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The number of possible melodies is unfathomably large, yet despite this virtually unlimited potential for melodic variation, melodies from different societies can be surprisingly similar. The motor constraint hypothesis accounts for certain similarities, such as scalar motion and contour shape, but not for other major common features, such as repetition, song length, and scale size. Here we investigate the role of information constraints arising from limitations on human memory in shaping these hallmarks of melodies. We measure determinants of information rate in 62 corpora of Folk melodies spanning several continents, finding multiple trade-offs that all act to constrain the information rate across societies. By contrast, 39 corpora of Art music from Europe (including Turkey) show longer, more complex melodies, and increased complexity over time, suggesting different cultural-evolutionary selection pressures in Art and Folk music, possibly due to the use of written versus oral transmission. Our parameter-free model predicts the empirical scale degree distribution using information constraints on scalar motion, melody length, and, most importantly, information rate. This provides strong evidence that information constraints during cultural transmission of music limit the number of notes in a scale, and proposes that preference for intermediate melodic complexity is a fundamental constraint on the cultural evolution of melody.

The standard theory of musical scales since antiquity has been based on harmony, rather than melody. Some recent analyses support either view, and we lack a comparative test on cross-cultural data. We address this longstanding problem through a rigorous, computational comparison of the main theories against 1,314 scales from 96 countries. There is near-universal support for melodic theories, which predict step-sizes of 1-3 semitones. Harmony accounts for the prevalence of some simple-integer-ratio intervals, particularly for music-theoretic scales from Eurasian societies, which may explain their dominance amongst Western scholars. However, harmony poorly predicts scales measured from ethnographic recordings, particularly outside of Eurasia. Overall, we show that the historical emphasis on harmony is misguided and that melody is the primary determinant of the world's musical scales.

Despite recent breakthroughs in understanding how protein sequence relates to structure and function, considerably less attention has been paid to the general features of protein surfaces beyond those regions involved in binding and catalysis. This paper provides a systematic survey of the universe of protein surfaces and quantifies the sizes, shapes, and curvatures of the positively/negatively charged and hydrophobic/hydrophilic surface patches as well as correlations between such patches. It then compares these statistics with the metrics characterizing nanoparticles functionalized with ligands terminated with positively and negatively charged ligands. These particles are of particular interest because they are also surface-patchy and have been shown to exhibit both antibiotic and anticancer activities - via selective interactions against various cellular structures - prompting loose analogies to proteins. Our analyses support such analogies in several respects (e.g., patterns of charged protrusions and hydrophobic niches similar to those observed in proteins), although there are also significant differences. Looking forward, this work provides a blueprint for the rational design of synthetic nanoobjects with further enhanced mimicry of proteins' surface properties.

A cylinder will roll down an inclined plane in a straight line. A cone will roll around a circle on that plane and then will stop rolling. We ask the inverse question: For which curves drawn on the inclined plane $\mathbb{R}^2$ can one carve a shape that will roll downhill following precisely this prescribed curve and its translationally repeated copies? This simple question has a solution essentially always, but it turns out that for most curves, the shape will return to its initial orientation only after crossing a few copies of the curve - most often two copies will suffice, but some curves require an arbitrarily large number of copies.

AI algorithms have proven to be excellent predictors of protein structure, but whether and how much these algorithms can capture the underlying physics remains an open question. Here, we aim to test this question using the Alphafold2 (AF) algorithm: We use AF to predict the subtle structural deformation induced by single mutations, quantified by strain, and compare with experimental datasets of corresponding perturbations in folding free energy $\Delta\Delta G$. Unexpectedly, we find that physical strain alone -- without any additional data or computation -- correlates almost as well with $\Delta\Delta G$ as state-of-the-art energy-based and machine-learning predictors. This indicates that the AF-predicted structures alone encode fine details about the energy landscape. In particular, the structures encode significant information on stability, enough to estimate (de-)stabilizing effects of mutations, thus paving the way for the development of novel, structure-based stability predictors for protein design and evolution.

Proteins are intricate molecular machines whose complexity arises from the heterogeneity of the amino acid building blocks and their dynamic network of many-body interactions. These nanomachines gain function when put in the context of a whole organism through interaction with other inhabitants of the biological realm. And this functionality shapes their evolutionary histories through intertwined paths of selection and adaptation. Recent advances in machine learning have solved the decades-old problem of how protein sequence determines their structure. However, the ultimate question regarding the basic logic of protein machines remains open: How does the collective physics of proteins lead to their functionality? and how does a sequence encode the full range of dynamics and chemical interactions that facilitate function? Here, we explore these questions within a physical approach that treats proteins as mechano-chemical machines, which are adapted to function via concerted evolution of structure, motion, and chemical interactions.

We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space RG in a lattice while considers the overall information loss in momentum-space RG. Here we compromise the two measures for the non-spatial data set. For weakly correlated data close to Gaussian, we use the correlation of data as a metric for the proximity of data points, but minimize an overall projection error for optimal coarse-graining steps. It compresses the data to maximize the correlation between the two data points to be compressed while minimizing the correlation between the paired data and other data points. We show that this approach can effectively reduce the dimensionality of the data while preserving the essential features. We extend our method to incorporate non-linear features by replacing correlation measures with mutual information. This results in an information-bottleneck-like trade-off: maximally compress the data while preserving the information among the compressed data and the rest. Indeed, our approach can be interpreted as an exact form of information-bottleneck-like trade off near linear data. We examine our method with random Gaussian data and the Ising model to demonstrate its validity and apply glass systems. Our approach has potential applications in various fields, including machine learning and statistical physics.

Nanoswimmers are ubiquitous in bio- and nano-technology but are extremely challenging to measure due to their minute size and driving forces. A simple method is proposed for detecting the elusive physical features of nanoswimmers by observing how they affect the motion of much larger, easily traceable particles. Modeling the swimmers as hydrodynamic force dipoles, we find direct, easy-to-calibrate relations between the observable power spectrum and diffusivity of the tracers and the dynamic characteristics of the swimmers: their force dipole moment and correlation times., Comment: 10 pages, 1 figure

AlphaFold2 (AF) is a promising tool, but is it accurate enough to predict single mutation effects? Here, we report that the localized structural deformation between protein pairs differing by only 1-3 mutations -- as measured by the effective strain -- is correlated across \num{3901} experimental and AF-predicted structures. Furthermore, analysis of ${\sim} 11000$ proteins shows that the local structural change correlates with various phenotypic changes. These findings suggest that AF can predict the range and magnitude of single-mutation effects on average, and we propose a method to improve precision of AF predictions and to indicate when predictions are unreliable.

The concept of quasiparticles -- long-lived low-energy particle-like excitations -- has become a keystone of condensed quantum matter, where it explains a variety of emergent many-body phenomena, such as superfluidity and superconductivity. Here, we use quasiparticles to explain the collective behavior of a classical system of hydrodynamically interacting particles in two dimensions. In the disordered phase of this matter, measurements reveal a sub-population of long-lived particle pairs. Modeling and simulation of the ordered crystalline phase identify the pairs as quasiparticles, emerging at the Dirac cones of the spectrum. The quasiparticles stimulate supersonic pairing avalanches, bringing about the melting of the crystal. In hexagonal crystals, where the intrinsic threefold symmetry of the hydrodynamic interaction matches that of the crystal, the spectrum forms a flat band dense with ultra-slow, low-frequency phonons whose collective interactions induce a much sharper melting transition. Altogether, these findings demonstrate the usefulness of concepts from quantum matter theory in understanding many-body physics in classical dissipative settings.

Proteins need to selectively interact with specific targets among a multitude of similar molecules in the cell. But despite a firm physical understanding of binding interactions, we lack a general theory of how proteins evolve high specificity. Here, we present such a model that combines chemistry, mechanics and genetics, and explains how their interplay governs the evolution of specific protein-ligand interactions. The model shows that there are many routes to achieving molecular discrimination - by varying degrees of flexibility and shape/chemistry complementarity - but the key ingredient is precision. Harder discrimination tasks require more collective and precise coaction of structure, forces and movements. Proteins can achieve this through correlated mutations extending far from a binding site, which fine-tune the localized interaction with the ligand. Thus, the solution of more complicated tasks is enabled by increasing the protein size, and proteins become more evolvable and robust when they are larger than the bare minimum required for discrimination. The model makes testable, specific predictions about the role of flexibility and shape mismatch in discrimination, and how evolution can independently tune affinity and specificity. Thus, the proposed theory of specific binding addresses the natural question of "why are proteins so big?". A possible answer is that molecular discrimination is often a hard task best performed by adding more layers to the protein.

Phylostratigraphy suggests that new genes are continually born de novo from non-genic sequences, and the genes that persist found new lineages, contributing to the adaptive evolution of organisms. While recent evidence supports the view that de novo gene birth is frequent and widespread, the mechanisms underlying this process are yet to be discovered. Here we hypothesize and examine a potential general mechanism of gene birth driven by the accumulation of beneficial mutations at non-genic loci. To demonstrate this possibility, we model this mechanism within the boundaries set by current knowledge on mutation effects. Estimates from this analysis are in line with observations of recurrent and extensive gene birth in genomics studies. Thus, we propose that, rather than being inactive and silent, non-genic regions are likely to be dynamic storehouses of potential genes.

Living systems have evolved to efficiently consume available energy sources using an elaborate circuitry of chemical reactions which, puzzlingly, bear a strict restriction to asymmetric chiral configurations. While autocatalysis is known to promote such chiral symmetry breaking, whether a similar phenomenon may also be induced in a more general class of configurable chemical systems -- via energy exploitation -- is a sensible yet underappreciated possibility. This work examines this question within a model of randomly generated complex chemical networks. We show that chiral symmetry breaking may occur spontaneously and generically by harnessing energy sources from external environmental drives. Key to this transition are intrinsic fluctuations of achiral-to-chiral reactions and tight matching of system configurations to the environmental drives, which together amplify and sustain diverged enantiomer distributions. These asymmetric states emerge through steep energetic transitions from the corresponding symmetric states and sharply cluster as highly-dissipating states. The results thus demonstrate a generic mechanism in which energetic drives may give rise to homochirality in an otherwise totally symmetrical environment, and from an early-life perspective, might emerge as a competitive, energy-harvesting advantage.

Scales, sets of discrete pitches that form the basis of melodies, are thought to be one of the most universal hallmarks of music. But we know relatively little about cross-cultural diversity of scales or how they evolved. To remedy this, we assemble a cross-cultural database (Database of Musical Scales: DaMuSc) of scale data, collected over the past century by various ethnomusicologists. Statistical analyses of the data highlight that certain intervals (e.g., the octave, fifth, second) are used frequently across cultures. Despite some diversity among scales, it is the similarities across societies which are most striking - most scales are found close to equidistant 5- and 7-note scales. We discuss the mechanisms of variation and selection in the evolution of scales, and how the assembled data may be used to examine the root causes of convergent evolution., Comment: 15 pages, 7 figures, 20 page supplement

Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and inventing new cell types. A hurdle to understanding developmental evolution is the difficulty of even describing the intertwined network of spatiotemporal processes underlying the development of complex multicellular organisms. Nonetheless, an overview of developmental trajectories can be obtained from cell type lineage maps. Here, we propose that these lineage maps can also reveal how developmental programs evolve: the modes of evolving new cell types in an organism should be visible in its developmental trajectories, and therefore in the geometry of its cell type lineage map. This idea is demonstrated using a parsimonious generative model of developmental programs, which allows us to reliably survey the universe of all possible programs and examine their topological features. We find that, contrary to belief, tree-like lineage maps are rare and lineage maps of complex multicellular organisms are likely to be directed acyclic graphs where multiple developmental routes can converge on the same cell type. While cell type evolution prescribes what developmental programs come into existence, natural selection prunes those programs which produce low-functioning organisms. Our model indicates that additionally, lineage map topologies are correlated with such a functional property: the ability of organisms to regenerate.

We report on the experimental observation of stochastic resonance (SR) in a nonGaussian active bath without any periodic modulation. A Brownian particle hopping in a nanoscale double-well potential under the influence of nonGaussian correlated noise, with mean interval ${{\tau }_{P}}$ and correlation time ${{\tau }_{c}}$, shows a series of equally-spaced peaks in the residence time distribution at integral multiples of ${{\tau }_{P}}$. The strength of the first peak is found to be maximum when the mean residence time ${{\bar{\tau }}_{d}}$ matches the double condition, $4{{\tau }_{c}}\approx {{\tau }_{P}}\approx {{\bar{\tau }}_{d}}\text{/}2$, demonstrating a new type of bona fide SR. The experimental findings agree with a simple model that explains the emergence of SR without periodic modulation of the double-well potential. Additionally, we show that generic SR under periodic modulation, known to degrade in strongly correlated continuous noise, is recovered by the discrete nonGaussian kicks.

Variation of positional information, measured by the two-body excess entropy $\mathsf{S}_\mathrm{2}$, is studied across the liquid-solid equilibrium transition in a simple two-dimensional system. Analysis reveals a master relation between $\mathsf{S}_\mathrm{2}$ and the freezing temperature $T_{\mathrm{f}}$, from which a scaling law is extracted: $-\mathsf{S}_\mathrm{2}\sim |T_{\mathrm{f}} - T| ^{-1/3}$. Theoretical and practical implications of the observed universality are discussed.

The cellular milieu is teeming with biochemical nano-machines whose activity is a strong source of correlated non-thermal fluctuations termed active noise. Essential elements of this circuitry are enzymes, catalysts that speed up the rate of metabolic reactions by orders of magnitude, thereby making life possible. Here, we examine the possibility that active noise in the cell, or in vitro, affects enzymatic catalytic rate by accelerating or decelerating the crossing rate of energy barriers during the reaction. Considering hydrodynamic perturbations induced by biochemical activity as a source of active noise, we evaluate their impact on the enzymatic cycle using a combination of analytic and numerical methods. Our estimates show that the fast component of the active noise spectrum enhances the rate of enzymes, while reactions remain practically unaffected by the slow noise spectrum. Revisiting the physics of barrier crossing under the influence of active hydrodynamic fluctuations suggests that the biochemical activity of macromolecules such as enzymes is coupled to active noise. Thus, we propose that enzymatic catalysis is a collective, many-body process in which enzymes may affect each other's activity via long-range hydrodynamic interaction, with potential impact on biochemical networks in living and artificial systems alike.

The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data -- by distilling underlying principles and mechanisms -- necessitates dimensional reduction. We propose that living systems achieve exquisite dimensional reduction, originating from their capacity to learn, through evolution and phenotypic plasticity, the relevant aspects of a non-random, smooth physical reality. We explain how geometric insights by mathematicians allow one to identify these genuine hallmarks of life and distinguish them from universal properties of generic data sets. We illustrate these principles in a concrete example of protein evolution, suggesting a simple general recipe that can be applied to understand other biological systems.

Hydrodynamics is shown to induce non-Hermitian topological phenomena in ordinary, passive soft matter. This is demonstrated for the first time by subjecting a 2D elastic lattice to a low-Reynolds viscous flow. The interplay of hydrodynamics and elasticity splits Dirac cones into bulk Fermi arcs, pairing exceptional points with opposite half-integer topological charges. The bulk Fermi arc is a generic hallmark of the system exhibited in all lattice and flow symmetries. Analytic model and simulations explain how the emergent singularities shape the spectral bands and give rise to a web of van Hove singularity lines in the density of states. The present findings suggest that non-Hermitian physics can be explored in a broad class of ordinary soft matter, living and artificial alike, opening avenues for topology-based technology in this regime.

The design of small scale non-equilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for non-equilibrium systems is lacking, making the design problem particularly difficult. Here we show we can exploit the large deviation behavior of a Brownian particle and design a variety of geometrically complex steady-state density distributions and flux field flows. We achieve this design target from direct knowledge of the joint large deviation functional for the empirical density and flow, and a "relaxation" algorithm on the desired target states via adjustable force field parameters. We validate the method by replicating analytical results, and demonstrate its capacity to yield complex prescribed targets, such as rose-curve or polygonal shapes on the plane. We consider this dynamical fluctuation approach a first step towards the design of more complex NESS where general frameworks are otherwise still lacking., Comment: 9 pages; 4 figures; Supplementary information; v3: fixed processing issue in v2

Molecular agitation more rapid than thermal Brownian motion is reported for cellular environments, motor proteins, synthetic molecular motors, enzymes, and common chemical reactions, yet that chemical activity couples to molecular motion contrasts with generations of accumulated knowledge about diffusion at equilibrium. To test the limits of this idea, a critical testbed is mobility of catalytically active enzymes. Sentiment is divided about reality of enhanced enzyme diffusion with evidence for and against. Here a master curve shows that enzyme diffusion coefficient increases in proportion to the energy release rate, the product of Michaelis-Menten reaction rate and Gibbs free energy change with the highly satisfactory correlation coefficient of 0.97. For ten catalytic enzymes (urease, acetylcholinesterase, seven enzymes from the glucose cascade cycle, and another), our measurements span from roughly 40% enhanced diffusion coefficient at high turnover rate and negative Gibbs free energy to no enhancement at slow turnover rate and positive Gibbs free energy. Moreover, two independent measures of mobility show consistency, provided that one avoids undesirable fluorescence photophysics. The master curve presented here quantifies the limits of both ideas, that enzymes display enhanced diffusion and that they do not within instrumental resolution, and has possible implications for understanding enzyme mobility in cellular environments. The striking linear dependence for the exergonic enzymes (negative Gibbs free energy) together with the vanishing effect for endergonic enzyme (positive Gibbs free energy) are consistent with a physical picture where the mechanism boosting the diffusion is an active one, utilizing the available work from the chemical reaction.

Proteins are translated from the N- to the C-terminus, raising the basic question of how this innate directionality affects their evolution. To explore this question, we analyze 16,200 structures from the protein data bank (PDB). We find remarkable enrichment of $\alpha$-helices at the C terminus and $\beta$-strands at the N terminus. Furthermore, this $\alpha$-$\beta$ asymmetry correlates with sequence length and contact order, both determinants of folding rate, hinting at possible links to co-translational folding (CTF). Hence, we propose the 'slowest-first' scheme, whereby protein sequences evolved structural asymmetry to accelerate CTF: the slowest of the cooperatively-folding segments are positioned near the N terminus so they have more time to fold during translation. A phenomenological model predicts that CTF can be accelerated by asymmetry, up to double the rate, when folding time is commensurate with translation time; analysis of the PDB reveals that structural asymmetry is indeed maximal in this regime. This correspondence is greater in prokaryotes, which generally require faster protein production. Altogether, this indicates that accelerating CTF is a substantial evolutionary force whose interplay with stability and functionality is encoded in sequence asymmetry., Comment: 10 pages, 5 figures

Thermodynamic uncertainty relations (TURs) set fundamental bounds on the fluctuation and dissipation of stochastic systems. Here, we examine these bounds, in experiment and theory, by exploring the entire phase space of a cyclic information engine operating in a non-equilibrium steady state. Close to its maximal efficiency, we find that the engine violates the original TUR. This first experimental demonstration of TUR violation agrees with recently proposed softer bounds: The engine satisfies two generalized TUR bounds derived from the detailed fluctuation theorem with feedback control and another bound linking fluctuation and dissipation to mutual information and Renyi divergence. We examine how the interplay of work fluctuation and dissipation shapes the information conversion efficiency of the engine, and find that dissipation is minimal at a finite noise level, where the original TUR is violated.

Understanding noisy information engines is a fundamental problem of non-equilibrium physics, particularly in biomolecular systems agitated by thermal and active fluctuations in the cell. By the generalized second law of thermodynamics, the efficiency of these engines is bounded by the mutual information passing through their noisy feedback loop. Yet, direct measurement of the interplay between mutual information and energy has so far been elusive. To allow such examination, we explore here the entire phase-space of a noisy colloidal information engine, and study efficiency fluctuations due to the stochasticity of the mutual information and extracted work. We find that the average efficiency is maximum for non-zero noise level, at which the distribution of efficiency switches from bimodal to unimodal, and the stochastic efficiency often exceeds unity. We identify a line of anomalous, noise-driven equilibrium states that defines a refrigerator-to-heater transition, and test the generalized integral fluctuation theorem for continuous engines.

Development combines three basic processes asymmetric --- cell division, signaling and gene regulation --- in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here, we attempt to chart this diversity using a generative model. We sample millions of biologically feasible developmental schemes, allowing us to comment on the statistical properties of cell-differentiation trajectories they produce. Our results indicate that, in contrast to common views, cell-type lineage graphs are unlikely to be tree-like. Instead, they are more likely to be directed acyclic graphs, with multiple lineages converging on the same terminal cell-type. Additionally, in line with the hypothesis that whole body regeneration is an epiphenomenon of development, a majority of the `organism' generated by our model can regenerate using pluripotent cells. The generative framework is modular and flexible, and can be adapted to test additional hypotheses about general features of development.

To mitigate errors induced by the cell's heterogeneous noisy environment, its main information channels and production networks utilize the kinetic proofreading (KPR) mechanism. Here, we examine two extensively-studied KPR circuits, DNA replication by the T7 DNA polymerase and translation by the E. coli ribosome. Using experimental data, we analyze the performance of these two vital systems in light of the fundamental bounds set by the recently-discovered thermodynamic uncertainty relation (TUR), which places an inherent trade-off between the precision of a desirable output and the amount of energy dissipation required. We show that the DNA polymerase operates close to the TUR lower bound, while the ribosome operates $\sim5$ times farther from this bound. This difference originates from the enhanced binding discrimination of the polymerase which allows it to operate effectively as a reduced reaction cycle prioritizing correct product formation. We show that approaching this limit also decouples the thermodynamic uncertainty factor from speed and error, thereby relaxing the accuracy-speed trade-off of the system. Altogether, our results show that operating near this reduced cycle limit not only minimizes thermodynamic uncertainty, but also results in global performance enhancement of KPR circuits., Comment: Main text: 9 pages, 6 figures. 2 tables; no supplementary information

Chaperone protein - the most disordered among all protein groups - help RNAs fold into their functional structure by destabilizing misfolded configurations or stabilizing the functional ones. But disentangling the mechanism underlying RNA chaperoning is challenging, mostly due to inherent disorder of the chaperones and the transient nature of their interactions with RNA. In particular, it is unclear how specific the interactions are and what role is played by amino acid charge and polarity patterns. Here, we address these questions in the RNA chaperone StpA. We adapted direct coupling analysis (DCA) into the $\alpha\beta$DCA method that can treat in tandem sequences written in two alphabets, nucleotides and amino acids. With $\alpha\beta$DCA, we could analyze StpA-RNA interactions and show consistency with a previously proposed two-pronged mechanism: StpA disrupts specific positions in the group I intron while globally and loosely binding to the entire structure. Moreover, the interactions are strongly associated with the charge pattern: negatively charged regions in the destabilizing StpA N-terminal affect a few specific positions in the RNA, located in stems and in the pseudoknot. In contrast, positive regions in the C-terminal contain strongly coupled amino acids that promote non-specific or weakly-specific binding to the RNA. The present study opens new avenues to examine the functions of disordered proteins and to design disruptive proteins based on their charge patterns.

The concept that catalytic enzymes can act as molecular machines transducing chemical activity into motion has conceptual and experimental support, but much of the claimed support comes from experimental conditions where the substrate concentration is higher than biologically relevant and accordingly exceeds kM, the Michaelis-Menten constant. Moreover, many of the enzymes studied experimentally to date are oligomeric. Urease, a hexamer of subunits, has been considered to be the gold standard demonstrating enhanced diffusion. Here we show that urease and certain other oligomeric enzymes of high catalytic activity above kM dissociate into their smaller subunit fragments that diffuse more rapidly, thus providing a simple physical mechanism of enhanced diffusion in this regime of concentrations. Mindful that this conclusion may be controversial, our findings are sup-ported by four independent analytical techniques, static light scattering, dynamic light scattering (DLS), size-exclusion chroma-tography (SEC), and fluorescence correlation spectroscopy (FCS). Data for urease are presented in the main text and the con-clusion is validated for hexokinase and acetylcholinesterase with data presented in supplementary information. For substrate concentration regimes below kM at which these enzymes do not dissociate, our findings from both FCS and DLS validate that enzymatic catalysis does lead to the enhanced diffusion phenomenon. INTRODUCT, Comment: 7 pages, 5 figures, supplementary information

Proteins are a matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with multifarious biochemistry. But it is also an instantiation along an evolutionary trajectory determined by the function performed by the protein within a hierarchy of interwoven interaction networks of the cell, the organism and the population. A physical theory of proteins therefore needs to unify both aspects, the biophysical and the evolutionary. Specifically, it should provide a model of how the DNA gene is mapped into the functional phenotype of the protein. We review several physical approaches to the protein problem, focusing on a mechanical framework which treats proteins as evolvable condensed matter: Mutations introduce localized perturbations in the gene, which are translated to localized perturbations in the protein matter. A natural tool to examine how mutations shape the phenotype are Green's functions. They map the evolutionary linkage among mutations in the gene (termed epistasis) to cooperative physical interactions among the amino acids in the protein. We discuss how the mechanistic view can be applied to examine basic questions of protein evolution and design.

Musical scales are used throughout the world, but the question of how they evolved remains open. Some suggest that scales based on the harmonic series are inherently pleasant, while others propose that scales are chosen that are easy to communicate. However, testing these theories has been hindered by the sparseness of empirical evidence. Here, we assimilate data from diverse ethnomusicological sources into a cross-cultural database of scales. We generate populations of scales based on multiple theories and assess their similarity to empirical distributions from the database. Most scales tend to include intervals which are close in size to perfect fifths (``imperfect fifths''), and packing arguments explain the salient features of the distributions. Scales are also preferred if their intervals are compressible, which may facilitate efficient communication and memory of melodies. While scales appear to evolve according to various selection pressures, the simplest h imperfect-fifths packing model best fits the empirical data., Comment: including SI

The Supercritical Fluid (SCF) is known to exhibit salient dynamic and thermodynamic crossovers and inhomogeneous molecular distribution. But the question as to what basic physics underlies these microscopic and macroscopic anomalies remains open. Here, using an order parameter extracted by machine learning, the fraction of gas-like (or liquid-like) molecules, we find simplicity and universality in SCF: First, all isotherms of a given fluid collapse onto a single master curve described by a scaling relation. The observed power law holds from the high-temperature and pressure regime down to the critical point where it diverges. Second, phase diagrams of different compounds collapse onto their master curves by the same scaling exponent, thereby demonstrating a putative law of corresponding supercritical states in simple fluids. The reported results support a model of the SCF as a mixture of two interchangeable microstates, whose spatiotemporal dynamics gives rise to unique macroscopic properties., Comment: 10 pages, 2 figures

All known life forms are based upon a hierarchy of interwoven feedback loops, operating over a cascade of space, time and energy scales. Among the most basic loops are those connecting DNA and proteins. For example, in genetic networks, DNA genes are expressed as proteins, which may bind near the same genes and thereby control their own expression. In this molecular type of self-reference, information is mapped from the DNA sequence to the protein and back to DNA. There is a variety of dynamic DNA-protein self-reference loops, and the purpose of this remark is to discuss certain geometrical and physical aspects related to the back and forth mapping between DNA and proteins. The discussion raises basic questions regarding the nature of DNA and proteins as self-referring matter, which are examined in a simple toy model., Comment: 17 pages, 9 figures; title updated and typos corrected

We report on a lossless information engine that converts nearly all available information from an error-free feedback protocol into mechanical work. Combining high-precision detection at resolution of 1 nm with ultrafast feedback control, the engine is tuned to extract the maximum work from information on the position of a Brownian particle. We show that the work produced by the engine achieves a bound set by a generalized second law of thermodynamics, demonstrating for the first time the sharpness of this bound. We validate a generalized Jarzynski equality for error-free feedback-controlled information engines.

We report on the coexistence of liquid-like and gas-like structures in supercritical fluid (SCF). The deltoid coexistence region encloses the Widom line, and may therefore be termed the "Widom delta". Machine learning analysis of simulation data shows continuous transition across the delta, from liquid-like to gas-like states, with fractions following a simplified two-state model. This suggests a microscopic view of the SCF as a mixture of liquid-like and gas-like structures, where the anomalous behavior near the critical point originates from fluctuations between the two types.

The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly-coupled amino acid network whose interactions and motions are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids, and thereby the transmission of forces. Mutations introduce localized perturbations to the propagator which scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis -- the interaction among mutations in the gene -- is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution, and observe long-range epistasis which facilitates collective functional modes., Comment: published in PNAS

How DNA is mapped to functional proteins is a basic question of living matter. We introduce and study a physical model of protein evolution which suggests a mechanical basis for this map. Many proteins rely on large-scale motion to function. We therefore treat protein as learning amorphous matter that evolves towards such a mechanical function: Genes are binary sequences that encode the connectivity of the amino acid network that makes a protein. The gene is evolved until the network forms a shear band across the protein, which allows for long-range, soft modes required for protein function. The evolution reduces the high-dimensional sequence space to a low-dimensional space of mechanical modes, in accord with the observed dimensional reduction between genotype and phenotype of proteins. Spectral analysis of the space of $10^6$ solutions shows a strong correspondence between localization around the shear band of both mechanical modes and the sequence structure. Specifically, our model shows how mutations of the gene and their correlations occur at amino acids whose interactions determine the functional mode.

We examine the binding of transcription factors to DNA in terms of an information transfer problem. The input of the noisy channel is the biophysical signal of a factor bound to a DNA site, and the output is a distribution of probable DNA sequences at this site. This task involves an inherent tradeoff between the information gain and the energetics of the binding interaction - high binding energies provide higher information gain but hinder the dynamics of the system as factors are bound too tightly. We show that adaptation of the binding interaction towards increasing information transfer under a general energy constraint implies that the information gain per specific binding energy at each base-pair is maximized. We analyze hundreds of prokaryote and eukaryote transcription factors from various organisms to evaluate the discrimination energies. We find that, in accordance with our theoretical argument, binding energies nearly maximize the information gain per energy. This work suggests the adaptation of information gain as a generic design principle of molecular recognition systems.

Bow-tie or hourglass structure is a common architectural feature found in biological and technological networks. A bow-tie in a multi-layered structure occurs when intermediate layers have much fewer components than the input and output layers. Examples include metabolism where a handful of building blocks mediate between multiple input nutrients and multiple output biomass components, and signaling networks where information from numerous receptor types passes through a small set of signaling pathways to regulate multiple output genes. Little is known, however, about how bow-tie architectures evolve. Here, we address the evolution of bow-tie architectures using simulations of multi-layered systems evolving to fulfill a given input-output goal. We find that bow-ties spontaneously evolve when two conditions are met: (i) the evolutionary goal is rank deficient, where the rank corresponds to the minimal number of input features on which the outputs depend, and (ii) The effects of mutations on interaction intensities between components are described by product rule - namely the mutated element is multiplied by a random number. Product-rule mutations are more biologically realistic than the commonly used sum-rule mutations that add a random number to the mutated element. These conditions robustly lead to bow-tie structures. The minimal width of the intermediate network layers (the waist or knot of the bow-tie) equals the rank of the evolutionary goal. These findings can help explain the presence of bow-ties in diverse biological systems, and can also be relevant for machine learning applications that employ multi-layered networks.

We study the average asymptotic growth rate of cells in randomly fluctuating environments, with multiple viable phenotypes per environment. We show that any information processing strategy has an asymptotic growth rate, which is the sum of: (i) the maximal growth rate at the worst possible distribution of environments, (ii) relative information between the actual distribution of environments to the worst one, and (iii) information utilization rate, which is the information rate of the sensory devices minus the "information dissipation rate", the amount of information not utilized by the cell for growth. In non-stationary environments, we find that the optimal phenotypic switching times equally partition the information dissipation rate between consecutive switching intervals.