A Model for the Generation and Transmission of Variations in Evolution

The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it does not prescribe, per se, the mechanisms by which this is operated. The mechanisms of inheritance are not, however, unconstrained, since they are themselves subject to natural selection. We introduce a general, analytically solvable mathematical model to compare the adaptive value of different schemes of inheritance. Our model allows for variations to be inherited, randomly produced, or environmentally induced, and, irrespectively, to be either transmitted or not during reproduction. The adaptation of the different schemes for processing variations is quantified for a range of fluctuating environments, following an approach that links quantitative genetics with stochastic control theory

Protein sectors: statistical coupling analysis versus conservation

Statistical coupling analysis (SCA) is a method for analyzing multiple sequence alignments that was used to identify groups of coevolving residues termed "sectors". The method applies spectral analysis to a matrix obtained by combining correlation information with sequence conservation. It has been asserted that the protein sectors identified by SCA are functionally significant, with different sectors controlling different biochemical properties of the protein. Here we reconsider the available experimental data and note that it involves almost exclusively proteins with a single sector. We show that in this case sequence conservation is the dominating factor in SCA, and can alone be used to make statistically equivalent functional predictions. Therefore, we suggest shifting the experimental focus to proteins for which SCA identifies several sectors. Correlations in protein alignments, which have been shown to be informative in a number of independent studies, would then be less dominated by sequence conservation.Comment: 36 pages, 17 figure

Environmental stresses can alleviate the average deleterious effect of mutations

BACKGROUND: Fundamental questions in evolutionary genetics, including the possible advantage of sexual reproduction, depend critically on the effects of deleterious mutations on fitness. Limited existing experimental evidence suggests that, on average, such effects tend to be aggravated under environmental stresses, consistent with the perception that stress diminishes the organism's ability to tolerate deleterious mutations. Here, we ask whether there are also stresses with the opposite influence, under which the organism becomes more tolerant to mutations. RESULTS: We developed a technique, based on bioluminescence, which allows accurate automated measurements of bacterial growth rates at very low cell densities. Using this system, we measured growth rates of Escherichia coli mutants under a diverse set of environmental stresses. In contrast to the perception that stress always reduces the organism's ability to tolerate mutations, our measurements identified stresses that do the opposite – that is, despite decreasing wild-type growth, they alleviate, on average, the effect of deleterious mutations. CONCLUSIONS: Our results show a qualitative difference between various environmental stresses ranging from alleviation to aggravation of the average effect of mutations. We further show how the existence of stresses that are biased towards alleviation of the effects of mutations may imply the existence of average epistatic interactions between mutations. The results thus offer a connection between the two main factors controlling the effects of deleterious mutations: environmental conditions and epistatic interactions

Contingency and Statistical Laws in Replicate Microbial Closed Ecosystems

SummaryContingency, the persistent influence of past random events, pervades biology. To what extent, then, is each course of ecological or evolutionary dynamics unique, and to what extent are these dynamics subject to a common statistical structure? Addressing this question requires replicate measurements to search for emergent statistical laws. We establish a readily replicated microbial closed ecosystem (CES), sustaining its three species for years. We precisely measure the local population density of each species in many CES replicates, started from the same initial conditions and kept under constant light and temperature. The covariation among replicates of the three species densities acquires a stable structure, which could be decomposed into discrete eigenvectors, or “ecomodes.” The largest ecomode dominates population density fluctuations around the replicate-average dynamics. These fluctuations follow simple power laws consistent with a geometric random walk. Thus, variability in ecological dynamics can be studied with CES replicates and described by simple statistical laws

Geometry of environment-to-phenotype mapping: Unifying adaptation strategies in varying environments

Biological organisms exhibit diverse strategies for adapting to varying environments. For example, a population of organisms may express the same phenotype in all environments (`unvarying strategy'), or follow environmental cues and express alternative phenotypes to match the environment (`tracking strategy'), or diversify into coexisting phenotypes to cope with environmental uncertainty (`bet-hedging strategy'). We introduce a general framework for studying how organisms respond to environmental variations, which models an adaptation strategy by an abstract mapping from environmental cues to phenotypic traits. Depending on the accuracy of environmental cues and the strength of natural selection, we find different adaptation strategies represented by mappings that maximize the longterm growth rate of a population. The previously studied strategies emerge as special cases of our model: the tracking strategy is favorable when environmental cues are accurate, whereas when cues are noisy, organisms can either use an unvarying strategy or, remarkably, use the uninformative cue as a source of randomness to bet-hedge. Our model of the environment-to-phenotype mapping is based on a network with hidden units; the performance of the strategies is shown to rely on having a high-dimensional internal representation, which can even be random.Comment: 12 pages, plus supplemental figure

Printing Multistrain Bacterial Patterns with a Piezoelectric Inkjet Printer

Many studies involving interacting microorganisms would benefit from simple devices able to deposit cells in precisely defined patterns. We describe an inexpensive bacterial piezoelectric inkjet printer (adapted from the design of the POSaM oligonucleotide microarrayer) that can be used to “print out” different strains of bacteria or chemicals in small droplets onto a flat surface at high resolution. The capabilities of this device are demonstrated by printing ordered arrays comprising two bacterial strains labeled with different fluorescent proteins. We also characterized several properties of this piezoelectric printer, such as the droplet volume (of the order of tens of pl), the distribution of number of cells in each droplet, and the dependence of droplet volume on printing frequency. We established the limits of the printing resolution, and determined that the printed viability of Escherichia coli exceeded 98.5%

Protein Mobility in the Cytoplasm of Escherichia coli

The rate of protein diffusion in bacterial cytoplasm may constrain a variety of cellular functions and limit the rates of many biochemical reactions in vivo. In this paper, we report noninvasive measurements of the apparent diffusion coefficient of green fluorescent protein (GFP) in the cytoplasm of Escherichia coli. These measurements were made in two ways: by photobleaching of GFP fluorescence and by photoactivation of a red-emitting fluorescent state of GFP (M. B. Elowitz, M. G. Surette, P. E. Wolf, J. Stock, and S. Leibler, Curr. Biol. 7:809-812, 1997). The apparent diffusion coefficient, Da, of GFP in E. coli DH5alpha was found to be 7.7 ± 2.5 µm^2/s. A 72-kDa fusion protein composed of GFP and a cytoplasmically localized maltose binding protein domain moves more slowly, with Da of 2.5 ± 0.6 µm^2/s. In addition, GFP mobility can depend strongly on at least two factors: first, Da is reduced to 3.6 ± 0.7 µm^2/s at high levels of GFP expression; second, the addition to GFP of a small tag consisting of six histidine residues reduces Da to 4.0 ± 2.0 µm^2/s. Thus, a single effective cytoplasmic viscosity cannot explain all values of Da reported here. These measurements have implications for the understanding of intracellular biochemical networks