Expressed Transcription Factors (TFs) not only bind to sites at target promoters but also to decoy sites scattered across the genome. Binding to such "decoys"sequesters TFs critically impacting the response time and stochasticity (noise) in TF and target gene expression level. When the TF is a stable molecule, whose concentration is diluted by cellular growth, our results show that for fixed mean concentration levels, such decoy bindings can both enhance or suppress random fluctuations in TF levels depending on the source of noise (i.e., intrinsic vs. extrinsic noise) and the strength of binding (i.e., weak vs. strong decoys). We implement negative autoregulation where free (unbound) TF molecules inhibit their synthesis. Our analytical results corroborated by numerical simulations reveal that sequestration accentuates the effects of feedback in the sense that noise attenuation by negative feedback is higher with sequestration than in the absence of feedback. We next consider an alternative form of feedback where the TF increases the production of its decoys, and such feedback architectures are frequently seen in endogenous gene regulation involving microRNA-TF circuits and in controlling cellular stress responses. For these circuits where decoy numbers are TF-regulated, we identify limits of noise suppression, and in many cases, these limits occur at intermediate TF-decoy binding affinities.

Large groups of active cilia collectively beat in a fluid medium as metachronal waves, essential for some microorganisms motility and for flow generation in mucociliary clearance. Several models can predict the emergence of metachronal waves, but what controls the properties of metachronal waves is still unclear. Here, we numerically investigate the respective impacts of active beating and viscous dissipation on the properties of metachronal waves in a collection of oscillators, using a simple model for cilia in the presence of noise on regular lattices in one and two dimensions. We characterize the wave using spatial correlation and the frequency of collective beating. Our results clearly show that the viscosity of the fluid medium does not affect the wavelength; the activity of the cilia does. These numerical results are supported by a dimensional analysis, which shows that the result of wavelength invariance is robust against the model taken for sustained beating and the structure of hydrodynamic coupling. Interestingly, the enhancement of cilia activity increases the wavelength and decreases the beating frequency, keeping the wave velocity almost unchanged. These results might have significance in understanding paramecium locomotion and mucociliary clearance diseases.

Expressed gene products often interact ubiquitously with binding sites at nucleic acids and macromolecular complexes, known as decoys. The binding of transcription factors (TFs) to decoys can be crucial in controlling the stochastic dynamics of gene expression. Here, we explore the impact of decoys on the timing of intracellular events, as captured by the time taken for the levels of a given TF to reach a critical threshold level, known as the first passage time (FPT). Although nonlinearity introduced by binding makes exact mathematical analysis challenging, employing suitable approximations and reformulating FPT in terms of an alternative variable, we analytically assess the impact of decoys. The stability of the decoy-bound TFs against degradation impacts FPT statistics crucially. Decoys reduce noise in FPT, and stable decoy-bound TFs offer greater timing precision with less expression cost than their unstable counterparts. Interestingly, when both bound and free TFs decay at the same rate, decoy binding does not directly alter FPT noise. We verify these results by performing exact stochastic simulations. These results have important implications for the precise temporal scheduling of events involved in the functioning of biomolecular clocks, development processes, cell-cycle control, and cell-size homeostasis.

Within cells, transcription factors (TFs) bind to a wide range of nonspecific genomic sites in addition to their target sites. Binding to such high affinity “decoys” has been shown to qualitatively alter the dynamics of gene regulatory circuits. Analyzing simple gene expression models with decoy binding we derive formulas for the TF response time as a function of the number of decoys, binding affinity, and stability of the decoy-bound TF. Our results show that while on one hand, decoys make the response sluggish whenever decoy binding stabilizes the TF, on the other hand, decoys can accelerate responses by destabilizing the bound TF. We apply these results in the context of a genetic oscillator based on an activator-repressor motif, where sustained oscillations result from a rapid activator-mediated positive feedback working in conjunction with a slow repressor-mediated negative feedback. Consistent with our response time analysis, we find that activator binding to decoy sites can destroy oscillations in the case of a stable decoy-activator complex that functions to slow down the positive feedback. In contrast, an unstable decoy-activator complex can expand the oscillatory parameter regime. In conclusion, our response time analysis provides intuitive insights into the emergence of sustained oscillations.

Timely progression of a genetic program is critical for embryonic development. However, gene expression involves inevitable fluctuations in biochemical reactions leading to substantial cell-to-cell variability (gene expression noise). One of the important questions in developmental biology is how pattern formation is reproducibly executed despite these unavoidable fluctuations in gene expression. Here, we studied the transcriptional variability of two paired zebrafish segmentation clock genes (her1 and her7) in multiple genetic backgrounds. Segmentation clock genes establish an oscillating self-regulatory system, presenting a challenging yet beautiful system in studying control of transcription variability. In this study, we found that a negative feedback loop established by the Her1 and Her7 proteins minimizes uncorrelated variability whereas gene copy number affects variability of both RNAs in a similar manner (correlated variability). We anticipate that these findings will help analyze the precision of other natural clocks and inspire the ideas for engineering precise synthetic clocks in tissue engineering.

The abundance of specific protein molecules in genetically identical cell populations exposed to the same external environment can show remarkable cell-to-cell variations as biochemical reactions are inherently stochastic and occur with low numbers of molecular copies. Such variations in gene products are commonly known as gene expression noise. One of the mechanisms for cells to reduce such noise is auto-regulatory negative feedback (auto-inhibition), commonly found across organisms. This auto-inhibition is subjected to unavoidable time-delays associated with transcriptional and translational processes. Sufficient time-delays and strong auto-inhibition can generate sustained oscillations in gene products, which is a common mechanism for precise timekeeping in many biomolecular clocks. While the importance of time-delays in the generation of oscillations is well appreciated, its role in stochastic dynamics is not well understood in the absence of sustained oscillations. Here, we investigate the interplay between the feedback strength and the time-delay to study the noise propagation in the non-oscillatory regime using linear stability analysis, the linear noise approximation, and stochastic simulations. From a simple auto-regulatory model with one protein species (no delay), we systematically introduce one-step and two-step time-delays by incorporating intermediate dynamics with additional second and third species, respectively. Interestingly, the negative feedback in the presence of time-delay can show counterintuitive noise behavior to our common perception about its role as a noise buffer.

Nonlinear feedback controllers are ubiquitous features of biological systems at different scales. A key motif arising in these systems is sequestration-based feedback. As a physiological example of this type of feedback architecture, platelets (specialized cells involved in blood clotting) differentiate from stem cells, and this process is activated by a protein called Thrombopoietin (TPO). Platelets actively sequester and degrade TPO, creating negative feedback whereby any depletion of platelets increases the levels of freely available TPO that upregulates platelet production. We show similar examples of sequestration-based feedback in intracellular biomolecular circuits involved in heat-shock response and microRNA regulation. Our systematic analysis of this feedback motif reveals that platelets-induced degradation of TPO is critical in enhancing system robustness to external disturbances. In contrast, reversible sequestration of TPO without degradation results in poor robustness to disturbances. We develop exact analytical results quantifying the limits to which the sensitivity to disturbances can be attenuated by sequestration-based feedback. In summary, our systematic analysis highlights design principles for enhancing the robustness of sequestration-based feedback mechanisms to external disturbances with applications to both physiological and cellular systems.

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. We investigate the effectiveness of proportional, integral and derivative (PID) based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as PID controllers are discussed, with particular focus on individual controllers separately, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances, particularly when the disturbance comes at low frequencies. Counter-intuitively, integral feedback is found to amplify external disturbances at intermediate frequencies. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

Triggering of cellular events often relies on the level of a key gene product crossing a critical threshold. Achieving precision in event timing despite noisy gene expression facilitates high-fidelity functioning of diverse processes from biomolecular clocks, apoptosis, and cellular differentiation. Here we investigate the role of an incoherent feedforward circuit in regulating the time taken by a bacterial virus (bacteriophage lambda) to lyse an infected Escherichia coli (E. coli) cell. Lysis timing is the result of expression and accumulation of a single lambda protein (holin) in the E. coli cell membrane up to a critical threshold level, which triggers the formation of membrane lesions. This easily visualized process provides a simple model system for characterizing event-timing stochasticity in single cells. Intriguingly, lambda's lytic pathway synthesizes two functionally opposite proteins: holin and antiholin, from the same mRNA in a 2:1 ratio. Antiholin sequesters holin and inhibits the formation of lethal membrane lesions, thus creating an incoherent feedforward circuit. We develop and analyze a stochastic model for this feedforward circuit that considers correlated bursty expression of holin/antiholin, and their concentrations are diluted from cellular growth. Interestingly, our analysis shows the noise in timing is minimized when both proteins are expressed at an optimal ratio, hence revealing an important regulatory role for antiholin. These results are in agreement with single-cell data, where removal of antiholin results in enhanced stochasticity in lysis timing.

Inside living cells, proteins or mRNA can show oscillations even without a periodic driving force. Such genetic oscillations are precise timekeepers for cell-cycle regulations, pattern formation during embryonic development in higher animals, and daily cycle maintenance in most organisms. The synchronization between oscillations in adjacent cells happens via intercellular coupling, which is essential for periodic segmentation formation in vertebrates and other biological processes. While molecular mechanisms of generating sustained oscillations are quite well understood, how do simple intercellular coupling produces robust synchronizations are still poorly understood? To address this question, we investigate two models of coupled gene oscillators - activator-based coupled oscillators (ACO) and repressor-based coupled oscillators (RCO) models. In our study, a single autonomous oscillator (that operates in a single cell) is based on a negative feedback, which is delayed by intracellular dynamics of an intermediate species. For the ACO model (RCO), the repressor protein of one cell activates (represses) the production of another protein in the neighbouring cell after a intercellular time delay. We investigate the coupled models in the presence of intrinsic noise due to the inherent stochasticity of the biochemical reactions. We analyze the collective oscillations from stochastic trajectories in the presence and absence of explicit coupling delay and make careful comparison between two models. Our results show no clear synchronizations in the ACO model when the coupling time delay is zero. However, a non-zero coupling delay can lead to anti-phase synchronizations in ACO. Interestingly, the RCO model shows robust in-phase synchronizations in the presence and absence of the coupling time delay. Our results suggest that the naturally occurring intercellular couplings might be based on repression rather than activation where in-phase synchronization is crucial.

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. 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: (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 numerically from stochastic simulations algorithm. 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.

During the morphogenesis of tissues and tumors, cells often interact with neighbors with different mechanical properties, but the understanding of its role is lacking. We use active Brownian dynamics simulations to study a model co-culture consisting of two types of cells with the same size and self-propulsion speed, but different mechanical stiffness and cell-cell adhesion. As time evolves, the system phase separates out into clusters with distinct morphologies and transport properties for the two cell types. The density structure factors and the growth of cell clusters deviate from behavior characteristic of the phase separation in binary fluids. Our results capture emergent structure and motility previously observed in co-culture experiments and provide mechanistic insights into intercellular phase separation during development and disease.

Living cells encode diverse biological clocks for circadian timekeeping and formation of rhythmic structures during embryonic development. A key open question is how these clocks synchronize across cells through intercellular coupling mechanisms. To address this question, we leverage the classical motif for genetic clocks the Goodwin oscillator where a gene product inhibits its own synthesis via time-delayed negative feedback. More specifically, we consider an interconnected system of two identical Goodwin oscillators (each operating in a single cell), where state information is conveyed between cells via a signaling pathway whose dynamics is modeled as a first-order system. In essence, the interaction between oscillators is characterized by an intercellular coupling strength and an intercellular time delay that represents the signaling response time. Systematic stability analysis characterizes the parameter regimes that lead to oscillatory dynamics, with high coupling strength found to destroy sustained oscillations. Within the oscillatory parameter regime we find both in-phase and anti-phase oscillations with the former more likely to occur for small intercellular time delays. Finally, we consider the stochastic formulation of the model with low-copy number fluctuations in biomolecular components. Interestingly, stochasticity leads to qualitatively different behaviors where in-phase oscillations are susceptible to inherent fluctuations but not the anti-phase oscillations. In the context of the segmentation clock, such synchronized in-phase oscillations between cells are critical for the proper generation of repetitive segments during embryo development that eventually leads to the formation of the vertebral column.

Many eukaryotic genes are expressed in randomly initiated bursts that are punctuated by periods of quiescence. Here, we show that the intermittent access of the promoters to transcription factors through relatively impervious chromatin contributes to this "noisy" transcription. We tethered a nuclease-deficient Cas9 fused to a histone acetyl transferase at the promoters of two endogenous genes in HeLa cells. An assay for transposase-accessible chromatin using sequencing showed that the activity of the histone acetyl transferase altered the chromatin architecture locally without introducing global changes in the nucleus and rendered the targeted promoters constitutively accessible. We measured the gene expression variability from the gene loci by performing single-molecule fluorescence in situ hybridization against mature messenger RNAs (mRNAs) and by imaging nascent mRNA molecules present at active gene loci in single cells. Because of the increased accessibility of the promoter to transcription factors, the transcription from two genes became less noisy, even when the average levels of expression did not change. In addition to providing evidence for chromatin accessibility as a determinant of the noise in gene expression, our study offers a mechanism for controlling gene expression noise which is otherwise unavoidable.

Biomolecular clocks are key drivers of oscillatory dynamics in diverse biological processes including cell-cycle regulation, circadian rhythms, and pattern formation during development. A minimal clock implementation is based on the classical Goodwin oscillator, in which a repressor protein inhibits its own synthesis via time-delayed negative feedback. Clock motifs, however, do not exist in isolation; its components are open to interacting with the complex environment inside cells. For example, there are ubiquitous high-affinity binding sites along the genome, known as decoys, where transcription factors such as repressor proteins can potentially interact. This binding affects the availability of transcription factors and has often been ignored in theoretical studies. How does such genomic decoy binding impact the clock's robustness and precision? To address this question, we systematically analyze deterministic and stochastic models of the Goodwin oscillator in the presence of reversible binding of the repressor to a finite number of decoy sites. Our analysis reveals that the relative stability of decoy-bound repressors compared to the free repressor plays distinct roles on the emergence and precision of oscillations. Interestingly, active degradation of the bound repressor can induce sustained oscillations that are otherwise absent without decoys. In contrast, decoy abundances can kill oscillation dynamics if the bound repressor is protected from degradation. Taking into account low copy-number fluctuations in clock components, we show that the degradation of the bound repressors enhances precision by attenuating noise in both the amplitude and period of oscillations. Overall, these results highlight the versatile role of otherwise hidden decoys in shaping the stochastic dynamics of biological clocks and emphasize the importance of synthetic decoys in designing robust clocks.

Genetically-identical cells can show remarkable intercellular variability in the level of a given protein which is commonly known as the gene expression noise. Besides intrinsic fluctuations that arise from the inherent stochasticity of the biochemical processes, a significant source of expression noise is extrinsic. Such extrinsic noise in gene expression arises from cell-to-cell differences in expression machinery, transcription factors, cell size, and cell cycle stage. Here, we consider the synthesis of a transcription factor (TF) whose production is impacted by a dynamic extrinsic disturbance, and systematically investigate the regulation of expression noise by decoy sites that can sequester the TF. Our analysis shows that increasing decoy numbers reduce noise in the level of the free (unbound) TF with noise levels approaching the Poisson limit for large number of decoys. Interestingly, the suppression of expression noise compared to no-decoy levels is maximized at intermediate disturbance timescales. Finally, we quantify the noise propagation from the TF to a downstream target protein and find counterintuitive behaviors. More specifically, for nonlinear dose responses of target-protein activation, the noise in the target protein can increase with the inclusion of decoys, and this phenomenon is explained by smaller but more prolonged fluctuations in the TF level. In summary, our results illustrates the nontrivial effects of high-affinity decoys in shaping the stochastic dynamics of gene expression to alter cell fate and phenotype at the single-cell level.

Abstract.: We study the flocking model introduced by Vicsek et al. (Phys. Rev. Lett. 75, 1226 (1995)) in the “coarsening” regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as Lρ(t)∼tθρ (with θρ≃ 0. 25 , while the velocity length scale grows much faster, viz., Lv(t)∼tθv (with θv≃ 0. 83 . The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod’s law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave vector, the scaled structure factors for the density and velocity fields decay with powers -2.6 and -1.52 , respectively. Graphical abstract: [Figure not available: see fulltext.].

How the noisy expression of regulatory proteins affects timing of intracellular events is an intriguing fundamental problem that influences diverse cellular processes. Here we use the bacteriophage λ to study event timing in individual cells where cell lysis is the result of expression and accumulation of a single protein (holin) in the Escherichia coli cell membrane up to a critical threshold level. Site-directed mutagenesis of the holin gene generated phage variants that vary in their lysis times from 30 to 190 min. Observation of the lysis times of single cells reveals an intriguing finding—the noise in lysis timing first decreases with increasing lysis time to reach a minimum and then sharply increases at longer lysis times. A mathematical model with stochastic expression of holin together with dilution from cell growth was sufficient to explain the non-monotonic noise profile and identify holin accumulation thresholds that generate precision in lysis timing. Biological Sciences; Cell Biology; In Silico Biology

Rhythms in gene regulatory networks are ubiquitous, from the bacterial circadian clock to the segmentation clock of vertebrates. There are many decoy binding sites in a genome where regulatory proteins bind and control the expression of a gene. The role decoys on oscillatory regulatory networks is not well understood. Here, in the presence of decoy binding sites, we investigate the stability and the precision of the well-known Goodwin oscillator, a minimal model for regulatory oscillators. We derive the stability criterion in the presence of decoys and find that decoy abundance increases the parameter space where oscillating solutions exist. If the Goodwin system does not show any oscillation without decoy binding sites, a sustained oscillation is possible in their presence. Finally, we study precision the oscillation using stochastic simulations and find that the decoy binding makes the oscillation more precise.

The genome contains several high-affinity non-functional binding sites for transcription factors (TFs) creating a hidden and unexplored layer of gene regulation. We investigate the role of such “decoy sites” in controlling noise (random fluctuations) in the level of a TF that is synthesized in stochastic bursts. Prior studies have assumed that decoy-bound TFs are protected from degradation, and in this case decoys function to buffer noise. Relaxing this assumption to consider arbitrary degradation rates for both bound/unbound TF states, we find rich noise behaviors. For low-affinity decoys, noise in the level of unbound TF always monotonically decreases to the Poisson limit with increasing decoy numbers. In contrast, for high-affinity decoys, noise levels first increase with increasing decoy numbers, before decreasing back to the Poisson limit. Interestingly, while protection of bound TFs from degradation slows the time-scale of fluctuations in the unbound TF levels, the decay of bound TFs leads to faster fluctuations and smaller noise propagation to downstream target proteins. In summary, our analysis reveals stochastic dynamics emerging from nonspecific binding of TFs and highlights the dual role of decoys as attenuators or amplifiers of gene expression noise depending on their binding affinity and stability of the bound TF.

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. Such random fluctuations in the level of a protein critically impact functioning of intracellular biological networks, and not surprisingly, cells encode diverse regulatory mechanisms to buffer noise. We investigate the effectiveness of proportional and derivative-based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as proportional and derivative controllers are discussed, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static inputoutput sensitivity of the open-loop system. As expected, the derivative controller performs poorly in terms of rejecting external disturbances. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

Sequestration of a protein by another decoy molecule, such that the protein is no longer available to perform its biological function, forms a fundamental layer of regulation in biomolecular systems. To quantify how fluctuations in protein level is controlled by decoys, we formulate a model where both proteins and decoys are stochastically expressed, with fast binding/unbinding of the protein to the decoy. Our analysis reveals that when the noise in the decoy copy number is small, the noise in the free protein numbers (as quantified by the Fano factor) monotonically decreases to the Poisson limit with the increasing average number of decoys. In contrast, for a high noise in decoys production, the response becomes nonmonotonic - the noise level in protein counts is amplified at first with the increasing decoy numbers, before attenuating back to the Poisson limit. Motivated by recent biological examples, we next implement feedback control in the sequestration process by having the free proteins upregulate the decoy synthesis. Thus any random increase in the abundance of free proteins also results in higher decoy numbers, and hence more sequestered proteins. Intriguingly, our results show that as before, noise in free protein levels can get amplified with increasing decoys, albeit with a lesser magnitude as compared to the no feedback case. In summary, molecular decoys can play a key role in either amplifying or dampening the stochastic fluctuation of protein levels, and this study systematically quantifies this behavior across parameter regimes.

The human T cell leukemia virus HTLV-1 establishes a persistent infection in vivo in which the viral sense-strand transcription is usually silent at a given time in each cell. However, cellular stress responses trigger the reactivation of HTLV-1, enabling the virus to transmit to a new host cell. Using single-molecule RNA FISH, we measured the kinetics of the HTLV-1 transcriptional reactivation in peripheral blood mononuclear cells (PBMCs) isolated from HTLV-1+ individuals. The abundance of the HTLV-1 sense and antisense transcripts was quantified hourly during incubation of the HTLV-1-infected PBMCs ex vivo. We found that, in each cell, the sense-strand transcription occurs in two distinct phases: The initial low-rate transcription is followed by a phase of rapid transcription. The onset of transcription peaked between 1 and 3 hours after the start of in vitro incubation. The variance in the transcription intensity was similar in polyclonal HTLV-1+ PBMCs (with tens of thousands of distinct provirus insertion sites), and in samples with a single dominant HTLV-1+ clone. A stochastic simulation model was developed to estimate the parameters of HTLV-1 proviral transcription kinetics. In PBMCs from a leukemic subject with one dominant T-cell clone, the model indicated that the average duration of HTLV-1 sense-strand activation by Tax (i.e. The rapid transcription) was less than one hour. HTLV-1 antisense transcription was stable during reactivation of the sense-strand. The antisense transcript HBZ was produced at an average rate of ~0.1 molecules per hour per HTLV-1+ cell; however, between 20% and 70% of HTLV-1-infected cells were HBZ-negative at a given time, the percentage depending on the individual subject. HTLV-1-infected cells are exposed to a range of stresses when they are drawn from the host, which initiate the viral reactivation. We conclude that whereas antisense-strand transcription is stable throughout the stress response, the HTLV-1 sensestrand reactivation is highly heterogeneous and occurs in short, self-Terminating bursts.

Inside cells, cargos such as vesicles and organelles are transported by molecular motors to their correct locations via active motion on cytoskeletal tracks and passive, Brownian diffusion. During the transportation of cargos, motor-cargo complexes (MCCs) navigate the confining and crowded environment of the cytoskeletal network and other macromolecules. Motivated by this, we study a minimal two-state model of motor-driven cargo transport in confinement and predict transport properties that can be tested in experiments. We assume that the motion of the MCC is directly affected by the entropic barrier due to confinement if it is in the passive, unbound state but not in the active, bound state where it moves with a constant bound velocity. We construct a lattice model based on a Fokker Planck description of the two-state system, study it using a kinetic Monte Carlo method and compare our numerical results with analytical expressions for a mean field limit. We find that the effect of confinement strongly depends on the bound velocity and the binding kinetics of the MCC. Confinement effectively reduces the effective diffusivity and average velocity, except when it results in an enhanced average binding rate and thereby leads to a larger average velocity than when unconfined.

Cilia are elastic hairlike protuberances of the cell membrane found in various unicellular organisms and in several tissues of most living organisms. In some tissues such as the airway tissues of the lung, the coordinated beating of cilia induces a fluid flow of crucial importance as it allows the continuous cleaning of our bronchia, known as mucociliary clearance. While most of the models addressing the question of collective dynamics and metachronal wave consider homogeneous carpets of cilia, experimental observations rather show that cilia clusters are heterogeneously distributed over the tissue surface. The purpose of this paper is to investigate the role of spatial heterogeneity on the coherent beating of cilia using a very simple one-dimensional model for cilia known as the rower model. We systematically study systems consisting of a few rowers to hundreds of rowers and we investigate the conditions for the emergence of collective beating. When considering a small number of rowers, a phase drift occurs, hence, a bifurcation in beating frequency is observed as the distance between rower clusters is changed. In the case of many rowers, a distribution of frequencies is observed. We found in particular the pattern of the patchy structure that shows the best robustness in collective beating behavior, as the density of cilia is varied over a wide range.

Gene expression is intrinsically a stochastic (noisy) process with important implications for cellular functions. Deciphering the underlying mechanisms of gene expression noise remains one of the key challenges of regulatory biology. Theoretical models of transcription often incorporate the kinetics of how transcription factors (TFs) interact with a single promoter to impact gene expression noise. However, inside single cells multiple identical gene copies as well as additional binding sites can compete for a limiting pool of TFs. Here we develop a simple kinetic model of transcription, which explicitly incorporates this interplay between TF copy number and its binding sites. We show that TF sharing enhances noise in mRNA distribution across an isogenic population of cells. Moreover, when a single gene copy shares it’s TFs with multiple competitor sites, the mRNA variance as a function of the mean remains unaltered by their presence. Hence, all the data for variance as a function of mean expression collapse onto a single master curve independent of the strength and number of competitor sites. However, this result does not hold true when the competition stems from multiple copies of the same gene. Therefore, although previous studies showed that the mean expression follows a universal master curve, our findings suggest that different scenarios of competition bear distinct signatures at the level of variance. Intriguingly, the introduction of competitor sites can transform a unimodal mRNA distribution into a multimodal distribution. These results demonstrate the impact of limited availability of TF resource on the regulation of noise in gene expression.

Bird flocks are a paradigmatic example of collective motion. One of the prominent traits of flocking is the presence of long range velocity correlations between individuals, which allow them to influence each other over the large scales, keeping a high level of group coordination. A crucial question is to understand what is the mutual interaction between birds generating such nontrivial correlations. Here we use the maximum entropy (ME) approach to infer from experimental data of natural flocks the effective interactions between individuals. Compared to previous studies, we make a significant step forward as we retrieve the full functional dependence of the interaction on distance, and find that it decays exponentially over a range of a few individuals. The fact that ME gives a short-range interaction even though its experimental input is the long-range correlation function, shows that the method is able to discriminate the relevant information encoded in such correlations and single out a minimal number of effective parameters. Finally, we show how the method can be used to capture the degree of anisotropy of mutual interactions.

The large scale fluctuations of the ordered state in active matter systems are usually characterized by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod's law. In this Letter we study the relationship between giant number fluctuations and structure functions for different models of active matter as well as other nonequilibrium systems. A unified picture emerges, with different models falling in four distinct classes depending on the nature of their structure functions. For one class, we show that experimentalists may find Porod's law violation, by measuring subleading corrections to the number fluctuations. © 2012 American Physical Society.

We propose two lattice models in one dimension, with stochastically hopping particles which aggregate on contact. The hops are guided by "velocity rates" which themselves evolve according to the rules of ballistic aggregation as in a sticky gas in continuum. Our lattice models have both velocity and density fields and an appropriate real time evolution, such that they can be compared directly with event-driven molecular dynamics (MD) results for the sticky gas. We demonstrate numerically that the long-time and large-distance behavior of the lattice models is identical to that of the MD, and some exact results known for the sticky gas. In particular, the exactly predicted form of the non-Gaussian tail of the velocity distribution function is clearly exhibited. This correspondence of the lattice models and the sticky gas in continuum is nontrivial, as the latter has a deterministic dynamics with a local kinematic constraint, in contrast with the former; yet the spatial velocity profiles (with shocks) of the lattice models and the MD have a striking match. Copyright © EPLA, 2011.

In a system of non-linear chemical reactions called the Brusselator, we show that intrinsic noise can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic resonance and aperiodic stochastic resonance, hitherto studied mostly with extrinsic noise, is demonstrated here to occur with inherent systemic noise using exact stochastic simulation algorithm due to Gillespie. The role of intrinsic noise in a couple of other phenomena is also discussed. © 2011 American Institute of Physics.

We solve the O(n) model, defined in terms of self- and mutually avoiding loops coexisting with voids, on a 3-simplex fractal lattice, using an exact real space renormalization group technique. As the density of voids is decreased, the model shows a critical point, and for even lower densities of voids, there is a dense phase showing power-law correlations, with critical exponents that depend on n, but are independent of density. At n = -2 on the dilute branch, a trivalent vertex defect acts as a marginal perturbation. We define a model of biconnected clusters which allows for a finite density of such vertices. As n is varied, we get a line of critical points of this generalized model, emanating from the point of marginality in the original loop model. We also study another perturbation of adding local bending rigidity to the loop model, and find that it does not affect the universality class. © 2008 IOP Publishing Ltd.