Gene copy number and negative feedback differentially regulate transcriptional variability of segmentation clock genes.

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.

Diverse role of decoys on emergence and precision of oscillations in a biomolecular clock.

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.

Noise suppression in stochastic genetic circuits using PID controllers.

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.

Differences in mechanical properties lead to anomalous phase separation in a model cell co-culture.

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.

Reduction in gene expression noise by targeted increase in accessibility at gene loci.

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.

Enhancement of gene expression noise from transcription factor binding to genomic decoy sites.

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.

Optimum Threshold Minimizes Noise in Timing of Intracellular Events.

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.

Coarsening dynamics in the Vicsek model of active matter.

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 [Formula: see text] (with [Formula: see text] , while the velocity length scale grows much faster, viz., [Formula: see text] (with [Formula: see text] . 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.

Kinetics of HTLV-1 reactivation from latency quantified by single-molecule RNA FISH and stochastic modelling.

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 sense-strand reactivation is highly heterogeneous and occurs in short, self-terminating bursts.

Active and passive transport of cargo in a corrugated channel: A lattice model study.

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.

Role of spatial heterogeneity in the collective dynamics of cilia beating in a minimal one-dimensional model.

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.

Effect of transcription factor resource sharing on gene expression noise.

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.

Short-range interactions versus long-range correlations in bird flocks.

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.

Spatial structures and giant number fluctuations in models of active matter.

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.

Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator.

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.