Search

Significance The standard genetic code (SGC) is common to all sufficiently explored Earth biota, suggesting a common origin for protein biosynthesis in every known organism. The ancient events leading to this near-universal biological characteristic are manifestly of scientific importance. The accompanying text presents a detailed pathway for formation of the SGC, as well as a method for identifying essential origin events. Significantly, the SGC can evolve using only well-characterized chemical, biochemical, and physical mechanisms, paralleling other known evolutionary transitions., Minimally evolved codes are constructed here; these have randomly chosen standard genetic code (SGC) triplets, completed with completely random triplet assignments. Such “genetic codes” have not evolved, but retain SGC qualities. Retained qualities are basic, part of the underpinning of coding. For example, the sensitivity of coding to arbitrary assignments, which must be < ∼10%, is intrinsic. Such sensitivity comes from the elementary combinatorial properties of coding and constrains any SGC evolution hypothesis. Similarly, assignment of last-evolved functions is difficult because of late kinetic phenomena, likely common across codes. Census of minimally evolved code assignments shows that shape and size of wobble domains controls the code’s fit into a coding table, strongly shifting accuracy of codon assignments. Access to the SGC therefore requires a plausible pathway to limited randomness, avoiding difficult completion while fitting a highly ordered, degenerate code into a preset three-dimensional space. Three-dimensional late Crick wobble in a genetic code assembled by lateral transfer between early partial codes satisfies these varied, simultaneous requirements. By allowing parallel evolution of SGC domains, this origin can yield shortened evolution to SGC-level order and allow the code to arise in smaller populations. It effectively yields full codes. Less obviously, it unifies previously studied chemical, biochemical, and wobble order in amino acid assignment, including a stereochemical minority of triplet–amino acid associations. Finally, fusion of intermediates into the final SGC is credible, mirroring broadly accepted later cellular evolution.

Significance Attaching sensors to crowd-sourced vehicles could provide a cheap and accurate way to monitor air pollution, road quality, and other aspects of a city’s health. But in order for so-called drive-by sensing to be practically useful, the sensor-equipped vehicle fleet needs to have large “sensing power”—that is, it needs to cover a large fraction of a city’s area during a given reference period. Here, we provide an analytic description of the sensing power of taxi fleets, which agrees with empirical data from nine major cities. Our results show taxis’ sensing power is unexpectedly large—in Manhattan; just 10 random taxis cover one-third of street segments daily, which certifies that drive-by sensing can be readily implemented in the real world., Sensors can measure air quality, traffic congestion, and other aspects of urban environments. The fine-grained diagnostic information they provide could help urban managers to monitor a city’s health. Recently, a “drive-by” paradigm has been proposed in which sensors are deployed on third-party vehicles, enabling wide coverage at low cost. Research on drive-by sensing has mostly focused on sensor engineering, but a key question remains unexplored: How many vehicles would be required to adequately scan a city? Here, we address this question by analyzing the sensing power of a taxi fleet. Taxis, being numerous in cities, are natural hosts for the sensors. Using a ball-in-bin model in tandem with a simple model of taxi movements, we analytically determine the fraction of a city’s street network sensed by a fleet of taxis during a day. Our results agree with taxi data obtained from nine major cities and reveal that a remarkably small number of taxis can scan a large number of streets. This finding appears to be universal, indicating its applicability to cities beyond those analyzed here. Moreover, because taxis’ motion combines randomness and regularity (passengers’ destinations being random, but the routes to them being deterministic), the spreading properties of taxi fleets are unusual; in stark contrast to random walks, the stationary densities of our taxi model obey Zipf’s law, consistent with empirical taxi data. Our results have direct utility for town councilors, smart-city designers, and other urban decision makers.

The concept of jamming has attracted great research interest due to its broad relevance in soft matter such as liquids, glasses, colloids, foams, and granular materials, and its deep connection to the sphere packing problem and optimization problems. Here we show that the domain of amorphous jammed states of frictionless spheres can be significantly extended, from the well-known jamming-point at a fixed density, to a jamming-plane that spans the density and shear strain axes. We explore the jamming-plane, via athermal and thermal simulations of compression and shear jamming, with a help of an efficient swap algorithm to prepare initial equilibrium configurations. The jamming-plane can be divided into reversible-jamming and irreversible-jamming regimes, based on the reversibility of the route from the initial configuration to jamming. Our results suggest that the irreversible-jamming behavior reflects an escape from the meta-stable glass basin to which the initial configuration belongs to, or the absence of such basins. All jammed states, either compression or shear jammed, are isostatic, and exhibit jamming criticality of the same universality class. However, the anisotropy of contact networks non-trivially depends on the jamming density and strain. Among all state points on the jamming-plane, the jamming-point is a unique one with the minimum jamming density and the maximum randomness. For lattice packings, the jamming-plane shrinks into a single shear jamming-line that is independent of initial configurations. Our study paves the way for solving the long-standing random close packing problem, and provides a more complete framework to understand jamming., 28 pages, 23 figures

Significance The structure of life emerged from randomness. This is attributed to selection by molecular Darwinian evolution. This study found that random templated ligation led to the simultaneous elongation and sequence selection of oligomers. Product strands showed highly structured sequence motifs which inhibited self-folding and built self-templating reaction networks. By the reduction of the sequence space, the kinetics of duplex formation increased and led to a faster replication through the ligation process. These findings imply that elementary binding properties of nucleotides can lead to an early selection of sequences even before the onset of Darwinian evolution. This suggests that such a simplification of sequence space could result in faster downstream selection for sequence-based function for the origin of life., The central question in the origin of life is to understand how structure can emerge from randomness. The Eigen theory of replication states, for sequences that are copied one base at a time, that the replication fidelity has to surpass an error threshold to avoid that replicated specific sequences become random because of the incorporated replication errors [M. Eigen, Naturwissenschaften 58 (10), 465–523 (1971)]. Here, we showed that linking short oligomers from a random sequence pool in a templated ligation reaction reduced the sequence space of product strands. We started from 12-mer oligonucleotides with two bases in all possible combinations and triggered enzymatic ligation under temperature cycles. Surprisingly, we found the robust creation of long, highly structured sequences with low entropy. At the ligation site, complementary and alternating sequence patterns developed. However, between the ligation sites, we found either an A-rich or a T-rich sequence within a single oligonucleotide. Our modeling suggests that avoidance of hairpins was the likely cause for these two complementary sequence pools. What emerged was a network of complementary sequences that acted both as templates and substrates of the reaction. This self-selecting ligation reaction could be restarted by only a few majority sequences. The findings showed that replication by random templated ligation from a random sequence input will lead to a highly structured, long, and nonrandom sequence pool. This is a favorable starting point for a subsequent Darwinian evolution searching for higher catalytic functions in an RNA world scenario.

Significance Systems biology seeks to combine experiments with computation to predict biological behaviors. However, despite tremendous data and knowledge, biological models make less-accurate predictions compared with other fields. By analyzing single-cell, single-molecule measurements of mRNA during yeast stress response, we explore why and how the shapes of experimental distributions control prediction accuracy. We show how asymmetric data distributions with long tails cause standard modeling approaches to yield excellent fits but make meaningless predictions. We show how these biases arise from the violation of fundamental assumptions in standard modeling approaches. We demonstrate how advanced computational tools solve this dilemma and achieve predictive understanding of spatiotemporal mechanisms of transcription control including RNA polymerase initiation and elongation and mRNA accumulation, transport, and decay., Despite substantial experimental and computational efforts, mechanistic modeling remains more predictive in engineering than in systems biology. The reason for this discrepancy is not fully understood. One might argue that the randomness and complexity of biological systems are the main barriers to predictive understanding, but these issues are not unique to biology. Instead, we hypothesize that the specific shapes of rare single-molecule event distributions produce substantial yet overlooked challenges for biological models. We demonstrate why modern statistical tools to disentangle complexity and stochasticity, which assume normally distributed fluctuations or enormous datasets, do not apply to the discrete, positive, and nonsymmetric distributions that characterize mRNA fluctuations in single cells. As an example, we integrate single-molecule measurements and advanced computational analyses to explore mitogen-activated protein kinase induction of multiple stress response genes. Through systematic analyses of different metrics to compare the same model to the same data, we elucidate why standard modeling approaches yield nonpredictive models for single-cell gene regulation. We further explain how advanced tools recover precise, reproducible, and predictive understanding of transcription regulation mechanisms, including gene activation, polymerase initiation, elongation, mRNA accumulation, spatial transport, and decay.

Significance Complex systems in many fields, because of their intrinsic nonlinear dynamics, can exhibit a tipping point (point of no return) at which a total collapse of the system occurs. In ecosystems, environmental deterioration can lead to evolution toward a tipping point. To predict tipping point is an outstanding and extremely challenging problem. Using complex bipartite mutualistic networks, we articulate a dimension reduction strategy and establish its general applicability to predicting tipping points using a large number of empirical networks. Not only can our reduced model serve as a paradigm for understanding the tipping point dynamics in real world ecosystems for safeguarding pollinators, the principle can also be extended to other disciplines to address critical issues, such as resilience and sustainability., Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a “point of no return”) at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability.

We discovered unique Anderson localization behaviors of pseudospin systems in a 1D disordered potential. For a pseudospin-1 system, due to the absence of backscattering under normal incidence and the presence of a conical band structure, the wave localization behaviors are entirely different from those of conventional disordered systems. We show that there exists a critical strength of random potential ([Formula: see text]), which is equal to the incident energy ([Formula: see text]), below which the localization length [Formula: see text] decreases with the random strength [Formula: see text] for a fixed incident angle [Formula: see text] But the localization length drops abruptly to a minimum at [Formula: see text] and rises immediately afterward. The incident angle dependence of the localization length has different asymptotic behaviors in the two regions of random strength, with [Formula: see text] when [Formula: see text] and [Formula: see text] when [Formula: see text] The existence of a sharp transition at [Formula: see text] is due to the emergence of evanescent waves in the systems when [Formula: see text] Such localization behavior is unique to pseudospin-1 systems. For pseudospin-1/2 systems, there is also a minimum localization length as randomness increases, but the transition from decreasing to increasing localization length at the minimum is smooth rather than abrupt. In both decreasing and increasing regions, the [Formula: see text] dependence of the localization length has the same asymptotic behavior [Formula: see text].

The threshold behavior of the transport properties of a random metal in the critical region near a metal–insulator transition is strongly affected by the measuring electromagnetic fields. In spite of the randomness, the electrical conductivity exhibits striking phase-coherent effects due to broken symmetry, which greatly sharpen the transition compared with the predictions of effective medium theories, as previously explained for electrical conductivities. Here broken symmetry explains the sign reversal of the T → 0 magnetoconductance of the metal–insulator transition in Si(B,P), also previously not understood by effective medium theories. Finally, the symmetry-breaking features of quantum percolation theory explain the unexpectedly very small electrical conductivity temperature exponent α = 0.22(2) recently observed in Ni(S,Se) 2 alloys at the antiferromagnetic metal–insulator transition below T = 0.8 K.

The need to assess the randomness of a single sequence, especially a finite sequence, is ubiquitous, yet is unaddressed by axiomatic probability theory. Here, we assess randomness via approximate entropy (ApEn), a computable measure of sequential irregularity, applicable to single sequences of both (even very short) finite and infinite length. We indicate the novelty and facility of the multidimensional viewpoint taken by ApEn, in contrast to classical measures. Furthermore and notably, for finite length, finite state sequences, one can identify maximally irregular sequences, and then apply ApEn to quantify the extent to which given sequences differ from maximal irregularity, via a set of deficit (def m ) functions. The utility of these def m functions which we show allows one to considerably refine the notions of probabilistic independence and normality, is featured in several studies, including ( i ) digits of e, π, √2, and √3, both in base 2 and in base 10, and ( ii ) sequences given by fractional parts of multiples of irrationals. We prove companion analytic results, which also feature in a discussion of the role and validity of the almost sure properties from axiomatic probability theory insofar as they apply to specified sequences and sets of sequences (in the physical world). We conclude by relating the present results and perspective to both previous and subsequent studies.

The question of whether proteins originate from random sequences of amino acids is addressed. A statistical analysis is performed in terms of blocked and random walk values formed by binary hydrophobic assignments of the amino acids along the protein chains. Theoretical expectations of these variables from random distributions of hydrophobicities are compared with those obtained from functional proteins. The results, which are based upon proteins in the SWISS-PROT data base, convincingly show that the amino acid sequences in proteins differ from what is expected from random sequences in a statistical significant way. By performing Fourier transforms on the random walks one obtains additional evidence for non-randomness of the distributions. We have also analyzed results from a synthetic model containing only two amino-acid types, hydrophobic and hydrophilic. With reasonable criteria on good folding properties in terms of thermodynamical and kinetic behavior, sequences that fold well are isolated. Performing the same statistical analysis on the sequences that fold well indicates similar deviations from randomness as for the functional proteins. The deviations from randomness can be interpreted as originating from anticorrelations in terms of an Ising spin model for the hydrophobicities. Our results, which differ from previous investigations using other methods, might have impact on how permissive with respect to sequence specificity the protein folding process is -- only sequences with non-random hydrophobicity distributions fold well. Other distributions give rise to energy landscapes with poor folding properties and hence did not survive the evolution., 16 pages, 8 Postscript figures. Minor changes, references added

The fundamental question "Are sequential data random?" arises in myriad contexts, often with severe data length constraints. Furthermore, there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness--e.g., to evaluate the efficacy of therapy in medicine. We address both these issues from a computable framework via a quantification of regularity. ApEn (approximate entropy), defining maximal randomness for sequences of arbitrary length, indicating the applicability to sequences as short as N = 5 points. An infinite sequence formulation of randomness is introduced that retains the operational (and computable) features of the finite case. In the infinite sequence setting, we indicate how the "foundational" definition of independence in probability theory, and the definition of normality in number theory, reduce to limit theorems without rates of convergence, from which we utilize ApEn to address rates of convergence (of a deficit from maximal randomness), refining the aforementioned concepts in a computationally essential manner. Representative applications among many are indicated to assess (i) random number generation output; (ii) well-shuffled arrangements; and (iii) (the quality of) bootstrap replicates.

Linear empirical Bayes estimators have been obtained for means and variances that apply to random sampling from populations whose structure is unknown or only partly known.

The transmission of complexity during DNA replication has been investigated to clarify the significance of this molecular property in a deterministic process. Complexity was equated with the amount of randomness within an ordered molecular structure and measured by the entropy of a posteriori probabilities for discrete (monomer sequences, atomic bonds) and continuous (torsion angle sequences) structural parameters in polynucleotides, proteins, and ligand molecules. A theoretical analysis revealed that sequence complexity decreases during transmission from DNA to protein. It was also found that sequence complexity limits the attainable complexity in the folding of a polypeptide chain and that a protein cannot interact with a ligand moiety of higher complexity. The analysis indicated, furthermore, that in any deterministic molecular process a cause possesses more complexity than its effect. This outcome broadly complies with Curie's symmetry principle. Results from an analysis of an extensive set of experimental data are presented; they corroborate these findings. It is suggested, therefore, that complexity governs the direction of order—order molecular transformations. Two biological implications are ( i ) replication of DNA in a stepwise, repetitive manner by a polymerase appears to be a necessary consequence of structural constraints imposed by complexity, and ( ii ) during evolution, increases in complexity had to involve a nondeterministic mechanism. This latter requirement apparently applied also to development of the first replicating system on earth.