Fundamental Limits to Position Determination by Concentration Gradients

Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially-varying distribution allows the measurement of position within the system. In order for these systems to work effectively, position determination must be robust to noise. Here, we calculate fundamental limits to the precision of position determination by concentration gradients due to unavoidable biochemical noise perturbing the gradients. We focus on gradient proteins with first order reaction kinetics. Systems of this type have been experimentally characterised in both developmental and cell biology settings. For a single gradient we show that, through time-averaging, great precision can potentially be achieved even with very low protein copy numbers. As a second example, we investigate the ability of a system with oppositely directed gradients to find its centre. With this mechanism, positional precision close to the centre improves more slowly with increasing averaging time, and so longer averaging times or higher copy numbers are required for high precision. For both single and double gradients, we demonstrate the existence of optimal length scales for the gradients, where precision is maximized, as well as analyzing how precision depends on the size of the concentration measuring apparatus. Our results provide fundamental constraints on the positional precision supplied by concentration gradients in various contexts, including both in developmental biology and also within a single cell.Comment: 24 pages, 2 figure

Optimal signal processing in small stochastic biochemical networks

We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we may do this without specifying the function performed by the network. Specifically, we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations. We perform this analysis for all biochemical circuits, including various feedback loops, that can be built out of 3 chemical species, each under the control of one regulator. We find that a generic network, constrained to low molecule numbers and reasonable response times, can transduce more information than a simple binary switch and, in fact, manages to achieve close to the optimal information transmission fidelity. These high-information solutions are robust to tenfold changes in most of the networks' biochemical parameters; moreover they are easier to achieve in networks containing cycles with an odd number of negative regulators (overall negative feedback) due to their decreased molecular noise (a result which we derive analytically). Finally, we demonstrate that a single circuit can support multiple high-information solutions. These findings suggest a potential resolution of the "cross-talk" dilemma as well as the previously unexplained observation that transcription factors which undergo proteolysis are more likely to be auto-repressive.Comment: 41 pages 7 figures, 5 table

Environmental statistics and optimal regulation

Any organism is embedded in an environment that changes over time. The timescale for and statistics of environmental change, the precision with which the organism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies-such as constitutive expression or graded response-for regulating protein levels in response to environmental inputs. We propose a general framework-here specifically applied to the enzymatic regulation of metabolism in response to changing concentrations of a basic nutrient-to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production. We use this framework to address three fundamental questions: (i) when a cell should prefer thresholding to a graded response; (ii) when there is a fitness advantage to implementing a Bayesian decision rule; and (iii) when retaining memory of the past provides a selective advantage. We specifically find that: (i) relative convexity of enzyme expression cost and benefit influences the fitness of thresholding or graded responses; (ii) intermediate levels of measurement uncertainty call for a sophisticated Bayesian decision rule; and (iii) in dynamic contexts, intermediate levels of uncertainty call for retaining memory of the past. Statistical properties of the environment, such as variability and correlation times, set optimal biochemical parameters, such as thresholds and decay rates in signaling pathways. Our framework provides a theoretical basis for interpreting molecular signal processing algorithms and a classification scheme that organizes known regulatory strategies and may help conceptualize heretofore unknown ones.Comment: 21 pages, 7 figure

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

Molecular Basis for poly(A) RNP Architecture and Recognition by the Pan2-Pan3 Deadenylase

The stability of eukaryotic mRNAs is dependent on a ribonucleoprotein (RNP) complex of poly(A)-binding proteins (PABPC1/Pab1) organized on the poly(A) tail. This poly(A) RNP not only protects mRNAs from premature degradation but also stimulates the Pan2-Pan3 deadenylase complex to catalyze the first step of poly(A) tail shortening. We reconstituted this process in vitro using recombinant proteins and show that Pan2-Pan3 associates with and degrades poly(A) RNPs containing two or more Pab1 molecules. The cryo-EM structure of Pan2-Pan3 in complex with a poly(A) RNP composed of 90 adenosines and three Pab1 protomers shows how the oligomerization interfaces of Pab1 are recognized by conserved features of the deadenylase and thread the poly(A) RNA substrate into the nuclease active site. The structure reveals the basis for the periodic repeating architecture at the 3' end of cytoplasmic mRNAs. This illustrates mechanistically how RNA-bound Pab1 oligomers act as rulers for poly(A) tail length over the mRNAs' lifetime.We would like to thank ... the MPIB cryo-EM, and core facilities ..

Localisation of the human hSuv3p helicase in the mitochondrial matrix and its preferential unwinding of dsDNA

We characterised the human hSuv3p protein belonging to the family of NTPases/helicases. In yeast mitochondria the hSUV3 orthologue is a component of the degradosome complex and participates in mtRNA turnover and processing, while in Caenorhabditis elegans the hSUV3 orthologue is necessary for viability of early embryos. Using immunofluorescence analysis, an in vitro mitochondrial uptake assay and sub‐fractionation of human mitochondria we show hSuv3p to be a soluble protein localised in the mitochondrial matrix. We expressed and purified recombinant hSuv3p protein from a bacterial expression system. The purified enzyme was capable of hydrolysing ATP with a Km of 41.9 µM and the activity was only modestly stimulated by polynucleotides. hSuv3p unwound partly hybridised dsRNA and dsDNA structures with a very strong preference for the latter. The presented analysis of the hSuv3p NTPase/helicase suggests that new functions of the protein have been acquired in the course of evolution

The Proteomics of N-terminal Methionine Cleavage

Methionine aminopeptidase (MAP) is a ubiquitous, essential enzyme involved in protein N-terminal methionine excision. According to the generally accepted cleavage rules for MAP, this enzyme cleaves all proteins with small side chains on the residue in the second position (P1′), but many exceptions are known. The substrate specificity of Escherichia coli MAP1 was studied in vitro with a large (\u3e120) coherent array of peptides mimicking the natural substrates and kinetically analyzed in detail. Peptides with Val or Thr at P1′ were much less efficiently cleaved than those with Ala, Cys, Gly, Pro, or Ser in this position. Certain residues at P2′, P3′, and P4′ strongly slowed the reaction, and some proteins with Val and Thr at P1′ could not undergo Met cleavage. These in vitro data were fully consistent with data for 862 E. coli proteins with known N-terminal sequences in vivo. The specificity sites were found to be identical to those for the other type of MAPs, MAP2s, and a dedicated prediction tool for Met cleavage is now available. Taking into account the rules of MAP cleavage and leader peptide removal, the N termini of all proteins were predicted from the annotated genome and compared with data obtained in vivo. This analysis showed that proteins displaying N-Met cleavage are overrepresented in vivo. We conclude that protein secretion involving leader peptide cleavage is more frequent than generally thought

Genomics analysis on the responses of E. coli cells to varying environmental conditions

The natural living environments of E. coli cells are diverse, varying from mammalian gastrointestinal tracts and soil. Each environment might require distinct metabolic pathways and transporter systems, and long-term evolution has established elaborate regulatory system for E. coli cells to quickly adapt to the changing conditions. Sensing outside stresses and then adopting a different phenotype enable them to take advantage of any possible nutrients and defend against hostile environment. A lot of regulatory mechanisms have been identified by genetic, biochemical and molecular biology methods, and our study aim to build a systematic view on the response of the whole genome to four different environmental conditions. We used statistical tests including Pearson’s tests and Spearman’s tests and multiple testing adjustments to identify feature genes that are induced or repressed significantly across treatment levels. The feature genes identified were partially supported by previous literatures, and some of the novel genes not found in any previous studies may infer a potential research blind spot. Additionally, we compared the correlation tests to the implementation of machine learning algorithms, and discussed the advantage and drawbacks of each method.Statistic