The large scale fluctuations of the ordered state in active matter systems are usually characterised 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 law. In this paper we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium 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 law violation, by measuring subleading corrections to the number fluctuations. [4][5][6]. In these, the "activity" refers to conscious decision making or internally generated cellular thrusts in the biological systems, or impulses from a vibrating plate for the granular systems. The combination of activity and interaction can lead to macroscopic order [7][8][9][10][11][12]. However, these systems are far from equilibrium and the usual notions of equilibrium phase transitions come under unexpected challenges [13,14]. In particular, macroscopic order, and large scale fluctuations reminiscent of critical equilibrium systems, coexist.Depending on their dynamics and symmetries, different active matter systems exhibit macroscopic polar, nematic, and/or density order. Polar ordering has been demonstrated in point polar particle (PP) models [7,9], experiments with granular disks [6], and continuum theories [13,14]. For polar rods (PR), continuum theories rule out macroscopic polar ordering [15], and experiment on mobile bacteria [2] and simulations of models of polar rods are in agreement [11,16]. Apolar rods (AR) or active nematics have been studied experimentally [4], in hydrodynamic theories [14,17], and in simulation [10] and exhibit nematic and density ordering.The density fluctuations in the ordered state has been characterised by the number fluctuations σ 2 l = n 2 l − n 2 l of particles in a finite box of linear size l, where n is the particle number. In active matter systems, σ 2 l ∼ n α with α > 1, indicating "giant" number fluctuations (GNF) in comparison to what is expected from the central limit theorem. The exponent α has been used to infer the long range correlations in the system. In two dimensions, for the PP [6, 9, 14], and PR [2, 11] systems, it is now known that α = 1.6, and for AR systems [4, 14, 17] α = 2.0.Consider now an active matter system relaxing to its ordered state from an initial disordered state. As the density order grows with time t, there is an increasing macroscopic length scale L(t) over which there is enhanced clustering. Information about the spatial structures in such a coarsening system can be obtained by studying the spatial density-density correlation function C(r, t) = ρ(0, t)ρ(r, t) where ρ(r, t) is the local density at poin...

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.

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 l 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. Sitedirected 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.

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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.