Therapies targeting signaling molecules mutated in cancers can often have striking short-term effects, but the emergence of resistant cancer cells is a major barrier to full cures 1,2 . Resistance can result from a secondary mutations 3,4 , but other times there is no clear genetic cause, raising the possibility of non-genetic rare cell variability [5][6][7][8][9][10][11] . Here, we show that melanoma cells can display profound transcriptional variability at the single cell level that predicts which cells will ultimately resist drug treatment. This variability involves infrequent, semi-coordinated transcription of a number of resistance markers at high levels in a very small percentage of cells. The addition of Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use: http://www.nature.com/authors/editorial_policies/license.html#terms Author contributions: SMS, AR designed the study. SMS performed all experiments and analysis except: MD, ST assisted with fluctuation analysis and RNA-sequencing; EAT, BE performed NGFR and AXL sort experiments; CK, MB, KS performed PDX experiments; PB, MH provided cell lines; MX performed WM989-A6 characterization; EE developed iterative RNA FISH protocol; INA, KN performed DNA sequencing. MH provided guidance. SMS, AR wrote the paper. Author information:AR receives consulting income and AR and SMS receive royalties related to Stellaris™ RNA FISH probes.

Gene expression occurs either as an episodic process, characterized by pulsatile bursts, or as a constitutive process, characterized by a Poisson-like accumulation of gene products. It is not clear which mode of gene expression (constitutive versus bursty) predominates across a genome or how transcriptional dynamics are influenced by genomic position and promoter sequence. Here, we use time-lapse fluorescence microscopy to analyze 8,000 individual human genomic loci and find that at virtually all loci, episodic bursting—as opposed to constitutive expression—is the predominant mode of expression. Quantitative analysis of the expression dynamics at these 8,000 loci indicates that both the frequency and size of the transcriptional bursts varies equally across the human genome, independent of promoter sequence. Strikingly, weaker expression loci modulate burst frequency to increase activity, whereas stronger expression loci modulate burst size to increase activity. Transcriptional activators such as trichostatin A (TSA) and tumor necrosis factor α (TNF) only modulate burst size and frequency along a constrained trend line governed by the promoter. In summary, transcriptional bursting dominates across the human genome, both burst frequency and burst size vary by chromosomal location, and transcriptional activators alter burst frequency and burst size, depending on the expression level of the locus.

Analysis of noise in gene expression has proven a powerful approach for analyzing gene regulatory architecture. To probe the regulatory mechanisms controlling expression of HIV-1, we analyze noise in gene-expression from HIV-1's long terminal repeat (LTR) promoter at different HIV-1 integration sites across the human genome. Flow cytometry analysis of GFP expression from the HIV-1 LTR shows high variability (noise) at each integration site. Notably, the measured noise levels are inconsistent with constitutive gene expression models. Instead, quantification of expression noise indicates that HIV-1 gene expression occurs through randomly timed bursts of activity from the LTR and that each burst generates an average of 2-10 mRNA transcripts before the promoter returns to an inactive state. These data indicate that transcriptional bursting can generate high variability in HIV-1 early gene products, which may critically influence the viral fate-decision between active replication and proviral latency.

In the stochastic formulation of chemical kinetics, the differential equation that describes the time evolution of the lower-order statistical moments for the number of molecules of the different species involved, is generally not closed, in the sense that the right-hand side of this equation depends on higher-order moments. Recent work has proposed a moment closure technique based on derivative-matching, which closes the moment equations by approximating higher-order moments as nonlinear functions of lower-order moments. We here provide a mathematical proof of this moment closure technique, and highlight its performance through comparisons with alternative methods. These comparisons reveal that this moment closure technique based on derivative-matching provides more accurate estimates of the moment dynamics, especially when the population size is small. Finally, we show that the accuracy of the proposed moment closure scheme can be arbitrarily increased by incurring additional computational effort.

Abstract. A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinite-dimensional linear ordinary differential equations (ODEs), which can be approximated by finite-dimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided.This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the master equation; a decaying-dimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schögl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available.