Turbulent coherent structures and the origin of life

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Life, as we know it, consists of replicating strings of nucleic acids. If life originated with such strings, it is reasonable to assume that they were quite short, slowly increasing in length and complexity over time. Pioneering work by Eigen and Schuster demonstrated that self-replication would have been constrained by an “error threshold”, a critical number of base-pair nucleotides above which it is unreasonable to assume a particular string could replicate itself faithfully enough to sustain an exact lineage for long times. As a consequence, more complicated replication machineries — metabolisms involving more than one string, such as primitive replicases and cooperative hypercycles — would have been necessary to avoid the error threshold. However, these metabolisms are susceptible to defection, i.e. metabolic collapse due to malfunction of one or more of the components. Two proposed mechanisms to avoid defectors are primitive cell membranes and spatial distributions which allow healthy metabolisms to evade defective elements. Membranes provide additional benefits, which can be defined by algorithmic procedures such as concentrating, splitting and merging, which make them more appealing than spatial structures. Here we show that naturally-occurring spatial structures in fluid flows can actually incorporate the benefits of both the membrane and spatialization theories, allowing for algorithmic processes to redistribute genetic material without any kind of physical membrane.

arXiv, PDF


Novel cytokine interactions identified during perturbed hematopoiesis

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Hematopoiesis is a dynamic process involving the up- and down-regulation of genes, as well as feedback loops that stimulate or suppress circulating cytokine concentrations. More complete pictures of the gene regulatory networks that control the production of the blood system have emerged with the advent of single-cell sequencing techniques and refinements to the capabilities of immunoassays. However, information about the regulatory networks of cytokines is still lacking. A novel mathematical technique (convergent cross-mapping, or CCM) allows for the extraction of causal relationships from data, which is of crucial importance for understanding these networks. To reconstruct the cytokine networks within the hematopoietic system we measured the concentrations of 63 cytokines, platelets, and thrombopoietin from an individual with cyclic thrombocytopenia (regular oscillations in the megakaryocytes and platelets) over 84 days. Using CCM, we identified 61 previously unreported cytokine relationships. Our approach is the first broad-scale investigation into causal relationships between cytokines in the blood and suggests a new paradigm for understanding how dynamic regulation occurs during hematopoiesis.

bioRxiv, PDF

Swimming in a confined liquid crystal


Microscopic lifeforms rarely locomote in an unconfined liquid. Solid boundaries representing biological membranes, other swimmers, or filaments much larger than the swimmer can represent elements of confinement. Due to the long range of hydrodynamic forces at this scale, the boundaries often have a dominant impact on the physics of locomotion. Here we extend previous work on locomotion of a swimmer with a prescribed stroke in confined isotropic fluids to anisotropic fluids, using the model of a nematic liquid crystal. The competition between elasticity, hydrodynamics, and anchoring conditions leads to a complex locomotion problem with unique transport properties. We examine this problem analytically and numerically for a model swimmer near a bounding wall which can itself also be elastic. For strong planar anchoring at a rigid wall, we find that the swimming speed goes to the isotropic Newtonian limit as the swimmer gets close to the wall, although the power required to maintain the swimmer’s speed depends on liquid crystal properties. We also report new findings on the swimming speed due to large-amplitude waveforms in unbounded liquid crystals.

Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Swimming in a confined liquid crystal”, arXiv, PDF


Effects of motion in structured populations


In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes in the distribution of types as mutations march toward fixation or extinction. We describe motion as the swapping of individuals on graphs, and also more generally as the shuffling of individuals between reproductive updates. Beginning with a one-dimensional graph, the cycle, we prove that motion suppresses natural selection for death-birth updating or for any process that combines birth-death and death-birth updating. If the rule is purely birth-death updating, no change in fixation probability appears in the presence of motion. We further investigate how motion affects evolution on the square lattice and on weighted graphs. In the latter case, we find that motion can be either an amplifier or a suppressor of natural selection. In some cases, whether it is one or the other can be a function of the relative reproductive rate, indicating that motion is a subtle and complex attribute of evolving populations.

Madison S. Krieger, A. McAvoy and M. A. Nowak, “Effects of motion in structured populations”, J. Roy. Soc. Interface 14(135), Arxiv, PDF

A minimal model of sound change


Social networks are an important structural property of evolutionary processes in culture and language. While great strides have been made in modeling the dynamics of discrete linguistic features in reproducing populations, such as individual signs (Nowak et. al. 1999) and grammatical rules (Niyogi 2006), these models haven’t been completely explored on graph structures, and continuous parameters such as those defining vowel formant frequencies or other cultural quantities of interest, such as garment length, are also ill-understood. We discuss a simple model for a reproducing population in which an individual occupies a node on a graph and decides on the value of a single continuous parameter based on the examples received from neighboring nodes. In the context of sound change, this model recapitulates many core results: dispersion of neighboring phonemes in chain shifts (Martinet 1955), the irreversibility of phoneme mergers (Garde 1961) and the uniform expansion of mergers (Herzog 1965). We also compare results of the model to existing studies of sound change in social networks (Labov 2001). These types of events in language evolution are largely “from below”, meaning they are little affected by other meaningful social variables. Time permitting, we will discuss how to expand the model to explore change “from above”, where nodes are decorated with other features to denote membership in different groups, and Sturtevant’s (Sturtevant 1947) conjecture that language change ends when social change ends.

arXiv, PDF

Gene Transfer in the Primitive Ocean


Some of the most critical evolutionary innovations occurred within single-celled prokaryotic organisms in the primitive ocean, such as the development of flagellar motility and the invention of oxidative photosynthesis. Prokaryotes have multiple vectors to exchange genetic material including transduction, transformation and conjugation. Being able to exchange genetic information allows important novel genes to be built up more quickly than if the population were waiting for the proper mutations to arise in a single lineage. However, these methods of genetic exchange require two differing lineages containing subsections of the novel gene to be in close proximity. Here we consider whether the transport properties of the primitive ocean may have accelerated this process. We consider two genetic components which arise via mutation at the same rate within a large background population and afford no selective advantage on their own. Once the pieces are combined via horizontal gene transfer in a single lineage, the selective advantage is immense. We examine the role of different fluid flows and components of complex oceanic flow on the time until the two lineages are united via theory and simulation.

arXiv, PDF

Long-term coexistence and regional heterogeneity of antibiotic-resistant infections reproduced by a simple spatial model


Antibiotic-resistant infections are a growing threat to human health. Mathematical models are a common tool to compare potential intervention strategies, but often struggle to reproduce a ubiquitous pattern seen in data: the long-term coexistence of both drug-susceptible and drug-resistant strains. Here we show that simple models of infection in structured or spatially-heterogeneous host populations lead to persistent coexistence where well-mixed models fail. This coexistence is robust over a wide range of treatment coverage, drug efficacies, costs of resistance, and mixing patterns. Perhaps more importantly, this model can explain other puzzling spatiotemporal features of drug resistance epidemiology that have received less attention, such as large differences in the prevalence of resistance between geographical regions that consume similar amounts of antibiotics or that neighbor one another. Our analysis identifies key features of host population structure that can be used to assess drug resistance risk and highlights the need to include spatial or demographic heterogeneity in models to guide resistance management.

bioRxiv, PDF