Simplicity of Completion Time Distributions for Common Complex Biochemical Processes

Biochemical processes typically involve huge numbers of individual reversible steps, each with its own dynamical rate constants. For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules. In this work, we study the transient properties of such systems and fully characterize their first passage (completion) time distributions. In particular, we provide explicit expressions for the mean and the variance of the completion time for a kinetic proofreading process and computational analyses for more complicated biochemical systems. We find that, for a wide range of parameters, as the system size grows, the completion time behavior simplifies: it becomes either deterministic or exponentially distributed, with a very narrow transition between the two regimes. In both regimes, the dynamical complexity of the full system is trivial compared to its apparent structural complexity. Similar simplicity is likely to arise in the dynamics of many complex multi-step biochemical processes. In particular, these findings suggest not only that one may not be able to understand individual elementary reactions from macroscopic observations, but also that such understanding may be unnecessary

Listening to the noise: random fluctuations reveal gene network parameters

The cellular environment is abuzz with noise originating from the inherent random motion of reacting molecules in the living cell. In this noisy environment, clonal cell populations show cell-to-cell variability that can manifest significant phenotypic differences. Noise-induced stochastic fluctuations in cellular constituents can be measured and their statistics quantified. We show that these random fluctuations carry within them valuable information about the underlying genetic network. Far from being a nuisance, the ever-present cellular noise acts as a rich source of excitation that, when processed through a gene network, carries its distinctive fingerprint that encodes a wealth of information about that network. We show that in some cases the analysis of these random fluctuations enables the full identification of network parameters, including those that may otherwise be difficult to measure. This establishes a potentially powerful approach for the identification of gene networks and offers a new window into the workings of these networks

Approximation Techniques for Stochastic Analysis of Biological Systems

There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic probabilistic behaviors of complex genetic circuit designs. However, its inability to scale limits its applicability in practice. This chapter addresses the scalability problem by presenting a state-space approximation method to remove unlikely states resulting in a reduced, finite state representation of the infinite-state continuous-time Markov chain that is amenable to probabilistic model checking. The proposed method is evaluated on a design of a genetic toggle switch. Comparisons with another state-of-art tool demonstrates both accuracy and efficiency of the presented method

Ribozyme-based insulator parts buffer synthetic circuits from genetic context

Synthetic genetic programs are built from circuits that integrate sensors and implement temporal control of gene expression. Transcriptional circuits are layered by using promoters to carry the signal between circuits. In other words, the output promoter of one circuit serves as the input promoter to the next. Thus, connecting circuits requires physically connecting a promoter to the next circuit. We show that the sequence at the junction between the input promoter and circuit can affect the input-output response (transfer function) of the circuit. A library of putative sequences that might reduce (or buffer) such context effects, which we refer to as 'insulator parts', is screened in Escherichia coli. We find that ribozymes that cleave the 5′ untranslated region (5′-UTR) of the mRNA are effective insulators. They generate quantitatively identical transfer functions, irrespective of the identity of the input promoter. When these insulators are used to join synthetic gene circuits, the behavior of layered circuits can be predicted using a mathematical model. The inclusion of insulators will be critical in reliably permuting circuits to build different programs.Life Technologies, Inc.United States. Defense Advanced Research Projects Agency (DARPA CLIO N66001-12-C-4018)United States. Office of Naval Research (N00014-10-1-0245)National Science Foundation (U.S.) (CCF-0943385)National Institutes of Health (U.S.) (AI067699)National Science Foundation (U.S.). Synthetic Biology Engineering Research Center (SynBERC, SA5284-11210

Special section dedicated to The Sixth q-bio Conference : meeting report and preface

This special section consists of ten original research reports that elaborate on work presented at The Sixth q-bio Conference, which took place on 8-12 August 2012 on the campus of St John's College in Santa Fe, NM, USA. The q-bio community is a vibrant group of researchers that develop and promote integrated modeling, theoretical and quantitative experimental approaches aimed at understanding cellular information processing and other related complex biological phenomena with the quantitative rigor of the physical sciences. This community is transforming the way research in biology is done, making it more quantitative, and using the power of mathematics to discover and systematize biological knowledge in a way that has long eluded the field. The q-bio Conference is our annual flagship conference, held every August in Santa Fe, NM, USA. It is a major system biology forum for exchanging results and ideas, networking and continued education in q-bio. Since its beginning in 2007, the conference has emphasized studies of cellular regulation, and it was originally called The q-bio Conference on Cellular Information Processing. To more effectively serve the community and impact other fields of biology, we later decided that the conference should broaden to include ecological and evolutionary contexts, and bridge into other areas in systems biology, cell biology, physical chemistry, bioengineering and biophysics. The scope of the conference has gradually expanded, and thus, since 2012, the conference has become known simply as The q-bio Conference. Even with its expanded scope, a majority of contributions to the conference continue to focus on cellular information processing and decision-making. In a field that spans a diverse array of biological systems and emphasizes multidisciplinary approaches, a unifying conference that brings together all of its constitutive groups (researchers from the life, physical and engineering sciences) continues to be as crucial as ever. With The q-bio Conference, we have aimed at creating a dynamic atmosphere where junior researchers can meet and interact with senior investigators in an intimate setting and also present their work in posters and talks. There is ample time for impromptu discussions and opportunities for interactions amongst attendees, which is not always the case at larger meetings. The q-bio Conference features a single-track programme, which unfolds over four days. The meeting continues its tradition of being hosted at the campus of St John's College in Santa Fe, NM, USA. This unique location in the foothills of the Sangre de Cristo Mountains has allowed the conference to capitalize, on the one hand, on the solitude of the campus, where most of the attendees sleep and eat on site, promoting spontaneous informal meetings and discussions, and, on the other hand, on the relative closeness to arts, culture and outdoors of Santa Fe, which provide participants and their families with recreational opportunities. The size of the conference (about 200-50 attendees) is aimed to be large enough to sustain a diverse field, and yet small enough to foster intimate interactions. The Sixth q-bio Conference included (see http://q-bio.org/wiki/2012_schedule for the detailed program): 21 invited talks (including four special talks), 27 contributed talks, 17 short poster spotlight talks and 131 poster presentations. The emphasis on contributed talks and posters places the focus of the conference on junior investigators, and, indeed, more than half of the attendees in 2012 were graduate students and postdoctoral scientists. Contributed and invited talks were anchored by four special presentations and events. For 2012, these included the following

Live-cell imaging reveals the spatiotemporal organization of endogenous RNA polymerase II phosphorylation at a single gene

Abstract: The carboxyl-terminal domain of RNA polymerase II (RNAP2) is phosphorylated during transcription in eukaryotic cells. While residue-specific phosphorylation has been mapped with exquisite spatial resolution along the 1D genome in a population of fixed cells using immunoprecipitation-based assays, the timing, kinetics, and spatial organization of phosphorylation along a single-copy gene have not yet been measured in living cells. Here, we achieve this by combining multi-color, single-molecule microscopy with fluorescent antibody-based probes that specifically bind to different phosphorylated forms of endogenous RNAP2 in living cells. Applying this methodology to a single-copy HIV-1 reporter gene provides live-cell evidence for heterogeneity in the distribution of RNAP2 along the length of the gene as well as Serine 5 phosphorylated RNAP2 clusters that remain separated in both space and time from nascent mRNA synthesis. Computational models determine that 5 to 40 RNAP2 cluster around the promoter during a typical transcriptional burst, with most phosphorylated at Serine 5 within 6 seconds of arrival and roughly half escaping the promoter in ~1.5 minutes. Taken together, our data provide live-cell support for the notion of efficient transcription clusters that transiently form around promoters and contain high concentrations of RNAP2 phosphorylated at Serine 5

Stochastic Gene Expression: Modeling, Analysis, and Identification *

Abstract Gene networks arise due to the interaction of genes through their protein products. Modeling such networks is key to understanding life at the most basic level. One of the emerging challenges to the analysis of genetic networks is that the cellular environment in which these genetic circuits function is abuzz with noise. The main source of this noise is the randomness that characterizes the motion of cellular constituents at the molecular level. Cellular noise not only results in random fluctuations (over time) within individual cells, but it is also a source of phenotypic variability among clonal cellular populations. In some instances fluctuations are suppressed downstream through intricate dynamical networks that act as noise filters. Yet in other important instances, noise induced fluctuations are exploited to the cell's advantage. The richness of stochastic phenomena in biology depends directly upon the interactions of dynamics and noise and upon the mechanisms through which these interactions occur. In this article, we explore the origins and impact of cellular noise, drawing examples from endogenous and synthetic biological networks. We motivate the need for stochastic models and outline the key tools for the modeling and analysis of stochasticity inside living cells. We show that tools from system theory can be effectively utilized for modeling, analysis, and identification of gene networks. * This article is an expanded version of a conference paper that appeared in the proceedings of IFAC 2009 SYSI