Diffusion, dimensionality and noise in transcriptional regulation

The precision of biochemical signaling is limited by randomness in the diffusive arrival of molecules at their targets. For proteins binding to the specific sites on the DNA and regulating transcription, the ability of the proteins to diffuse in one dimension by sliding along the length of the DNA, in addition to their diffusion in bulk solution, would seem to generate a larger target for DNA binding, consequently reducing the noise in the occupancy of the regulatory site. Here we show that this effect is largely cancelled by the enhanced temporal correlations in one dimensional diffusion. With realistic parameters, sliding along DNA has surprisingly little effect on the physical limits to the precision of transcriptional regulation.Comment: 8 pages, 2 figure

An operational view of intercellular signaling pathways

Animal cells use a conserved repertoire of intercellular signaling pathways to communicate with one another. These pathways are well-studied from a molecular point of view. However, we often lack an “operational” understanding that would allow us to use these pathways to rationally control cellular behaviors. This requires knowing what dynamic input features each pathway perceives and how it processes those inputs to control downstream processes. To address these questions, researchers have begun to reconstitute signaling pathways in living cells, analyzing their dynamic responses to stimuli, and developing new functional representations of their behavior. Here we review important insights obtained through these new approaches, and discuss challenges and opportunities in understanding signaling pathways from an operational point of view

Serially-regulated biological networks fully realize a constrained set of functions

We show that biological networks with serial regulation (each node regulated by at most one other node) are constrained to {\it direct functionality}, in which the sign of the effect of an environmental input on a target species depends only on the direct path from the input to the target, even when there is a feedback loop allowing for multiple interaction pathways. Using a stochastic model for a set of small transcriptional regulatory networks that have been studied experimentally, we further find that all networks can achieve all functions permitted by this constraint under reasonable settings of biochemical parameters. This underscores the functional versatility of the networks.Comment: 9 pages, 3 figure

Rules for biological regulation based on error minimization

The control of gene expression involves complex mechanisms that show large variation in design. For example, genes can be turned on either by the binding of an activator (positive control) or the unbinding of a repressor (negative control). What determines the choice of mode of control for each gene? This study proposes rules for gene regulation based on the assumption that free regulatory sites are exposed to nonspecific binding errors, whereas sites bound to their cognate regulators are protected from errors. Hence, the selected mechanisms keep the sites bound to their designated regulators for most of the time, thus minimizing fitness-reducing errors. This offers an explanation of the empirically demonstrated Savageau demand rule: Genes that are needed often in the natural environment tend to be regulated by activators, and rarely needed genes tend to be regulated by repressors; in both cases, sites are bound for most of the time, and errors are minimized. The fitness advantage of error minimization appears to be readily selectable. The present approach can also generate rules for multi-regulator systems. The error-minimization framework raises several experimentally testable hypotheses. It may also apply to other biological regulation systems, such as those involving protein-protein interactions.Comment: biological physics, complex networks, systems biology, transcriptional regulation http://www.weizmann.ac.il/complex/tlusty/papers/PNAS2006.pdf http://www.pnas.org/content/103/11/3999.ful

Nonlinear Protein Degradation and the Function of Genetic Circuits

The functions of most genetic circuits require sufficient degrees of cooperativity in the circuit components. While mechanisms of cooperativity have been studied most extensively in the context of transcriptional initiation control, cooperativity from other processes involved in the operation of the circuits can also play important roles. In this study, we examine a simple kinetic source of cooperativity stemming from the nonlinear degradation of multimeric proteins. Ample experimental evidence suggests that protein subunits can degrade less rapidly when associated in multimeric complexes, an effect we refer to as cooperative stability. For dimeric transcription factors, this effect leads to a concentration-dependence in the degradation rate because monomers, which are predominant at low concentrations, will be more rapidly degraded. Thus cooperative stability can effectively widen the accessible range of protein levels in vivo. Through theoretical analysis of two exemplary genetic circuits in bacteria, we show that such an increased range is important for the robust operation of genetic circuits as well as their evolvability. Our calculations demonstrate that a few-fold difference between the degradation rate of monomers and dimers can already enhance the function of these circuits substantially. These results suggest that cooperative stability needs to be considered explicitly and characterized quantitatively in any systematic experimental or theoretical study of gene circuits.Comment: 42 pages, 10 figure

Brf1 posttranscriptionally regulates pluripotency and differentiation responses downstream of Erk MAP kinase

AU-rich element mRNA-binding proteins (AUBPs) are key regulators of development, but how they are controlled and what functional roles they play depends on cellular context. Here, we show that Brf1 (zfp36l1), an AUBP from the Zfp36 protein family, operates downstream of FGF/Erk MAP kinase signaling to regulate pluripotency and cell fate decision making in mouse embryonic stem cells (mESCs). FGF/Erk MAP kinase signaling up-regulates Brf1, which disrupts the expression of core pluripotency-associated genes and attenuates mESC self-renewal without inducing differentiation. These regulatory effects are mediated by rapid and direct destabilization of Brf1 targets, such as Nanog mRNA. Enhancing Brf1 expression does not compromise mESC pluripotency but does preferentially regulate mesendoderm commitment during differentiation, accelerating the expression of primitive streak markers. Together, these studies demonstrate that FGF signals use targeted mRNA degradation by Brf1 to enable rapid posttranscriptional control of gene expression in mESCs

Dynamic Ligand Discrimination in the Notch Signaling Pathway

The Notch signaling pathway comprises multiple ligands that are used in distinct biological contexts. In principle, different ligands could activate distinct target programs in signal-receiving cells, but it is unclear how such ligand discrimination could occur. Here, we show that cells use dynamics to discriminate signaling by the ligands Dll1 and Dll4 through the Notch1 receptor. Quantitative single-cell imaging revealed that Dll1 activates Notch1 in discrete, frequency-modulated pulses that specifically upregulate the Notch target gene Hes1. By contrast, Dll4 activates Notch1 in a sustained, amplitude-modulated manner that predominantly upregulates Hey1 and HeyL. Ectopic expression of Dll1 or Dll4 in chick neural crest produced opposite effects on myogenic differentiation, showing that ligand discrimination can occur in vivo. Finally, analysis of chimeric ligands suggests that ligand-receptor clustering underlies dynamic encoding of ligand identity. The ability of the pathway to utilize ligands as distinct communication channels has implications for diverse Notch-dependent processes

Optimizing information flow in small genetic networks. I

In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an over--simplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS Computational Biolog

Inferring Cell-State Transition Dynamics from Lineage Trees and Endpoint Single-Cell Measurements

As they proliferate, living cells undergo transitions between specific molecularly and developmentally distinct states. Despite the functional centrality of these transitions in multicellular organisms, it has remained challenging to determine which transitions occur and at what rates without perturbations and cell engineering. Here, we introduce kin correlation analysis (KCA) and show that quantitative cell-state transition dynamics can be inferred, without direct observation, from the clustering of cell states on pedigrees (lineage trees). Combining KCA with pedigrees obtained from time-lapse imaging and endpoint single-molecule RNA-fluorescence in situ hybridization (RNA-FISH) measurements of gene expression, we determined the cell-state transition network of mouse embryonic stem (ES) cells. This analysis revealed that mouse ES cells exhibit stochastic and reversible transitions along a linear chain of states ranging from 2C-like to epiblast-like. Our approach is broadly applicable and may be applied to systems with irreversible transitions and non-stationary dynamics, such as in cancer and development