Edo Kussell

Recovery of protein structure from contact maps

BACKGROUND Prediction of a proteins structure from its amino acid sequence is a key issue in molecular biology. While dynamics, performed in the space of two-dimensional contact maps, eases the necessary conformational search, it may also lead to maps that do not correspond to any real three-dimensional structure. To remedy this, an efficient procedure is needed to reconstruct three-dimensional conformations from their contact maps. RESULTS We present an efficient algorithm to recover the three-dimensional structure of a protein from its contact map representation. We show that when a physically realizable map is used as target, our method generates a structure whose contact map is essentially similar to the target. furthermore, the reconstructed and original structures are similar up to the resolution of the contact map representation. Next, we use nonphysical target maps, obtained by corrupting a physical one; in this case, our method essentially recovers the underlying physical map and structure. Hence, our algorithm will help to fold proteins, using dynamics in the space of contact maps. Finally, we investigate the manner in which the quality of the recovered structure degrades when the number of contacts is reduced. CONCLUSIONS The procedure is capable of assigning quickly and reliably a three-dimensional structure to a given contact map. It is well suited for use in parallel with dynamics in contact map space to project a contact map onto its closest physically allowed structural counterpart.

A structure-based method for derivation of all-atom potentials for protein folding.

A method for deriving all-atom protein folding potentials is presented and tested on a three-helix bundle protein, as well as on hairpin and helical sequences. The potentials obtained are composed of a contact term between pairs of atoms, and a local density term for each atom, mimicking solvent exposure preferences. Using this potential in an all-atom protein folding simulation, we repeatedly folded the three-helix bundle, with the lowest energy conformations having a Cα distance rms from the native structure of less than 2 Å. Similar results were obtained for the hairpin and helices by using different potentials. We derived potentials for several different proteins and found a high correlation between the derived parameters, suggesting that a potential of this form eventually could be found that folds multiple, unrelated proteins at the atomic level of detail.

Individual histories and selection in heterogeneous populations

The strength of selection in populations has traditionally been inferred by measuring changes in bulk population parameters, such as mean reproductive rates. Untangling the effect of selection from other factors, such as specific responses to environmental fluctuations, poses a significant problem both in microbiology and in other fields, including cancer biology and immunology, where selection occurs within phenotypically heterogeneous populations of cells. Using “individual histories”—temporal sequences of all reproduction events and phenotypic changes of individuals and their ancestors—we present an alternative approach to quantifying selection in diverse experimental settings. Selection is viewed as a process that acts on histories, and a measure of selection that employs the distribution of histories is introduced. We apply this measure to phenotypically structured populations in fluctuating environments across different evolutionary regimes. Additionally, we show that reproduction events alone, recorded in the population’s tree of cell divisions, may be sufficient to accurately measure selection. The measure is thus applicable in a wide range of biological systems, from microorganisms—including species for which genetic tools do not yet exist—to cellular populations, such as tumors and stem cells, where detailed temporal data are becoming available.

Memory and Fitness Optimization of Bacteria under Fluctuating Environments

Bacteria prudently regulate their metabolic phenotypes by sensing the availability of specific nutrients, expressing the required genes for their metabolism, and repressing them after specific metabolites are depleted. It is unclear, however, how genetic networks maintain and transmit phenotypic states between generations under rapidly fluctuating environments. By subjecting bacteria to fluctuating carbon sources (glucose and lactose) using microfluidics, we discover two types of non-genetic memory in Escherichia coli and analyze their benefits. First, phenotypic memory conferred by transmission of stable intracellular lac proteins dramatically reduces lag phases under cyclical fluctuations with intermediate timescales (1–10 generations). Second, response memory, a hysteretic behavior in which gene expression persists after removal of its external inducer, enhances adaptation when environments fluctuate over short timescales (<1 generation). Using a mathematical model we analyze the benefits of memory across environmental fluctuation timescales. We show that memory mechanisms provide an important class of survival strategies in biology that improve long-term fitness under fluctuating environments. These results can be used to understand how organisms adapt to fluctuating levels of nutrients, antibiotics, and other environmental stresses.

Interlocked feedforward loops control cell type-specific Rhodopsin expression in the Drosophila eye

How complex networks of activators and repressors lead to exquisitely specific cell-type determination during development is poorly understood. In the Drosophila eye, expression patterns of Rhodopsins define at least eight functionally distinct though related subtypes of photoreceptors. Here, we describe a role for the transcription factor gene defective proventriculus (dve) as a critical node in the network regulating Rhodopsin expression. dve is a shared component of two opposing, interlocked feedforward loops (FFLs). Orthodenticle and Dve interact in an incoherent FFL to repress Rhodopsin expression throughout the eye. In R7 and R8 photoreceptors, a coherent FFL relieves repression by Dve while activating Rhodopsin expression. Therefore, this network uses repression to restrict and combinatorial activation to induce cell-type-specific expression. Furthermore, Dve levels are finely tuned to yield cell-type- and region-specific repression or activation outcomes. This interlocked FFL motif may be a general mechanism to control terminal cell-fate specification.

Evolutionary pressures on simple sequence repeats in prokaryotic coding regions

Simple sequence repeats (SSRs) are indel mutational hotspots in genomes. In prokaryotes, SSR loci can cause phase variation, a microbial survival strategy that relies on stochastic, reversible on–off switching of gene activity. By analyzing multiple strains of 42 fully sequenced prokaryotic species, we measure the relative variability and density distribution of SSRs in coding regions. We demonstrate that repeat type strongly influences indel mutation rates, and that the most mutable types are most strongly avoided across genomes. We thoroughly characterize SSR density and variability as a function of N→C position along protein sequences. Using codon-shuffling algorithms that preserve amino acid sequence, we assess evolutionary pressures on SSRs. We find that coding sequences suppress repeats in the middle of proteins, and enrich repeats near termini, yielding U-shaped SSR density curves. We show that for many species this characteristic shape can be attributed to purely biophysical constraints of protein structure. In multiple cases, however, particularly in certain pathogenic bacteria, we observe over enrichment of SSRs near protein N-termini significantly beyond expectation based on structural constraints. This increases the probability that frameshifts result in non-functional proteins, revealing that these species may evolutionarily tune SSR positions in coding regions to facilitate phase variation.

Noise-driven growth rate gain in clonal cellular populations

Significance Differences between individuals exist even in the absence of genetic differences, e.g., in identical twins. Over the last decade, experiments have shown that even genetically identical microbes exhibit large cell-to-cell differences. In particular, the timing of cell division events is highly variable between single bacterial cells. The effect of this variability on long-term growth and survival of bacteria, however, remains elusive. Here, we present a striking finding showing that a bacterial population grows faster on average than its constituent cells. To explain this counterintuitive result, we present a mathematical model that precisely predicts our measurements. Furthermore, we show an empirical growth law that constrains the maximal growth rate of Escherichia coli. Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a “speed limit” for proliferation.

Evolution in Microbes

This review presents a broad survey of experimental microbial evolution, covering diverse topics including trade-offs, epistasis, fluctuating conditions, spatial dynamics, cooperation, aging, and stochastic switching. Emphasis is placed on examples that highlight key conceptual points or address theoretical predictions. Experimental evolution is discussed from two points of view. First, population trajectories are described as adaptive walks on a fitness landscape, whose genetic structure can be probed by experiments. Second, populations are viewed from a physiological perspective, and their nongenetic heterogeneity is examined. Bringing together these two viewpoints remains a major challenge for the future.

Side‐chain dynamics and protein folding

The processes by which protein side chains reach equilibrium during a folding reaction are investigated using both lattice and all‐atom simulations. We find that rates of side‐chain relaxation exhibit a distribution over the protein structure, with the fastest relaxing side chains located in positions kinetically important for folding. Traversal of the major folding transition state corresponds to the freezing of a small number of side chains, belonging to the folding nucleus, whereas the rest of the protein proceeds toward equilibrium via backbone fluctuations around the native fold. The postnucleation processes by which side chains relax are characterized by very slow dynamics and many barrier crossings, and thus resemble the behavior of a glass. Proteins 2003;52:303–321.

OPTIMAL LINEAGE PRINCIPLE FOR AGE-STRUCTURED POPULATIONS

We present a formulation of branching and aging processes that allows age distributions along lineages to be studied within populations, and provides a new interpretation of classical results in the theory of aging. We establish a variational principle for the stable age distribution along lineages. Using this optimal lineage principle, we show that the response of a population’s growth rate to age‐specific changes in mortality and fecundity—a key quantity that was first calculated by Hamilton—is given directly by the age distribution along lineages. We apply our method also to the Bellman–Harris process, in which both mother and progeny are rejuvenated at each reproduction event, and show that this process can be mapped to the classic aging process such that age statistics in the population and along lineages are identical. Our approach provides both a theoretical framework for understanding the statistics of aging in a population, and a new method of analytical calculations for populations with age structure. We discuss generalizations for populations with multiple phenotypes, and more complex aging processes. We also provide a first experimental test of our theory applied to bacterial populations growing in a microfluidics device.