Long range segmentation of prokaryotic genomes by gene age and functionality.

Bacterial and archaeal genomes encompass numerous operons that typically consist of two to five genes. On larger scales, however, gene order is poorly conserved through the evolution of prokaryotes. Nevertheless, non-random localization of different classes of genes on prokaryotic chromosomes could reflect important functional and evolutionary constraints. We explored the patterns of genomic localization of evolutionarily conserved (ancient) and variable (young) genes across the diversity of bacteria and archaea. Nearly all bacterial and archaeal chromosomes were found to encompass large segments of 100-300 kb that were significantly enriched in either ancient or young genes. Similar clustering of genes with lethal knockout phenotype (essential genes) was observed as well. Mathematical modeling of genome evolution suggests that this long-range gene clustering in prokaryotic chromosomes reflects perpetual genome rearrangement driven by a combination of selective and neutral processes rather than evolutionary conservation.

Toward a theory of evolution as multilevel learning.

We apply the theory of learning to physically renormalizable systems in an attempt to outline a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution that appear to be necessary and sufficient to render a universe observable and show that they entail the major features of biological evolution, including replication and natural selection. It is shown that these cornerstone phenomena of biology emerge from the fundamental features of learning dynamics such as the existence of a loss function, which is minimized during learning. We then sketch the theory of evolution using the mathematical framework of neural networks, which provides for detailed analysis of evolutionary phenomena. To demonstrate the potential of the proposed theoretical framework, we derive a generalized version of the Central Dogma of molecular biology by analyzing the flow of information during learning (back propagation) and predicting (forward propagation) the environment by evolving organisms. The more complex evolutionary phenomena, such as major transitions in evolution (in particular, the origin of life), have to be analyzed in the thermodynamic limit, which is described in detail in the paper by Vanchurin et al. [V. Vanchurin, Y. I. Wolf, E. V. Koonin, M. I. Katsnelson, Proc. Natl. Acad. Sci. U.S.A. 119, 10.1073/pnas.2120042119 (2022)].

Thermodynamics of evolution and the origin of life.

We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for minimization of the loss function is employed to derive a canonical ensemble of organisms (population), the corresponding partition function (macroscopic counterpart of fitness), and free energy (macroscopic counterpart of additive fitness). We further define the biological counterparts of temperature (evolutionary temperature) as the measure of stochasticity of the evolutionary process and of chemical potential (evolutionary potential) as the amount of evolutionary work required to add a new trainable variable (such as an additional gene) to the evolving system. We then develop a phenomenological approach to the description of evolution, which involves modeling the grand potential as a function of the evolutionary temperature and evolutionary potential. We demonstrate how this phenomenological approach can be used to study the "ideal mutation" model of evolution and its generalizations. Finally, we show that, within this thermodynamics framework, major transitions in evolution, such as the transition from an ensemble of molecules to an ensemble of organisms, that is, the origin of life, can be modeled as a special case of bona fide physical phase transitions that are associated with the emergence of a new type of grand canonical ensemble and the corresponding new level of description.

Evolution in the weak-mutation limit: Stasis periods punctuated by fast transitions between saddle points on the fitness landscape.

A mathematical analysis of the evolution of a large population under the weak-mutation limit shows that such a population would spend most of the time in stasis in the vicinity of saddle points on the fitness landscape. The periods of stasis are punctuated by fast transitions, in lnNe/s time (Ne , effective population size; s, selection coefficient of a mutation), when a new beneficial mutation is fixed in the evolving population, which accordingly moves to a different saddle, or on much rarer occasions from a saddle to a local peak. Phenomenologically, this mode of evolution of a large population resembles punctuated equilibrium (PE) whereby phenotypic changes occur in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but the phenotype does not change substantially. Theoretically, PE has been linked to self-organized criticality (SOC), a model in which the size of "avalanches" in an evolving system is power-law-distributed, resulting in increasing rarity of major events. Here we show, however, that a PE-like evolutionary regime is the default for a very simple model of an evolving population that does not rely on SOC or any other special conditions.

Multiscale structural complexity of natural patterns.

Complexity of patterns is key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multistep renormalization of the pattern of interest and computing the overlap between neighboring renormalized layers. This way, we can define a single number characterizing the structural complexity of an object. We apply this definition to quantify complexity of various magnetic patterns and demonstrate that not only does it reflect the intuitive feeling of what is "complex" and what is "simple" but also, can be used to accurately detect different phase transitions and gain information about dynamics of nonequilibrium systems. When employed for that, the proposed scheme is much simpler and numerically cheaper than the standard methods based on computing correlation functions or using machine learning techniques.

Gating Orbital Memory with an Atomic Donor.

Orbital memory is defined by two stable valencies that can be electrically switched and read out. To explore the influence of an electric field on orbital memory, we studied the distance-dependent influence of an atomic Cu donor on the state favorability of an individual Co atom on black phosphorus. Using low temperature scanning tunneling microscopy and spectroscopy, we characterized the electronic properties of individual Cu donors, corroborating this behavior with ab initio calculations based on density functional theory. We studied the influence of an individual donor on the charging energy and stochastic behavior of an individual Co atom. We found a strong impact on the state favorability in the stochastic limit. These findings provide quantitative information about the influence of local electric fields on atomic orbital memory.

On the feasibility of saltational evolution.

Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multimutation leaps, that is, several mutations occurring simultaneously, within a single generation in 1 genome, and being fixed all together in the evolving population. The results indicate that, for typical, empirically observed combinations of the parameters of the evolutionary process, namely, effective population size, mutation rate, and distribution of selection coefficients of mutations, the probability of a multimutation leap is low, and accordingly the contribution of such leaps is minor at best. However, we show that, taking sign epistasis into account, leaps could become an important factor of evolution in cases of substantially elevated mutation rates, such as stress-induced mutagenesis in microbes. We hypothesize that stress-induced mutagenesis is an evolvable adaptive strategy.

High-Pressure Synthesis of Dirac Materials: Layered van der Waals Bonded BeN_{4} Polymorph.

High-pressure chemistry is known to inspire the creation of unexpected new classes of compounds with exceptional properties. Here, we employ the laser-heated diamond anvil cell technique for synthesis of a Dirac material BeN_{4}. A triclinic phase of beryllium tetranitride tr-BeN_{4} was synthesized from elements at ∼85 GPa. Upon decompression to ambient conditions, it transforms into a compound with atomic-thick BeN_{4} layers interconnected via weak van der Waals bonds and consisting of polyacetylene-like nitrogen chains with conjugated π systems and Be atoms in square-planar coordination. Theoretical calculations for a single BeN_{4} layer show that its electronic lattice is described by a slightly distorted honeycomb structure reminiscent of the graphene lattice and the presence of Dirac points in the electronic band structure at the Fermi level. The BeN_{4} layer, i.e., beryllonitrene, represents a qualitatively new class of 2D materials that can be built of a metal atom and polymeric nitrogen chains and host anisotropic Dirac fermions.

Physical foundations of biological complexity.

Biological systems reach hierarchical complexity that has no counterpart outside the realm of biology. Undoubtedly, biological entities obey the fundamental physical laws. Can today's physics provide an explanatory framework for understanding the evolution of biological complexity? We argue that the physical foundation for understanding the origin and evolution of complexity can be gleaned at the interface between the theory of frustrated states resulting in pattern formation in glass-like media and the theory of self-organized criticality (SOC). On the one hand, SOC has been shown to emerge in spin-glass systems of high dimensionality. On the other hand, SOC is often viewed as the most appropriate physical description of evolutionary transitions in biology. We unify these two faces of SOC by showing that emergence of complex features in biological evolution typically, if not always, is triggered by frustration that is caused by competing interactions at different organizational levels. Such competing interactions lead to SOC, which represents the optimal conditions for the emergence of complexity. Competing interactions and frustrated states permeate biology at all organizational levels and are tightly linked to the ubiquitous competition for limiting resources. This perspective extends from the comparatively simple phenomena occurring in glasses to large-scale events of biological evolution, such as major evolutionary transitions. Frustration caused by competing interactions in multidimensional systems could be the general driving force behind the emergence of complexity, within and beyond the domain of biology.

Disentangling the effects of selection and loss bias on gene dynamics.

We combine mathematical modeling of genome evolution with comparative analysis of prokaryotic genomes to estimate the relative contributions of selection and intrinsic loss bias to the evolution of different functional classes of genes and mobile genetic elements (MGE). An exact solution for the dynamics of gene family size was obtained under a linear duplication-transfer-loss model with selection. With the exception of genes involved in information processing, particularly translation, which are maintained by strong selection, the average selection coefficient for most nonparasitic genes is low albeit positive, compatible with observed positive correlation between genome size and effective population size. Free-living microbes evolve under stronger selection for gene retention than parasites. Different classes of MGE show a broad range of fitness effects, from the nearly neutral transposons to prophages, which are actively eliminated by selection. Genes involved in antiparasite defense, on average, incur a fitness cost to the host that is at least as high as the cost of plasmids. This cost is probably due to the adverse effects of autoimmunity and curtailment of horizontal gene transfer caused by the defense systems and selfish behavior of some of these systems, such as toxin-antitoxin and restriction modification modules. Transposons follow a biphasic dynamics, with bursts of gene proliferation followed by decay in the copy number that is quantitatively captured by the model. The horizontal gene transfer to loss ratio, but not duplication to loss ratio, correlates with genome size, potentially explaining increased abundance of neutral and costly elements in larger genomes.

Anisotropic Two-Dimensional Screening at the Surface of Black Phosphorus.

Electronic screening can have direct consequences for structural arrangements on the nanoscale, such as on the periodic ordering of adatoms on a surface. So far, such ordering phenomena have been explained in terms of isotropic screening of free electronlike systems. Here, we directly illustrate the structural consequences of anisotropic screening, making use of a highly anisotropic two-dimensional electron gas (2DEG) near the surface of black phosphorous. The presence of the 2DEG and its filling is controlled by adsorbed potassium atoms, which simultaneously serve to probe the electronic ordering. Using scanning tunneling microscopy, we show that the anisotropic screening leads to the formation of potassium chains with a well-defined orientation and spacing. We quantify the mean interaction potential utilizing statistical methods and find that the dimensionality and anisotropy of the screening is consistent with the presence of a band bending-induced 2DEG near the surface. The electronic dispersion of the 2DEG inferred by electronic ordering is consistent with that measured by angle-resolved photoemission spectroscopy.

Probing Single Vacancies in Black Phosphorus at the Atomic Level.

Utilizing a combination of low-temperature scanning tunneling microscopy/spectroscopy (STM/STS) and electronic structure calculations, we characterize the structural and electronic properties of single atomic vacancies within several monolayers of the surface of black phosphorus. We illustrate, with experimental analysis and tight-binding calculations, that we can depth profile these vacancies and assign them to specific sublattices within the unit cell. Measurements reveal that the single vacancies exhibit strongly anisotropic and highly delocalized charge density, laterally extended up to 20 atomic unit cells. The vacancies are then studied with STS, which reveals in-gap resonance states near the valence band edge and a strong p-doping of the bulk black phosphorus crystal. Finally, quasiparticle interference generated near these vacancies enables the direct visualization of the anisotropic band structure of black phosphorus.

Observing Imperfection in Atomic Interfaces for van der Waals Heterostructures.

Vertically stacked van der Waals heterostructures are a lucrative platform for exploring the rich electronic and optoelectronic phenomena in two-dimensional materials. Their performance will be strongly affected by impurities and defects at the interfaces. Here we present the first systematic study of interfaces in van der Waals heterostructure using cross-sectional scanning transmission electron microscope (STEM) imaging. By measuring interlayer separations and comparing these to density functional theory (DFT) calculations we find that pristine interfaces exist between hBN and MoS2 or WS2 for stacks prepared by mechanical exfoliation in air. However, for two technologically important transition metal dichalcogenide (TMDC) systems, MoSe2 and WSe2, our measurement of interlayer separations provide the first evidence for impurity species being trapped at buried interfaces with hBN interfaces that are flat at the nanometer length scale. While decreasing the thickness of encapsulated WSe2 from bulk to monolayer we see a systematic increase in the interlayer separation. We attribute these differences to the thinnest TMDC flakes being flexible and hence able to deform mechanically around a sparse population of protruding interfacial impurities. We show that the air sensitive two-dimensional (2D) crystal NbSe2 can be fabricated into heterostructures with pristine interfaces by processing in an inert-gas environment. Finally we find that adopting glovebox transfer significantly improves the quality of interfaces for WSe2 compared to processing in air.

Chiral Second-Sound Collective Modes at the Edge of 2D Systems with a Nontrivial Berry Curvature.

We study the thermal transport in two-dimensional systems with a nontrivial Berry curvature texture. The physical realizations are many; for the sake of definiteness, we consider undoped graphene gapped by the presence of an aligned hexagonal-boron-nitride substrate. The same phenomenology applies, i.e., to surface states of 3D topological insulators in the presence of a uniform magnetization. We find that chiral valley-polarized second-sound collective modes propagate along the edges of the system. The localization length of the edge modes has a topological origin stemming from the anomalous velocity term in the quasiparticle current. At low temperature, the single-particle contribution to the transverse thermal conductance is exponentially suppressed, and only second-sound modes carry heat along the boundary. A sharp change in the behavior of the thermal Hall conductance, extracted from nonlocal measurements of the temperature along the edge, marks the onset of ballistic heat transport due to second-sound edge modes.

Self-Induced Glassiness and Pattern Formation in Spin Systems Subject to Long-Range Interactions.

We study the glass formation in two- and three-dimensional Ising and Heisenberg spin systems subject to competing interactions and uniaxial anisotropy with a mean-field approach. In three dimensions, for sufficiently strong anisotropy the systems always modulate in a striped phase. Below a critical strength of the anisotropy, a glassy phase exists in a finite range of temperature, and it becomes more stable as the system becomes more isotropic. In two dimensions the criticality is always avoided and the glassy phase always exists.

Edge Plasmons in Two-Component Electron Liquids in the Presence of Pseudomagnetic Fields.

We study the properties of edge plasmons in two-component electron liquids in the presence of pseudomagnetic fields, which have opposite signs for the two different electronic populations and therefore preserve the time-reversal symmetry. The physical realizations of such systems are many. We discuss the case of strained graphene, solving the problem with the Wiener-Hopf technique. We show (i) that two charged counterpropagating acoustic edge modes exist at the boundary and (ii) that, in the limit of large pseudomagnetic fields, each of them involves oscillations of only one of the two electronic components. We suggest that the edge pseudomagnetoplasmons of graphene can be used to selectively address the electrons of one specific valley, a feature relevant for the emerging field of valleytronics. Our solution highlights new features missing in previous (similar) results obtained with uncontrolled approximations, namely a logarithmic divergence of the plasmon velocity, and the absence of gapped edge modes inside the bulk-plasmon gap.

Anomalous Magnetothermopower in a Metallic Frustrated Antiferromagnet.

We report the temperature T and magnetic field H dependence of the thermopower S of an itinerant triangular antiferromagnet PdCrO_{2} in high magnetic fields up to 32 T. In the paramagnetic phase, the zero-field thermopower is positive with a value typical of good metals with a high carrier density. In marked contrast to typical metals, however, S decreases rapidly with increasing magnetic field, approaching zero at the maximum field scale for T>70 K. We argue here that this profound change in the thermoelectric response derives from the strong interaction of the 4d correlated electrons of the Pd ions with the short-range spin correlations of the Cr^{3+} spins that persist beyond the Néel ordering temperature due to the combined effects of geometrical frustration and low dimensionality.

Interaction phenomena in graphene seen through quantum capacitance.

Capacitance measurements provide a powerful means of probing the density of states. The technique has proved particularly successful in studying 2D electron systems, revealing a number of interesting many-body effects. Here, we use large-area high-quality graphene capacitors to study behavior of the density of states in this material in zero and high magnetic fields. Clear renormalization of the linear spectrum due to electron-electron interactions is observed in zero field. Quantizing fields lead to splitting of the spin- and valley-degenerate Landau levels into quartets separated by interaction-enhanced energy gaps. These many-body states exhibit negative compressibility but the compressibility returns to positive in ultrahigh B. The reentrant behavior is attributed to a competition between field-enhanced interactions and nascent fractional states.