We employ fully quantum-mechanical molecular dynamics simulations to evaluate the force between two methanes dissolved in water, as a model for hydrophobic association. A stable configuration is found near the methane-methane contact separation, while a shallow second potential minimum occurs for the solvent-separated configuration. The strength and shape of the potential of mean force are in conflict with earlier classical force-field simulations but agree well with a simple hydrophobic burial model which is based on solubility experiments. Examination of solvent dynamics reveals stable water cages at several specific methane-methane separations.
Outer membrane beta-barrel proteins in gram-negative bacteria, such as Escherichia coli, must be translocated from their site of synthesis in the cytoplasm to the periplasm and finally delivered to the outer membrane. At least a dozen proteins located in the cytoplasm, the periplasm, and both the inner and outer membranes are required to catalyze this complex assembly process. At normal growth temperatures and conditions the transport and assembly processes are so fast that assembly intermediates cannot be detected. Using cells grown at a low temperature to slow the assembly process and pulse-chase analysis with immunodetection methods, we followed newly synthesized LamB molecules during their transit through the cell envelope. The quality and reproducibility of the data allowed us to calculate rate constants for three different subassembly reactions. This kinetic analysis revealed that secB and secD mutants exhibit nearly identical defects in precursor translocation from the cytoplasm. However, subsequent subassembly reaction rates provided no clear evidence for an additional role for SecD in LamB assembly. Moreover, we found that surA mutants are qualitatively indistinguishable from yfgL mutants, suggesting that the products of both of these genes share a common function in the assembly process, most likely the delivery of LamB to the YaeT assembly complex in the outer membrane.
Complexes of chemoreceptors in the bacterial cytoplasmic membrane allow for the sensing of ligands with remarkable sensitivity. Despite the excellent characterization of the chemotaxis signaling network, very little is known about what controls receptor complex size. Here we use in vitro signaling data to model the distribution of complex sizes. In particular, we model Tar receptors in membranes as an ensemble of different sized oligomer complexes, i.e., receptor dimers, dimers of dimers, and trimers of dimers, where the relative free energies, including receptor modification, ligand binding, and interaction with the kinase CheA determine the size distribution. Our model compares favorably with a variety of signaling data, including dose-response curves of receptor activity and the dependence of activity on receptor density in the membrane. We propose that the kinetics of complex assembly can be measured in vitro from the temporal response to a perturbation of the complex free energies, e.g., by addition of ligand.
Sourjik, Victor, and Ned S Wingreen. “Turning to the cold.”. Nat Cell Biol 99 (2007): , 9, 9, 1029-31. Web.
The chemotaxis network in Escherichia coli is remarkable for its sensitivity to small relative changes in the concentrations of multiple chemical signals. We present a model for signal integration by mixed clusters of interacting two-state chemoreceptors. Our model results compare favorably to the results obtained by Sourjik and Berg with in vivo fluorescence resonance energy transfer. Importantly, we identify two distinct regimes of behavior, depending on the relative energies of the two states of the receptors. In regime I, coupling of receptors leads to high sensitivity, while in regime II, coupling of receptors leads to high cooperativity, i.e., high Hill coefficient. For homogeneous receptors, we predict an observable transition between regime I and regime II with increasing receptor methylation or amidation.
Many organisms possess internal biochemical clocks, known as circadian oscillators, which allow them to regulate their biological activity with a 24-hour period. It was recently discovered that the circadian oscillator of photosynthetic cyanobacteria is able to function in a test tube with only three proteins, KaiA, KaiB, and KaiC, and ATP. Biochemical events are intrinsically stochastic, and this tends to desynchronize oscillating protein populations. We propose that stability of the Kai-protein oscillator relies on active synchronization by (i) monomer exchange between KaiC hexamers during the day, and (ii) formation of clusters of KaiC hexamers at night. Our results highlight the importance of collective assembly or disassembly of proteins in biochemical networks, and may help guide design of novel protein-based oscillators.
We describe a graduate course in quantitative biology that is based on original path-breaking papers in diverse areas of biology; each of these papers depends on quantitative reasoning and theory as well as experiment. Close reading and discussion of these papers allows students with backgrounds in physics, computational sciences or biology to learn essential ideas and to communicate in the languages of disciplines other than their own.
Subcellular protein localization is a universal feature of eukaryotic cells, and the ubiquity of protein localization in prokaryotic species is now acquiring greater appreciation. Though some targeting anchors are known, the origin of polar and division-site localization remains mysterious for a large fraction of bacterial proteins. Ultimately, the molecular components responsible for such symmetry breaking must employ a high degree of self-organization. Here we propose a novel physical mechanism, based on the two-dimensional curvature of the membrane, for spontaneous lipid targeting to the poles and division site of rod-shaped bacterial cells. If one of the membrane components has a large intrinsic curvature, the geometrical constraint of the plasma membrane by the more rigid bacterial cell wall naturally leads to lipid microphase separation. We find that the resulting clusters of high-curvature lipids are large enough to spontaneously and stably localize to the two cell poles. Recent evidence of localization of the phospholipid cardiolipin to the poles of bacterial cells suggests that polar targeting of some proteins may rely on the membrane's differential lipid content. More generally, aggregates of lipids, proteins, or lipid-protein complexes may localize in response to features of cell geometry incapable of localizing individual molecules.
The chemotaxis network in Escherichia coli is remarkable for its sensitivity to small relative changes in the concentrations of multiple chemical signals over a broad range of ambient concentrations. Key to this sensitivity is an adaptation system that relies on methylation and demethylation (or deamidation) of specific modification sites of the chemoreceptors by the enzymes CheR and CheB, respectively. It was recently discovered that these enzymes can access five to seven receptors when tethered to a particular receptor. We show that these "assistance neighborhoods" are necessary for precise adaptation in a model for signaling by clusters of chemoreceptors. In agreement with experiment, model clusters composed of receptors of different types exhibit high sensitivity and precise adaptation over a wide range of chemical concentrations and the response of adapted clusters to addition/removal of attractant scales with free-energy change. We predict two limits of precise adaptation at large attractant concentrations: Either receptors reach full methylation and turn off, or receptors become saturated and cease to respond to attractant but retain their adapted activity.
Receptor coupling is believed to explain the high sensitivity of the Escherichia coli chemotaxis network to small changes in levels of chemoattractant. We compare in detail the activity response of coupled two-state receptors for different models of receptor coupling: weakly-coupled extended one-dimensional and two-dimensional lattice models and the Monod-Wyman-Changeux model of isolated strongly-coupled clusters. We identify features in recent data that distinguish between the models. Specifically, researchers have measured the receptor activity response to steps of chemoattractant for a variety of engineered E. coli strains using in vivo fluorescence resonance energy transfer. We find that the fluorescence resonance energy transfer results for wild-type and for a low-activity mutant are inconsistent with the lattice models of receptor coupling, but consistent with the Monod-Wyman-Changeux model of receptor coupling, suggesting that receptors form isolated strongly-coupled clusters.
Transcription-factor proteins bind to specific DNA sequences to regulate gene expression in cells. DNA-binding sites are often identified using weight matrices calculated from multiple known binding sites. However, in many cases the number of examples is limited. Here, we report on an atomistic method that starts from an x-ray co-crystal structure of the protein bound to one particular DNA sequence, and infers other binding sites, which are used to construct a weight matrix. The emphasis of the paper is on using the Wang-Landau Monte Carlo algorithm to efficiently sample high-affinity binding sites, which demonstrates that sampling can produce accurate weight matrices in analogy to bioinformatics approaches. For cases of low complexity, we compare to the exhaustive (but slow) dead-end elimination algorithm. To recover crystal binding sites, it is important to include bound water in the protein-DNA interface. Our approach can, in principle, even be applied when no native protein-DNA co-crystal structure is available, only the structure of a closely related homologous protein whose amino-acid sequence is changed to the protein of interest.
Protein backbones have characteristic secondary structures, including alpha-helices and beta-sheets. Which structure is adopted locally is strongly biased by the local amino acid sequence of the protein. Accurate (probabilistic) mappings from sequence to structure are valuable for both secondary-structure prediction and protein design. For the case of alpha-helix caps, we test whether the information content of the sequence-structure mapping can be self-consistently improved by using a relaxed definition of the structure. We derive helix-cap sequence motifs using database helix assignments for proteins of known structure. These motifs are refined using Gibbs sampling in competition with a null motif. Then Gibbs sampling is repeated, allowing for frameshifts of +/-1 amino acid residue, in order to find sequence motifs of higher total information content. All helix-cap motifs were found to have good generalization capability, as judged by training on a small set of non-redundant proteins and testing on a larger set. For overall prediction purposes, frameshift motifs using all training examples yielded the best results. Frameshift motifs using a fraction of all training examples performed best in terms of true positives among top predictions. However, motifs without frameshifts also performed well, despite a roughly one-third lower total information content.
Protein folds are built primarily from the packing together of two types of structures: alpha-helices and beta-sheets. Neither structure is rigid, and the flexibility of helices and sheets is often important in determining the final fold (e.g., coiled coils and beta-barrels). Recent work has quantified the flexibility of alpha-helices using a principal component analysis (PCA) of database helical structures (J. Mol. Bio. 2003, 327, pp. 229-237). Here, we extend the analysis to beta-sheet flexibility using PCA on a database of beta-sheet structures. For sheets of varying dimension and geometry, we find two dominant modes of flexibility: twist and bend. The distributions of amplitudes for these modes are found to be Gaussian and independent, suggesting that the PCA twist and bend modes can be identified as the soft elastic normal modes of sheets. We consider the scaling of mode eigenvalues with sheet size and find that parallel beta-sheets are more rigid than antiparallel sheets over the entire range studied. Finally, we discuss the application of our PCA results to modeling and design of beta-sheet proteins.
This review reviews the ammonium/methylammonium transport (Amt) proteins of Escherichia coli and Salmonella enterica serovar Typhimurium. The Amt proteins and their homologs, the methylammonium/ammonium permease proteins of Saccharomyces cerevisiae, constitute a distinct class of membrane-associated ammonia transporters. Members of the Amt family are found in archaea, bacteria, fungi, plants, and invertebrate animals. In E. coli and serovar Typhimurium, the Amt proteins are essential to maintain maximal growth at low concentrations of ammonia, the preferred nitrogen source. Soupene and coworkers showed that a mutant of E. coli with only the low-affinity glutamate dehydrogenase pathway for assimilation of ammonia, which therefore grows slowly at low ammonia concentrations, is not relieved of its growth defect by overexpression of AmtB. A recent study on an Amt protein from tomato concluded that it was a specific transporter for NH4+. A trimeric stoichiometry for AmtB is supported by the observation of a direct interaction between AmtB and the trimeric signal-transduction protein GlnK. In E. coli, GlnK has been observed to associate with the membrane in an AmtB-dependent fashion. Both GlnK and GlnB are sensors of nitrogen status. Their interaction with AmtB suggests a role for AmtB in nitrogen regulation. In summary, AmtB is a membrane-associated ammonia transporter that is important for growth at external concentrations of the uncharged species (NH3) below about 50 nM. The preponderance of evidence suggests that AmtB specifically transports the charged species (NH4+) and that this transport is passive and, hence, bidirectional.
Protein solvation energies are often taken to be proportional to solvent-accessible surface areas. Computation of these areas is numerically demanding and may become a bottleneck for folding and design applications. Fast graph-based methods, such as dead-end elimination (DEE), become possible if all energies, including solvation energies, are expressed as single-residue and pair-residue terms. To this end, Street and Mayo originated a pair-residue approximation for solvent-accessible surface areas (Street AG, Mayo SL. Pairwise calculation of protein solvent accessible surface areas. Fold Des 1998;3:253-258). The dominant source of error in this method is the overlapping burial of side-chain surfaces in the protein core. Here we report a new pair-residue approximation, which greatly reduces this overlap error by the use of optimized generic side-chains. We have tested the generic-side-chain method for the ten proteins studied by Street and Mayo and for 377 single-domain proteins from the CATH database (Orengo CA, Michie AD, Jones S, Jones DT, Swindells MB, Thornton JM. CATH-A hierarchic classification of protein domain structures. Structure 1997;5:1093-1108). With little additional cost in computation, the new method consistently reduces error for total areas and residue-by-residue areas by more than a factor of two. For example, the residue-by-residue error (for buried area) is reduced from 7.42 A(2) to 3.70 A(2). This difference translates into a solvation energy difference of approximately 0.2 kcal/mol per residue, amounting to a reduction in root-mean-square energy error of 2 kcal/mol for a 100 residue chain, a potentially critical difference for both protein folding and design applications.
In rod-shaped Escherichia coli cells, the Min proteins, which are involved in division-site selection, oscillate from pole-to-pole. The homologs of the Min proteins from the round bacterium Neisseria gonorrhoeae also form a spatial oscillator when expressed in wild-type and round, rodA- mutants of E. coli, suggesting that the Min proteins form an oscillator in N. gonorrhoeae. Here we report that a numerical model for Min-protein oscillations in rod-shaped cells also produces oscillations in round cells (cocci). Our numerical results explain why the MinE-protein rings found in wild-type E. coli are absent in round mutants. In addition, we find that for round cells there is a minimum radius below which oscillations do not occur, and a maximum radius above which oscillations become mislocalized. Finally, we demonstrate that Min-protein oscillations can select the long axis in nearly round cells based solely on geometry, a potentially important factor in division-plane selection in cocci.
In E. coli, accurate cell division depends upon the oscillation of Min proteins from pole to pole. We provide a model for the polar localization of MinD based only on diffusion, a delay for nucleotide exchange, and different rates of attachment to the bare membrane and the occupied membrane. We derive analytically the probability density, and correspondingly the length scale, for MinD attachment zones. Our simple analytical model illustrates the processes giving rise to the observed localization of cellular MinD zones.
Quorum-sensing bacteria communicate with extracellular signal molecules called autoinducers. This process allows community-wide synchronization of gene expression. A screen for additional components of the Vibrio harveyi and Vibrio cholerae quorum-sensing circuits revealed the protein Hfq. Hfq mediates interactions between small, regulatory RNAs (sRNAs) and specific messenger RNA (mRNA) targets. These interactions typically alter the stability of the target transcripts. We show that Hfq mediates the destabilization of the mRNA encoding the quorum-sensing master regulators LuxR (V. harveyi) and HapR (V. cholerae), implicating an sRNA in the circuit. Using a bioinformatics approach to identify putative sRNAs, we identified four candidate sRNAs in V. cholerae. The simultaneous deletion of all four sRNAs is required to stabilize hapR mRNA. We propose that Hfq, together with these sRNAs, creates an ultrasensitive regulatory switch that controls the critical transition into the high cell density, quorum-sensing mode.