Tuning noise in gene expression

Stochastic Modeling of Gene Regulation by Noncoding Small RNAs in the Strong Interaction Limit

Noncoding small RNAs (sRNAs) are known to play a key role in regulating diverse cellular processes, and their dysregulation is linked to various diseases such as cancer. Such diseases are also marked by phenotypic heterogeneity, which is often driven by the intrinsic stochasticity of gene expression. Correspondingly, there is significant interest in developing quantitative models focusing on the interplay between stochastic gene expression and regulation by sRNAs. We consider the canonical model of regulation of stochastic gene expression by sRNAs, wherein interaction between constitutively expressed sRNAs and mRNAs leads to stoichiometric mutual degradation. The exact solution of this model is analytically intractable given the nonlinear interaction term between sRNAs and mRNAs, and theoretical approaches typically invoke the mean-field approximation. However, mean-field results are inaccurate in the limit of strong interactions and low abundances; thus, alternative theoretical approaches are needed. In this work, we obtain analytical results for the canonical model of regulation of stochastic gene expression by sRNAs in the strong interaction limit. We derive analytical results for the steady-state generating function of the joint distribution of mRNAs and sRNAs in the limit of strong interactions and use the results derived to obtain analytical expressions characterizing the corresponding protein steady-state distribution. The results obtained can serve as building blocks for the analysis of genetic circuits involving sRNAs and provide new insights into the role of sRNAs in regulating stochastic gene expression in the limit of strong interactions.

Profiling of Invasive Breast Carcinoma Circulating Tumour Cells-Are We Ready for the 'Liquid' Revolution?

As dissemination through blood and lymph is the critical step of the metastatic cascade, circulating tumour cells (CTCs) have attracted wide attention as a potential surrogate marker to monitor progression into metastatic disease and response to therapy. In patients with invasive breast carcinoma (IBC), CTCs are being considered nowadays as a valid counterpart for the assessment of known prognostic and predictive factors. Molecular characterization of CTCs using protein detection, genomic and transcriptomic panels allows to depict IBC biology. Such molecular profiling of circulating cells with increased metastatic abilities appears to be essential, especially after tumour resection, as well as in advanced disseminated disease, when information crucial for identification of therapeutic targets becomes unobtainable from the primary site. If CTCs are truly representative of primary tumours and metastases, characterization of the molecular profile of this easily accessible ‘biopsy’ might be of prime importance for clinical practice in IBC patients. This review summarizes available data on feasibility and documented benefits of monitoring of essential IBC biological features in CTCs, with special reference to multifactorial proteomic, genomic, and transcriptomic panels of known prognostic or predictive value.

Transcriptomic Characterization of the Human Cell Cycle in Individual Unsynchronized Cells

The highly fine-tuned dynamics of cell cycle gene expression have been intensely studied for several decades. However, some previous observations may be difficult to fully decouple from artifacts induced by traditional cell synchronization procedures. In addition, bulk cell measurements may have disguised intricate details. Here, we address this by sorting and transcriptomic sequencing of single cells progressing through the cell cycle without prior synchronization. Genes and pathways with known cell cycle roles are confirmed, associated regulatory sequence motifs are determined, and we also establish ties between other biological processes and the unsynchronized cell cycle. Importantly, we find the G1 phase to be surprisingly heterogeneous, with transcriptionally distinct early and late time points. We additionally note that mRNAs accumulate to reach maximum total levels at mitosis and find that stable transcripts show reduced cell-to-cell variability, consistent with the transcriptional burst model of gene expression. Our study provides the first detailed transcriptional profiling of an unsynchronized human cell cycle.

Geometric structure and information change in phase transitions

We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length L, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale τ of information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation γ of a control parameter from the critical state in BPs while increasing logarithmically with γ in FPs. L scales as |lnD| and D^{-1/2} in FPs and BPs, respectively, where D measures the strength of the stochastic forcing. These differing scalings with γ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).

Universal attenuators and their interactions with feedback loops in gene regulatory networks

Using a combination of mathematical modelling, statistical simulation and large-scale data analysis we study the properties of linear regulatory chains (LRCs) within gene regulatory networks (GRNs). Our modelling indicates that downstream genes embedded within LRCs are highly insulated from the variation in expression of upstream genes, and thus LRCs act as attenuators. This observation implies a progressively weaker functionality of LRCs as their length increases. When analyzing the preponderance of LRCs in the GRNs of Escherichia coli K12 and several other organisms, we find that very long LRCs are essentially absent. In both E. coli and M. tuberculosis we find that four-gene LRCs are intimately linked to identical feedback loops that are involved in potentially chaotic stress response, indicating that the dynamics of these potentially destabilising motifs are strongly restrained under homeostatic conditions. The same relationship is observed in a human cancer cell line (K562), and we postulate that four-gene LRCs act as ‘universal attenuators’. These findings suggest a role for long LRCs in dampening variation in gene expression, thereby protecting cell identity, and in controlling dramatic shifts in cell-wide gene expression through inhibiting chaos-generating motifs.

Frequency modulation of stochastic gene expression bursts by strongly interacting small RNAs

The sporadic nature of gene expression at the single-cell level-long periods of inactivity punctuated by bursts of mRNA or protein production-plays a critical role in diverse cellular processes. To elucidate the cellular role of bursting in gene expression, synthetic biology approaches have been used to design simple genetic circuits with bursty mRNA or protein production. Understanding how such genetic circuits can be designed with the ability to control burst-related parameters requires the development of quantitative stochastic models of gene expression. In this work, we analyze stochastic models for the regulation of gene expression bursts by strongly interacting small RNAs. For the parameter range considered, results based on mean-field approaches are significantly inaccurate and alternative analytical approaches are needed. Using simplifying approximations, we obtain analytical results for the corresponding steady-state distributions that are in agreement with results from stochastic simulations. These results indicate that regulation by small RNAs, in the strong interaction limit, can be used to effectively modulate the frequency of bursting. We explore the consequences of such regulation for simple genetic circuits involving feedback effects and switching between promoter states.

Self-Organized Bistability Associated with First-Order Phase Transitions

Self-organized criticality elucidates the conditions under which physical and biological systems tune themselves to the edge of a second-order phase transition, with scale invariance. Motivated by the empirical observation of bimodal distributions of activity in neuroscience and other fields, we propose and analyze a theory for the self-organization to the point of phase coexistence in systems exhibiting a first-order phase transition. It explains the emergence of regular avalanches with attributes of scale invariance that coexist with huge anomalous ones, with realizations in many fields.

From Structural Variation of Gene Molecules to Chromatin Dynamics and Transcriptional Bursting

Transcriptional activation of eukaryotic genes is accompanied, in general, by a change in the sensitivity of promoter chromatin to endonucleases. The structural basis of this alteration has remained elusive for decades; but the change has been viewed as a transformation of one structure into another, from "closed" to "open" chromatin. In contradistinction to this static and deterministic view of the problem, a dynamical and probabilistic theory of promoter chromatin has emerged as its solution. This theory, which we review here, explains observed variation in promoter chromatin structure at the level of single gene molecules and provides a molecular basis for random bursting in transcription-the conjecture that promoters stochastically transition between transcriptionally conducive and inconducive states. The mechanism of transcriptional regulation may be understood only in probabilistic terms.