Physical Review E

We study the emission of photons from germinating seeds using an experimental technique designed to detect photons of extremely small intensity when the signal/noise ratio is low. We analyze the dark count signal in the absence of germinating seeds as well as the photon emission during the germination process. The technique of analysis adopted here was originally designed to measure the temporal complexity of astrophysical, sociological and physiological processes. The foundation of this method, called Diffusion Entropy Analysis (DEA), rests on Kolmogorov complexity. The updated version of DEA used in this paper is designed to determine if the signal complexity is generated by either non-ergodic crucial events with a non-stationary correlation function or by the infinite memory of a stationary but non-integrable correlation function or by a mixture of both processes. We find that dark count yields the ordinary scaling, thereby showing that no complexity of either kinds may occur in the absence of any seeds in the chamber. In the presence of seeds in the chamber anomalous scaling emerges, reminiscent of that found in neuro-physiological processes. However, this is a mixture of both processes and with the progress of germination the non-ergodic component tends to vanish and complexity is dominated by the stationary infinite memory. We argue that this may be a sign of quantum coherence that according to some authors is the important ingredient of cognition.

A prototypical morphogen gradient that plays a key role in the early embryonic development of fruit flies, by providing positional information to cells, is that of the transcription factor Bicoid (Bcd). Recently a one-dimensional quantum walk model has been utilised to explain its multiple dynamic modes observed through fluorescence correlation spectroscopy (FCS) studies using a closed quantum system approach. In this work we use an open quantum system approach to the dynamics of the Bcd gradient formation and show that exactly the same dynamics are obtained through this more rigorous analysis. We then use the thus obtained expression for the fast dynamic modes to explain the Bcd transcription factor search times for binding to the promoter regions along the DNA. Specifically, we find that the large values of diffusivity allowed by quantum mechanics can avoid the paradox of faster-than-diffusion association rates without any need for the transcription factor to constantly alternate between 1D and 3D diffusion-based search processes. This might help explain the fast and precise transcriptional response elicited by such factors. We conclude that, since many transcription factors share a common search strategy for target gene regulatory regions, our mechanism may have a wide range of applicability.

Extracellular diffusion coupled with degradation is considered as the dominant mechanism behind the establishment of morphogen gradients. However, the fundamental nature of these biophysical processes visa viz the Bicoid (Bcd) morphogen gradient remains unclear. Fluorescence correlation spectroscopy (FCS) has recently revealed multiple modes of Bcd transport at different spatial and temporal locations across the embryo. We here show that these observations, and a few others, are fitted by a model fundamentally based on quantum mechanics. We also indicate that the abstract and auxiliary feature called chirality of the said formalism finds a natural expression in our model of the Bcd gradient formation that might be verified in future experiments on the system.

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.

We present a general theory of noisy genetic oscillators with externally regulated production rate. The observables that characterize the genetic oscillator are discussed, and it is shown how their statistics depend on the statistics of the external regulator. We show that these observables have generic features that are observed in two different experimental systems: the expression of the circadian clock genes in fibroblasts, and in the transient and oscillatory dynamics of the segmentation clock genes observed in cells disassociated from zebrafish embryos. Our work shows that genetic oscillations with diverse biological contexts can be understood in a common framework based on delayed negative feedback system, and slow regulator dynamics.

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.

We demonstrate that it is possible to draw direct numerical correlations between virus particles and effective virus-like particle (VLP) derived vaccines through extraction of a Bragg-Williams order parameter from electron microscopy. The method has its roots in studies of disorder in metal alloys, and is adapted to describe the type and occurrence of structural motifs within the arrangement of viral coat proteins, captured by the value of the order parameter as a measure of disorder. A conventional approach to viral vaccine design consists of replicating select proteins to create a VLP designed to trigger an immune response while remaining non-infectious. Understanding variations between viruses and vaccine strains therefore tends to focus on differences between proteins, which can be characterized through genetic analysis. While such an approach provides vital information about the functioning and interactions of the proteins, it does not yet yield an early-stage pathway towards predicting the efficacy of a vaccine, and so large-scale clinical trials are required to obtain critical information. With the urgency associated with pandemics, including Coronavirus Disease-2019 (COVID-19) originating from the SARS-CoV-2 virus, there is a need for earlier indications of whether a vaccine has the necessary characteristics. Application of the methodology to Dengue and influenza virus particles indicates that temperature and pH during incubation could potentially be exploited to fine-tune the order parameter of VLP-based vaccines to match the corresponding virus. Additionally, utilization of an Ising model plot reveals a clear relationship between case fatality rate and order parameter for distinct virus families.

In Nature there are significant relationships known between microorganisms from two kingdoms of life, as in the supply of vitamin B12 by bacteria to algae. Such interactions motivate general investigations into the spatio-temporal dynamics of metabolite exchanges. Here we study by experiment and theory a model system: a coculture of the bacterium B. subtilis, an obligate aerobe that is chemotactic to oxygen, and a nonmotile mutant of the alga C. reinhardtii, which photosynthetically produces oxygen when illuminated. Strikingly, when a shaft of light illuminates a thin, initially uniform suspension of the two, the chemotactic influx of bacteria to the photosyn-thetically active region leads to expulsion of the algae from that area. This effect arises from algal transport due to spatially-varying collective behavior of bacteria, and is mathematically related to the "turbulent diamagnetism" associated with magnetic flux expulsion in stars.

Escherichia coli serves as prototype for the study of peritrichous enteric bacteria that perform runs and tumbles alternately. Bacteria run forward as a result of the counterclockwise (CCW) rotation of their flagella bundle, which is located rearward, and perform tumbles when at least one of their flagella rotates clockwise (CW), moving away from the bundle. The flagella are hooked to molecular rotary motors of nanometric diameter able to make transitions between CCW and CW rotations that last up to one hundredth of a second. At the same time, flagella move or rotate the bacterias body microscopically during lapses that range between a tenth and ten seconds. We assume that the transitions between CCW and CW rotations occur solely by fluctuations of CheY-P molarity in the presence of two threshold values, and that a veto rule selects the run or tumble motions. We present Langevin equations for the CheY-P molarity in the vicinity of each molecular motor. This model allows to obtain the run- or tumble-time distribution as a linear combination of decreasing exponentials that is a function of the steady molarity of CheY-P in the neighbourhood of the molecular motor, which fits experimental data. In turn, if the internal signaling system is unstimulated, we show that the runtime distributions reach power-law behaviour, a characteristic of self-organized systems, in some time range and, afterwards, exponential cutoff. In addition, our model explains without any fitting parameters the ultrasensitivity of the flagella motors as a function of the steady state of CheY-P molarity. In addition, we show that the tumble bias for peritrichous bacterium has a similar sigmoid-shape to the CW bias, although shifted to lower concentrations when the flagella number increases. Thus, the increment in the flagella number allows lower operational values for each motor increasing amplification and robustness of the chemotatic signaling pathway.

The establishment and interpretation of the concentration distribution of the morphogen Bicoid (BCD) is considered crucial for the successful embryonic development of fruit flies. However, the biophysical mechanisms behind the timely formation and subsequent interpretation of the BCD morphogen by its target genes are not yet completely understood. Here a discrete-time, one-dimensional quantum walk model of BCD gradient formation is used to explain both the observed values of diffusivity and its precise interpretation. It is shown that the decoding of positional information from the BCD morphogen by its primary target gene hb, with the observed precision of [~] 10%, takes a time period of less than a second, as expected on the basis of recent experimental observations. From this the on-rate (kon) for the binding of BCD to its target loci is obtained. Furthermore, the model is also used to explain certain key observations of recent optogenetic experiments concerning the time windows for BCD interpretation. Finally, it is argued that the presented model represents a significant step in the utilization of quantum computation-based techniques in studying the dynamics of biological systems in general and in the field of developmental biophysics in particular.

The set of T cells that express the same T cell receptor (TCR) sequence represent a T cell clone. The number of different naive T cell clones in an organism reflects the number of different T cell receptors (TCRs) arising from recombination of the V(D)J gene segments during T cell development in the thymus. TCR diversity and more specifically, the clone abundance distribution is an important factor in immune function. Specific recombination patterns occur more frequently than others while subsequent interactions between TCRs and self-antigens are known to trigger proliferation and sustain naive T cell survival. These processes are TCR-dependent, leading to clone-dependent thymic export and naive T cell proliferation rates. Using a mean-field approximation to the solution of a regulated birth-death-immigration model, we systematically quantify how TCR-dependent heterogeneities in immigration and proliferation rates affect the shape of clone abundance distributions (the number of different clones that are represented by a specific number of cells). By comparing predicted clone abundances derived from our heterogeneous birth-death-immigration model with experimentally sampled clone abundances, we quantify the heterogeneity necessary to generate the observed abundances. Our findings indicate that heterogeneity in proliferation rates is more likely the mechanism underlying the observed clone abundance distributions than heterogeneity in immigration rates.\n\nAuthor SummaryThe abundance distribution of different T cell receptors (TCRs) expressed on naive T cells depends on their rates of thymic output, homeostatic proliferation, and death. However, measured TCR count distributions do not match, even qualitatively, those predicted from a multiclone birth death-immigration process when constant birth, death, and immigration rates are used (a neutral model). We show how non-neutrality in the birth-death-immigration process, where naive T cells with different TCRs are produced and proliferate with a distribution of rates shape the predicted sampled clone abundance distributions (the clone counts). Using physiological parameters, we find that heterogeneity in proliferation rates, and not in thymic output rates, is the main determinant in generating the observed clone counts. These findings are consistent with proliferation-driven maintenance of the T cell population in humans.

Cilia are hair-like micro-actuators whose cyclic motion is specialized to propel extracellular fluids at low Reynolds numbers. Clusters of these organelles can form synchronized beating patterns, called metachronal waves, which presumably arise from hydrodynamic interactions. We model hydrodynamically interacting cilia by microspheres elastically bound to circular orbits, whose inclinations with respect to the cellular wall model the ciliary power and recovery stroke, resulting in an anisotropy of the viscous flow. We derive a coupled phase oscillator description by reducing the microsphere dynamics to the slow time scale of synchronization and determine analytical metachronal wave solutions and their stability in a periodic chain setting. In this framework, a simple intuition for the hydrodynamic coupling between phase oscillators is established by relating the geometry of near-wall flow to the directionality of the hydrodynamic coupling functions. This intuition naturally explains the properties of the linear stability of metachronal waves. The flow confinement at the wall stabilizes metachronal waves with long wavelengths propagating in the direction of the power stroke and, moreover, metachronal waves with short wave lengths propagating perpendicularly to the power stroke. Performing simulations of phase oscillator chains with periodic boundary conditions, we indeed find that both wave types emerge with a variety of linearly stable wave numbers. In open chains of phase oscillators, the dynamics of metachronal waves is fundamentally different. Here, the elasticity of the model cilia controls the wave direction and selects a particular wave number: At large elasticity, waves traveling in the direction of the power stroke are stable, whereas at smaller elasticity waves in the opposite direction are stable. For intermediate elasticity both wave directions coexist. In this regime, waves propagating towards both ends of the chain form, but only one wave direction prevails, depending on the elasticity and initial conditions.

AO_SCPCAPBSTRACTC_SCPCAPBiological molecular machines are enzymes that simultaneously catalyze two processes, one donating free energy and second accepting it. Recent studies show that most native protein enzymes have a rich stochastic dynamics of conformational transitions which often manifests in fluctuating rates of the catalyzed processes and the presence of short-term memory resulting from the preference of certain conformations. For arbitrarily complex stochastic dynamics of protein machines, we proved the generalized fluctuation theorem predicting the possibility of reducing free energy dissipation at the expense of creating some information stored in memory. That this may be the case has been shown by interpreting results of computer simulations for a complex model network of stochastic transitions. The subject of the analysis was the time course of the catalyzed processes expressed by sequences of jumps at random moments of time. Since similar signals can be registered in the observation of real systems, all theses of the paper are open to experimental verification. STATEMENT OF SIGNIFICANCEThe transient utilization of memory for storing information turns out to be crucial for the movement of protein motors and the reason for most protein machines to operate as dimers or higher organized assemblies. From a broader physical point of view, the division of free energy into the operation and organization energies is worth emphasizing. Information can be assigned a physical meaning of a change in the value of both these functions of state.

We present quantitative predictions for experimental observables--amplitude, frequency and wavelength--of the eukaryotic flagellar beat in terms of underlying molecular chemomechanical parameters. Flagellar beating, an incompletely understood self-organized process arising from the collective action of dynein molecular motors, is modelled as a reaction-diffusion (RD) system with an oscillatory instability arising from motor-induced microtubule sliding. While the RD model accurately reproduces beating patterns of bull spermatozoa and C. Reinhardtii, existing linear analyses and simulations are unable to provide a complete framework for understanding nonlinear waveform formation. Here, we derive analytical expressions that reveal the nonlinear dependence of beat characteristics on parameters such as motor binding duty ratio, stepping velocity, and axonemal resistance. Our analysis uncovers a novel out-of-equilibrium mechanism for base-to-tip wave propagation, involving an interference pattern between unstable standing wave modes that generates travelling waves. Predicted beat patterns agree remarkably with numerical simulations, even far from the critical point marking the onset of oscillations. This unveils key molecular parameters that govern oscillation initiation, amplitude saturation, frequency shifts, and the spatial phase gradient crucial for generating propulsive hydrodynamic force. Our results yield biophysical understanding of how molecular interactions shape flagellar beating patterns, allowing for the inference of molecular properties from macroscopic observations. This challenges existing hypotheses on wave generation and demonstrates the power of nonlinear analysis to uncover new phenomena beyond the reach of linear models and computational studies alone.

Diffusion-limited processes (DLP) are found in various physical, biological, and engineering systems, yet their quantification within complex spatial domains remains a challenge. In this study, we develop novel one-dimensional non-periodic and periodic pair-correlation functions (PCF) to assess the spatial patterns of DLP within a cylindrical domain. By refining previous PCF formulations, we introduce an efficient binning-based approach that significantly reduces computational costs, making the method feasible for large-scale simulations. Our analysis provides a comprehensive examination of PCF variability, distinguishing between global deviations from complete spatial randomness state and sampling-induced variation. An off-lattice agent-based model is implemented, successfully reproducing self-organized patterns reminiscent of classical DLP studies and aligning with fractal-like aggregation behaviours. We demonstrate the utility of periodic PCFs in capturing key spatial correlations in DLP, particularly in azimuthal and Cartesian projections, while highlighting the conditions under which non-periodic PCFs remain preferable. Our findings underscore the potential of PCFs as robust summary statistics for complex spatial models, with applications ranging from microbial colony formation and blood clotting dynamics to image analysis and classification algorithms.

The mechanism by which microtubules find kinetochores during spindle formation is a key question in cell biology. Previous experimental studies have shown that although search-and-capture of kinetochores by dynamic microtubules is a dominant mechanism in many organisms, several other capture mechanisms are also possible. One such mechanism reported in Schizosaccharomyces pombe shows that microtubules can exhibit a prolonged pause between growth and shrinkage. During the pause, the microtubules pivoted at the spindle pole body search for the kinetochores by performing an angular diffusion. Is the latter mechanism purely accidental, or could there be any physical advantage underlying its selection? To compare the efficiency of these two mechanisms, we numerically study distinct models and compute the timescales of kinetochore capture as a function of microtubule number N. We find that the capture timescales have non-trivial dependences on microtubule number, and one mechanism may be preferred over the other depending on this number. While for small N (as in fission yeast), the typical capture times due to rotational diffusion are lesser than those for search-and-capture, the situation is reversed beyond a certain N. The capture times for rotational diffusion tend to saturate due to geometrical constraints, while those for search-and-capture reduce monotonically with increasing N making it physically more efficient. The results provide a rationale for the common occurrence of classic search-and-capture process in many eukaryotes which have few hundreds of dynamic microtubules, as well as justify exceptions in cells with fewer microtubules.

Microbes exhibit complex dynamic behavior as the result of a large number of biochemical processes, spatial and temporal interactions, environmental variations, and evolutionary pressure. Although significant progress has been achieved in understanding microbial ecological dynamics, multiple open questions remain, including the microscopic mechanisms of growth and the roles of nutrients and stochasticity. In this work, we present a minimal theoretical approach to clarify the link between consumption of resources by microbes and their growth. A stochastic model that accounts for a single microbial species consuming a single type of resource while growing via cell division is studied analytically and via Monte Carlo computer simulations. We identify three distinct dynamical regimes of microbial growth determined by the relative magnitudes of resource uptake and division rates and initial conditions. We also show that stochasticity influences the dynamic behavior when the amounts of microbes or resources are low. The model recovers Monod growth kinetics and provides a mechanistic interpretation of the Monod constant and maximal growth rate. The theoretical framework presented captures a wide spectrum of dynamic behaviors in microbial systems, providing a clearer microscopic picture to explain their underlying complex mechanisms.

From atomic spins in magnets to galaxies, and from embryonic development to patchy vegetation in arid environments, the physical world is filled with complex systems that spontaneously form spatial patterns. While simple mathematical models, such as reaction-diffusion systems, can explain the formation of such patterns, the complexity of the physical systems these models aim to describe necessitates the analysis of model robustness. Our work utilizes random matrix theory to provide arguably the first definition of robustness that is analytically tractable, providing an easy guide for identifying spatial interactions that robustly generate spatial patterns. We illustrate our theory on examples from mathematical biology, showing that diffusion alone cannot robustly generate spatial Turing patterns in large and unstructured systems, while advection, chemotaxis and non-local interactions can robustly promote pattern formation. Furthermore, we use our theory to prove that the spinodal decompositon of soft condensed matter is dynamically robust and predict the dynamics beyond regimes permitted by the standard Landau-Ginzburg theory. By classifying different spatial interactions based on the robustness of pattern formation, this work provides insights into which mechanisms are fundamental for pattern formation in large and unstructured physical systems.

The establishment and interpretation of the concentration gradient of the morphogen Bicoid (Bcd) is crucial for the successful embryonic development of fruit flies. However, the biophysical mechanisms behind the timely formation and subsequent interpretation of this prototypical morphogen gradient by its target genes are not yet completely understood. Recently a discrete time, one-dimensional quantum walk model of Bcd gradient formation has been successfully used to explain the observed multiple dynamic modes of the system. However, the question of its precise interpretation by its primary target gene hunchback (hb) remains still unanswered. In this paper it will be shown that the interpretation of the Bcd gradient by its primary target gene hb, with the observed precision of [~] 10%, takes a time period of less than a second, as expected on the basis of recent experimental observations. Furthermore, the quantum walk model is also used to explain certain key observations of recent optogenetic experiments concerning the time windows for Bcd interpretation. Finally, it is concluded that the incorporation of quantum effects into the treatment of Bcd gradient represents a viable step in exploring its dynamics.

Building on the known scaling law that a single timescale, a cellular unit of time, governs stochastic growth and division of individual bacterial cells under constant growth conditions, here we propose that a dynamic rescaling of the cellular unit of time serves to capture the dominant effect of changing conditions on the cell age distribution. This temporal scaling ansatz provides a natural representation for these time-dependent dynamics in whose terms the cell age distribution evolves under time-invariant rules! Finally, we discuss relevance of these results to recent high-precision experiments on individual bacterial cells growing and dividing in dynamic environments.