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Abstract Background The evolution of the full repertoire of proteins encoded in a given genome is mostly driven by gene duplications, deletions, and sequence modifications of existing proteins. Indirect information about relative rates and other intrinsic parameters of these three basic processes is contained in the proteome-wide distribution of sequence identities of pairs of paralogous proteins. Results We introduce a simple mathematical framework based on a stochastic birth-and-death model that allows one to extract some of this information and apply it to the set of all pairs of paralogous proteins in H. pylori, E. coli, S. cerevisiae, C. elegans, D. melanogaster, and H. sapiens. It was found that the histogram of sequence identities p generated by an all-to-all alignment of all protein sequences encoded in a genome is well fitted with a power-law form ~ p-γ with the value of the exponent γ around 4 for the majority of organisms used in this study. This implies that the intra-protein variability of substitution rates is best described by the Gamma-distribution with the exponent α ≈ 0.33. Different features of the shape of such histograms allow us to quantify the ratio between the genome-wide average deletion/duplication rates and the amino-acid substitution rate. Conclusion We separately measure the short-term ("raw") duplication and deletion rates rdup∗ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemOCai3aa0baaSqaaiabbsgaKjabbwha1jabbchaWbqaaiabgEHiQaaaaaa@3283@, rdel∗ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemOCai3aa0baaSqaaiabbsgaKjabbwgaLjabbYgaSbqaaiabgEHiQaaaaaa@325B@ which include gene copies that will be removed soon after the duplication event and their dramatically reduced long-term counterparts rdup, rdel. High deletion rate among recently duplicated proteins is consistent with a scenario in which they didn't have enough time to significantly change their functional roles and thus are to a large degree disposable. Systematic trends of each of the four duplication/deletion rates with the total number of genes in the genome were analyzed. All but the deletion rate of recent duplicates rdel∗ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemOCai3aa0baaSqaaiabbsgaKjabbwgaLjabbYgaSbqaaiabgEHiQaaaaaa@325B@ were shown to systematically increase with Ngenes. Abnormally flat shapes of sequence identity histograms observed for yeast and human are consistent with lineages leading to these organisms undergoing one or more whole-genome duplications. This interpretation is corroborated by our analysis of the genome of Paramecium tetraurelia where the p-4 profile of the histogram is gradually restored by the successive removal of paralogs generated in its four known whole-genome duplication events.

Background: Gene covariation networks are commonly used to study biological processes. The inference of gene covariation networks from observational data can be challenging, especially considering the large number of players involved and the small number of biological replicates available for analysis. Results: We propose a new statistical method for estimating the number of erroneous edges in reconstructed networks that strongly enhances commonly used inference approaches. This method is based on a special relationship between sign of correlation (positive/negative) and directionality (up/down) of gene regulation, and allows for the identification and removal of approximately half of all erroneous edges. Using the mathematical model of Bayesian networks and positive correlation inequalities we establish a mathematical foundation for our method. Analyzing existing biological datasets, we find a strong correlation between the results of our method and false discovery rate (FDR). Furthermore, simulation analysis demonstrates that our method provides a more accurate estimate of network error than FDR. Conclusions: Thus, our study provides a new robust approach for improving reconstruction of covariation networks. [ABSTRACT FROM AUTHOR]

Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system's overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints. [ABSTRACT FROM AUTHOR]