Physical Review E

We present an analysis of the coronavirus RNA genome via a study of its Fourier spectral density based on a binary representation of the nucleotide sequence. We find that at low frequencies, the power spectrum presents a small and distinct departure from the behavior expected from an uncorrelated sequence. We provide a couple of simple models to characterize such deviations. Away from a small low-frequency domain, the spectrum presents largely stochastic fluctuations about fixed values which vary inversely with the genome size generally. It exhibits no other peaks apart from those associated with triplet codon usage. We uncover an interesting, new scaling law for the coronavirus genome: the complexity of the genome scales linearly with the power-law exponent that characterizes the enveloping curve of the low-frequency domain of the spectral density.

Nucleosomes and their modifications often facilitate gene regulation in eukaryotes. Certain genomic regions may obtain alternate epigenetic states through enzymatic reactions forming positive feedback between nucleosome states. How a system of nucleosome states maintains confinement is an open question. Here we explore a family of stochastic dynamic models with combinations of readwrite enzymes. We find that a larger number of intermediate nucleosome states increases both the robustness of linear spreading in models with only local recruitment processes and the degree of bi-stability under conditions with at least one non-local recruitment. Further, supplementing the positive feedback with one negative feedback acting over long distances along the genome enables effective confinement of epigenetic, bistable regions. Our study emphasizes the importance of determining whether each particular read-write enzyme acts only locally or between distant nucleosomes.

Stochastic resonance (SR) describes the synchronization between noise of a system and an applied oscillating field to achieve an optimized response signal. In this work, we use simulations to investigate the phenomenon of SR of a single stranded DNA driven through a nanopore when an oscillating electric field is added. The system is comprised of a MspA protein nanopore embedded in a membrane and different lengths of DNA is driven from one end of the pore to the other via a constant potential difference. We superimposed an oscillating electric field on top of the existing electric field. The source of noise is due to thermal fluctuations, since the system is immersed in solution at room temperature. Here, the signal optimization we seek is the increase in translocation time of DNA through the protein nanopore. Normally, translocation time scales linearly with DNA length and inversely with driving force in a drift dominated regime. We found a non-monotonic dependence of the mean translocation time with the frequency of the oscillating field. This non-monotonic behavior of the translocation time is observed for all lengths of DNA, but SR occurs only for longer DNA. Furthermore, we also see evidence of DNA extension being influenced by the oscillating field while moving through the nanopore.

Biomolecular clocks produce sustained oscillations in mRNA/protein copy numbers that are subject to inherent copy-number fluctuations with important implications for proper cellular timekeeping. These random fluctuations embedded within periodic variations in copy numbers make the quantification of noise particularly challenging in stochastic gene oscillatory systems, unlike other non-oscillatory circuits. Motivated by diurnal cycles driving circadian clocks, we investigate the noise properties in the well-known Goodwin oscillator in the presence and absence of a periodic driving signal. We use two approaches to compute the noise as a function of time: (i) solving the moment dynamics derived from the linear noise approximation (LNA) assuming fluctuations are small relative to the mean and (ii) analyzing trajectories obtained from exact stochastic simulations of the Goodwin oscillator. Our results demonstrate that the LNA can predict the noise behavior quite accurately when the system shows damped oscillations or in the presence of external periodic forcing. However, the LNA could be misleading in the case of sustained oscillations without an external signal due to the propagation of large noise. Finally, we study the effect of random bursting of gene products on the clock stochastic dynamics. Our analysis reveals that the burst of mRNAs enhances the noise in the copy number regardless of the presence of external forcing, although the extent of fluctuations becomes less due to the forcing.

Computational biology holds immense promise as a domain that can leverage quantum advantages due to its involvement in a wide range of challenging computational tasks. Researchers have recently explored the applications of quantum computing in genome assembly implementation. However, the issue of repetitive sequences remains unresolved. In this paper, we propose a hybrid assembly quantum algorithm using high-accuracy short reads and error-prone long reads to deal with sequencing errors and repetitive sequences. The proposed algorithm builds upon the variational quantum eigensolver and utilizes divide-and-conquer strategies to approximate the ground state of larger Hamiltonian while conserving quantum resources. Using simulations of 10-qubit quantum computers, we address problems as large as 140 qubits, yielding optimal assembly results. The convergence speed is significantly improved via the problem-inspired ansatz based on the known information about the assembly problem. Besides, entanglement within quantum circuits is qualitatively verified to notably accelerate the assembly path optimization.

AO_SCPLOWBSTRACTC_SCPLOWFinding vaccine or specific antiviral treatment for global pandemic of virus diseases (such as the ongoing COVID-19) requires rapid analysis, annotation and evaluation of metagenomic libraries to enable a quick and efficient screening of nucleotide sequences. Traditional sequence alignment methods are not suitable and there is a need for fast alignment-free techniques for sequence analysis. Information theory and data compression algorithms provide a rich set of mathematical and computational tools to capture essential patterns in biological sequences. In 2013, our research group (Nagaraj et al., Eur. Phys. J. Special Topics 222(3-4), 2013) has proposed a novel measure known as Effort-To-Compress (ETC) based on the notion of compression-complexity to capture the information content of sequences. In this study, we propose a compression-complexity based distance measure for automatic identification of SARS coronavirus strains from a set of viruses using only short fragments of nucleotide sequences. We also demonstrate that our proposed method can correctly distinguish SARS-CoV-2 from SARS-CoV-1 viruses by analyzing very short segments of nucleotide sequences. This work could be extended further to enable medical practitioners in automatically identifying and characterizing SARS coronavirus strain in a fast and efficient fashion using short and/or incomplete segments of nucleotide sequences. Potentially, the need for sequence assembly can be circumvented. NoteThe main ideas and results of this research were first presented at the International Conference on Nonlinear Systems and Dynamics (CNSD-2013) held at Indian Institute of Technology, Indore, December 12, 2013. In this manuscript, we have extended our preliminary analysis to include SARS-CoV-2 virus as well.

The beating of cilia and flagella is essential to perform many important biological functions, including generating fluid flows on the cell surface or propulsion of micro-organisms. In this work, we analyze the motion of isolated and demembranated flagella from green algae Chlamydomonas reinhardtii, which act as ATP-driven micro-swimmers. The waveform of the Chlamydomonas beating flagella has an asymmetric waveform that is known to involve the superposition of a static component, corresponding to a fixed, intrinsic curvature, and a dynamic wave component traveling in the base-to-tip direction at the fundamental beat frequency, plus higher harmonics. Here, we demonstrate that these modes are not sufficient to reproduce the observed flagella waveforms. We find that two extra modes play an essential role to describe the motion: first, a time-symmetric mode, which corresponds to a global oscillation of the axonemal curvature, and second, a secondary tip-to-base wave component at the fundamental frequency that propagates opposite to the dominant base-to-tip wave, albeit with a smaller amplitude. Although the time-symmetric mode cannot, by itself, contribute to propulsion (scallop theorem), it does enhance the translational and rotational velocities of the flagellum by approximately a factor of 2. This mode highlights a long-range coupled on/off activity of force-generating dynein motors and can provide further insight into the underling biology of the ciliary beat.

Many biological systems exhibit sustained, coherent oscillations despite substantial noise. In contrast, chemical reaction systems governed by Markovian dynamics cannot sustain coherent ensemble oscillations, as the stochastic nature of state transitions inevitably causes the oscillation period to drift. To overcome this limitation, we propose a general mechanism that couples a Markovian system to at least one other degree of freedom, such as a mechanical system, to achieve noiseresistant coherent oscillations with a desired frequency. We introduce two approaches, targeting different dynamical modes in the Markovian system, and derive a governing principle for the non-Markovian system by analyzing the eigenvalues of the coupled dynamics. This principle is validated using a trimolecular reaction system, successfully producing sustained and coherent oscillations. Our study provides theoretical insights into how any chemical system can be coupled to another non-Markovian system to produce sustained and coherent oscillations with a precise period. We also make a fundamental observation that stability and control of stable limit cycles must arise from the non-Markovian part of the coupled system.

A variety of living and non-living systems exhibit collective motion. From swarm robotics to bacterial swarms, and tissue wound healing to human crowds, examples of collective motion are highly diverse but all of them share the common necessary ingredient of moving and interacting agents. While collective motion has been extensively studied in non-proliferating systems, how the proliferation of constituent agents affects their collective behavior is not well understood. Here, we focus on growing active agents as a model for cells and study how the interplay between noise in their direction of movement and proliferation determines the overall spatial pattern of collective motion. In this agent-based model, motile cells possess the ability to adhere to each other through cell-cell adhesion, grow in size and divide. Cell-cell interactions influence not only the direction of cell movement but also cell growth through a force-dependent mechanical feedback process. We show that noise in the direction of a cells motion has striking effects on the emergent spatial distribution of cell collectives and proliferation. While higher noise strength leads to a random spatial distribution of cells, we also observe increased cell proliferation. On the other hand, low noise strength leads to a ring-like spatial distribution of cell collectives together with lower proliferation. Our findings provide insight into how noise in the direction of cell motion determines the local spatial organization of cells with consequent mechanical feedback on cell division impacting cell proliferation due to the formation of cell clusters.

The statistics of correlations are central quantities characterizing the collective dynamics of recurrent neural networks. We derive exact expressions for the statistics of correlations of nonlinear recurrent networks in the limit of a large number N of neurons, including systematic 1/N corrections. Our approach uses a path-integral representation of the networks stochastic dynamics, which reduces the description to a few collective variables and enables efficient computation. This generalizes previous results on linear networks to include a wide family of nonlinear activation functions, which enter as interaction terms in the path integral. These interactions can resolve the instability of the linear theory and yield a strictly positive participation dimension. We present explicit results for power-law activations, revealing scaling behavior controlled by the network coupling. In addition, we introduce a class of activation functions based on Pade approximants and provide analytic predictions for their correlation statistics. Numerical simulations confirm our theoretical results with excellent agreement.

As of 21st May 2020, there have been 4.89M confirmed cases worldwide and over 323,000 deaths of people who have tested positive for SARS-CoV-2. The outbreak of COVID-19, has not only caused widespread morbidity and mortality, but has also led to a catastrophic breakdown in the global economy and unprecedented social disruption. To lessen the global health consequences of COVID-19, sweeping COVID-19 lockdown and quarantine measures have been imposed within many nations. These measures have significantly impacted the worlds economy and in many cases has led to the loss of livelihood. Mathematical modeling of pandemics is of critical importance to understand the unfolding of transmission events and to formulate control measures. In this research letter, we have introduced a novel approach to forecasting epidemics like COVID-19. The proposed mathematical model stems from the fundamental principles of fluid dynamics, and can be utilized to make projections of the number of infected people. This unique mathematical model can be beneficial for predicting and designing potential strategies to mitigate the spread and impact of pandemics.

To understand the choice and competition of sites in nature, we consider an ecological environment in a chemostat consisting of a polymorphic microbial population that can float in the fluid or settle down on the wall of the chemostat. For the transition of a microbe from its floating state to its settled state at a particular settling rate involving the choice and competition of sites on the wall, we consider three different mechanisms: (i) unimolecular-Bourgeois settling, i.e., floaters land freely on the wall, but in an occupied site, the owner keeps the site (Bourgeois behaviour); (ii) unimolecular-anti-Bourgeois settling, i.e., floaters land freely on the wall, but in an occupied site, the intruder gets the site (anti-Bourgeois behaviour); (iii) bimolecular settling, i.e., floaters land only on the vacant sites of the wall. Employing the framework of adaptive dynamics, we study the evolution of the settling rate with different settling mechanisms and investigate how physical operating conditions affect the evolutionary dynamics. Our results indicate that settling mechanisms and physical operating conditions have significant influences on the direction of evolution and the diversity of phenotypes. (1) For constant nutrient input, theoretical analysis shows that the population is always monomorphic during the long-term evolution. Notably, the direction of evolution depends on the settling mechanisms and physical operating conditions, which further determines the composition of the population. Moreover, we find two exciting transformations of types of Pairwise Invasibility Plots, which are the gradual transformation and the bang-bang transformation. (2) For periodic nutrient input, numerical analysis reveals that evolutionary coexistence is possible, and the population eventually maintains dimorphism. Remarkably, for all three settling mechanisms, the long-term evolution leads to one of the two coexisting species settle down totally on the wall if the input is low-frequency but float entirely in the fluid if the input becomes high-frequency.

A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the networks Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytical expression for the covariance eigenvalue distribution in the large-network limit can be obtained using results from random matrices. The distribution has a finitely supported smooth bulk spectrum and exhibits an approximate power-law tail for coupling matrices near the critical edge. We generalize the results to include connectivity motifs and discuss extensions to Excitatory-Inhibitory networks. The theoretical results are compared with those from finite-size networks and and the effects of temporal and spatial sampling are studied. Preliminary application to whole-brain imaging data is presented. Using simple connectivity models, our work provides theoretical predictions for the covariance spectrum, a fundamental property of recurrent neuronal dynamics, that can be compared with experimental data.

We investigate a spatially explicit metapopulation model consisting of one predator and two hierarchically competing prey species on a discrete lattice. Each local population follows stochastic rules for extinction, colonisation, competition, and predation. From the master equation of this individual-based model, we rigorously derive the corresponding mean-field equations. The analysis of these first-principles mean-field equations reveals the existence of a rich phase diagram with different coexistence regimes depending on parameter values. We identify both stable and spiral nodes, in agreement with the damped oscillations observed in Monte Carlo simulations in the latter case. We find qualitative agreement between the mean-field results and Monte Carlo simulations for the three-species coexistence and for the coexistence of the two prey species. However, the mean-field description fails to reproduce the coexistence between the predator and the inferior prey at high predator coverages. We argue that this discrepancy arises from spatial prey aggregation, which the mean-field approach cannot capture since it neglects correlations. In the stochastic model, spatial clustering acts as a crucial protective mechanism against predation, particularly for the best coloniser. Our findings suggest that prey aggregation contributes to system stability when colonisation and predation operate at comparable spatial scales. The combination of first-principles mean-field equations and stochastic simulations constitutes a powerful framework for clarifying the roles of hierarchical interactions, predation, colonisation, spatial organisation and stochasticity in multi-species coexistence.

Self-propelled bacteria can exhibit a large variety of non-equilibrium self-organized phenomena. Swarming is one such fascinating dynamical scenario where a number of motile individuals grouped into clusters and move in synchronized flows and vortices. While precedent investigations in rod-like particles confirm that increased aspect-ratio promotes alignment and order, recent experimental studies in bacteria Bacillus subtilis show a non-monotonic dependence of cell-aspect ratio on their swarming motion. Here, by computer simulations of an agent-based model of selfpropelled, mechanically interacting, rod-shaped bacteria in overdamped condition, we explore the collective dynamics of bacterial swarm subjected to a variation of cell-aspect ratio. When modeled with an identical self-propulsion speed across a diverse range of cell aspect ratio, simulations demonstrate that both shorter and longer bacteria exhibit slow dynamics whereas the fastest speed is obtained at an intermediate aspect ratio. Our investigation highlights that the origin of this observed non-monotonic trend of bacterial speed and vorticity with cell-aspect ratio is rooted in the cell-size dependence of motility force. The swarming features remain robust for a wide range of surface density of the cells, whereas asymmetry in friction attributes a distinct effect. Our analysis identifies that at an intermediate aspect ratio, an optimum cell size and motility force promote alignment, which reinforces the mechanical interactions among neighboring cells leading to the overall fastest motion. Mechanistic underpinning of the collective motions reveals that it is a joint venture of the short-range repulsive and the size-dependent motility forces, which determines the characteristics of swarming.

The study of interfacial roughening is common in physics, from epitaxial growth in the lab to pio-neering mathematical descriptions of universality in models of growth processes. These studies led to the identification of a series of general principles. Typically, stochastic growth produces an interface that becomes rougher as the deposit grows larger; this roughening can only be counteracted by mechanisms that act on the top of deposit, such as surface tension or surface diffusion. However, even when relaxation mechanisms are present, interfaces that continue to grow stochastically continue to change; new peaks and troughs emerge and disappear as stochastic growth produces a constantly changing, dynamic interface. These universal phenomena have been observed for bacterial colonies in a variety of contexts. However, previous studies have not characterized the interfacial phenomena at the top surface of a colony, i.e., the colony-air interface, when activity is only present at the bottom surface, i.e., the colony-solid interface, where nutrients are available, over long times. As traditional interfacial roughening models primarily focus on activity occurring at the top surface it is unclear what phenomena to expect over long times. Here, we use white light interferometry to study the roughening of bacterial biofilms, from many different species. We find that these colonies are remarkably smooth, suggesting that a mechanism of interfacial relaxation is at play. However, colonies remain remarkably smooth even after growing large. We discover that topographic fluctuations "freeze" in place, despite the fact that growth continues for hundreds of microns more. With simple simulations, we show that this emergent freezing is due to the dampening of fluctuations from cell growth by the cells between the growing zone and the surface. We find that the displacement field caused by a single perturbation decays exponentially, with a decay length of{delta} L. In line with that observation we also show that the topography ceases to change when perturbations are a distance{delta} L away from the surface. Thus, over-damped systems in which activity occurs at the bottom surface represent a distinct class of interfacial growth phenomena, capable of producing frozen topographies and remarkably smooth surfaces from spatially and temporally stochastic growth.

We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via delayed synaptic coupling between the excitatory neurons, while each inhibitory neuron is connected only to the corresponding excitatory neuron in the same population. We show that multiple equilibria can exist depending on the strength of the excitatory coupling between the populations. We conduct linear stability analysis of the equilibria and derive necessary conditions for delay-induced Hopf bifurcation. We show that these can induce two qualitatively different phase-locked behaviors, with the type of behavior determined by the sizes of the coupling delays. Numerical bifurcation analysis and simulations supplement and confirm our analytical results. Our work shows that the resting equilibrium point is unaffected by the coupling, thus the network exhibits bistability between a rest state and an oscillatory state. This may help understand how rhythms spontaneously arise neuronal networks.

Genes are connected in complex networks of interactions where often the product of one gene is a transcription factor that alters the expression of another. Many of these networks are based on a few fundamental motifs leading to switches and oscillators of various kinds. And yet, there is more to the story than which transcription factors control these various circuits. These transcription factors are often themselves under the control of effector molecules that bind them and alter their level of activity. Traditionally, much beautiful work has shown how to think about the stability of the different states achieved by these fundamental regulatory architectures by examining how parameters such as transcription rates, degradation rates and dissociation constants tune the circuit, giving rise to behavior such as bistability. However, such studies explore dynamics without asking how these quantities are altered in real time in living cells as opposed to at the fingertips of the synthetic biologists pipette or on the computational biologists computer screen. In this paper, we make a departure from the conventional dynamical systems view of these regulatory motifs by using statistical mechanical models to focus on endogenous signaling knobs such as effector concentrations rather than on the convenient but more experimentally remote knobs such as dissociation constants, transcription rates and degradation rates that are often considered. We also contrast the traditional use of Hill functions to describe transcription factor binding with more detailed thermodynamic models. This approach provides insights into how biological parameters are tuned to control the stability of regulatory motifs in living cells, sometimes revealing quite a different picture than is found by using Hill functions and tuning circuit parameters by hand.

In this work, we build upon a simple model of a primitive nervous system presented in a prior companion paper. Within this model, we formulate and solve an optimization problem, aiming to mirror the process of evolutionary optimization of the nervous system. The formally derived predictions include the emergence of sharp peaks of neural activity ( spikes), an increasing sensory sensitivity to external signals and a dramatic reduction in the cost of the functioning of the nervous system due to evolutionary optimization. Our work implies that we may be able to make general predictions about the behavior and characteristics of the nervous system irrespective of specific molecular mechanisms or evolutionary trajectories. It also underscores the potential utility of evolutionary optimization as a key principle in mathematical modeling of the nervous system and offers examples of analytical derivations possible in this field. Though grounded in a simple model, our findings offer a novel perspective, merging theoretical frameworks from nonequilibrium statistical physics with evolutionary principles. This perspective may guide more comprehensive inquiries into the intricate nature of neural networks.

1The description of transcription as a stochastic process provides a framework for the analysis of intrinsic and extrinsic noise in cells. To better understand the behaviors and possible extensions of existing models, we design an exact stochastic simulation algorithm for a multimolecular transcriptional system with an Ornstein-Uhlenbeck birth rate that is implemented via a special function-based time-stepping algorithm. We demonstrate that its joint copy-number distributions reduce to analytically well-studied cases in several limiting regimes, and suggest avenues for generalizations.