Organismal lineages, and so organisms as we know them, did not exist at these early stages. The universal phylogenetic tree, therefore, is not an organismal tree at its base but gradually becomes one as its peripheral branchings emerge. The universal ancestor is not a discrete entity. It is, rather, a diverse community of cells that survives and evolves as a biological unit. This communal ancestor has a physical history but not a genealogical one. Over time, this ancestor refined into a smaller number of increasingly complex cell types with the ancestors of the three primary groupings of organisms arising as a result.
A theory for the evolution of cellular organization is presented. The model is based on the (data supported) conjecture that the dynamic of horizontal gene transfer (HGT) is primarily determined by the organization of the recipient cell. Aboriginal cell designs are taken to be simple and loosely organized enough that all cellular componentry can be altered and/or displaced through HGT, making HGT the principal driving force in early cellular evolution. Primitive cells did not carry a stable organismal genealogical trace. Primitive cellular evolution is basically communal. The high level of novelty required to evolve cell designs is a product of communal invention, of the universal HGT field, not intralineage variation. It is the community as a whole, the ecosystem, which evolves. The individual cell designs that evolved in this way are nevertheless fundamentally distinct, because the initial conditions in each case are somewhat different. As a cell design becomes more complex and interconnected a critical point is reached where a more integrated cellular organization emerges, and vertically generated novelty can and does assume greater importance. This critical point is called the “Darwinian Threshold” for the reasons given.
This study develops a useful metric for quantifying codon usage adaptation - the Codon Adaptation Index of Species (CAIS). This metric permits direct comparisons of the strength of selection at the molecular level across species. The study is based on solid evidence, and the authors identify relationships between CAIS and the presence of disordered protein domains. Other correlations, such as the one between CAIS and body size, are weak and non-significant. In summary, the study introduces an interesting new approach to quantifying codon usage across species, which may be helpful in attempts to measure selection at the molecular level.
The nearly neutral theory of molecular evolution posits variation among species in the effectiveness of selection. In an idealized model, the census population size determines both this minimum magnitude of the selection coefficient required for deleterious variants to be reliably purged, and the amount of neutral diversity. Empirically, an ‘effective population size’ is often estimated from the amount of putatively neutral genetic diversity and is assumed to also capture a species’ effectiveness of selection. A potentially more direct measure of the effectiveness of selection is the degree to which selection maintains preferred codons. However, past metrics that compare codon bias across species are confounded by among-species variation in %GC content and/or amino acid composition. Here, we propose a new Codon Adaptation Index of Species (CAIS), based on Kullback–Leibler divergence, that corrects for both confounders. We demonstrate the use of CAIS correlations, as well as the Effective Number of Codons, to show that the protein domains of more highly adapted vertebrate species evolve higher intrinsic structural disorder.
Biological Systems
The Genetic Code Is One in a Million
Statistical and biochemical studies of the genetic code have found evidence of nonrandom patterns in the distribution of codon assignments. It has, for example, been shown that the code minimizes the effects of point mutation or mistranslation: erroneous codons are either synonymous or code for an amino acid with chemical properties very similar to those of the one that would have been present had the error not occurred. This work has suggested that the second base of codons is less efficient in this respect, by about three orders of magnitude, than the first and third bases. These results are based on the assumption that all forms of error at all bases are equally likely. We extend this work to investigate (1) the effect of weighting transition errors differently from transversion errors and (2) the effect of weighting each base differently, depending on reported mistranslation biases. We find that if the bias affects all codon positions equally, as might be expected were the code adapted to a mutational environment with transition/transversion bias, then any reasonable transition/transversion bias increases the relative efficiency of the second base by an order of magnitude. In addition, if we employ weightings to allow for biases in translation, then only 1 in every million random alternative codes generated is more efficient than the natural code. We thus conclude not only that the natural genetic code is extremely efficient at minimizing the effects of errors, but also that its structure reflects biases in these errors, as might be expected were the code the product of selection.
A molecular dynamics calculation of the amino acid polar requirement is used to score the canonical genetic code. Monte Carlo simulation shows that this computational polar requirement has been optimized by the canonical genetic code, an order of magnitude more than any previously known measure, effectively ruling out a vertical evolution dynamics. The sensitivity of the optimization to the precise metric used in code scoring is consistent with code evolution having proceeded through the communal dynamics of statistical proteins using horizontal gene transfer, as recently proposed. The extreme optimization of the genetic code therefore strongly supports the idea that the genetic code evolved from a communal state of life prior to the last universal common ancestor.