Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries.
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Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson-Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pKas and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye-Huckel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pKa calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pKa estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large deltapKas of a subset of ionizable groups with the overall robustness of the DH model. (+info)
Temporal and multiple quantitative trait loci analyses of resistance to bacterial wilt in tomato permit the resolution of linked loci.
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Ralstonia solanacearum is a soil-borne bacterium that causes the serious disease known as bacterial wilt in many plant species. In tomato, several QTL controlling resistance have been found, but in different studies, markers spanning a large region of chromosome 6 showed strong association with the resistance. By using two different approaches to analyze the data from a field test F3 population, we show that at least two separate loci approximately 30 cM apart on this chromosome are most likely involved in the resistance. First, a temporal analysis of the progression of symptoms reveals a distal locus early in the development of the disease. As the disease progresses, the maximum LOD peak observed shifts toward the proximal end of the chromosome, obscuring the distal locus. Second, although classical interval mapping could only detect the presence of one locus, a statistical "two-QTL model" test, specifically adapted for the resolution of linked QTL, strongly supported the hypothesis for the presence of two loci. These results are discussed in the context of current molecular knowledge about disease resistance genes on chromosome 6 and observations made by tomato breeders during the production of bacterial wilt-resistant varieties. (+info)
Local control models of cardiac excitation-contraction coupling. A possible role for allosteric interactions between ryanodine receptors.
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In cardiac muscle, release of activator calcium from the sarcoplasmic reticulum occurs by calcium- induced calcium release through ryanodine receptors (RyRs), which are clustered in a dense, regular, two-dimensional lattice array at the diad junction. We simulated numerically the stochastic dynamics of RyRs and L-type sarcolemmal calcium channels interacting via calcium nano-domains in the junctional cleft. Four putative RyR gating schemes based on single-channel measurements in lipid bilayers all failed to give stable excitation-contraction coupling, due either to insufficiently strong inactivation to terminate locally regenerative calcium-induced calcium release or insufficient cooperativity to discriminate against RyR activation by background calcium. If the ryanodine receptor was represented, instead, by a phenomenological four-state gating scheme, with channel opening resulting from simultaneous binding of two Ca2+ ions, and either calcium-dependent or activation-linked inactivation, the simulations gave a good semiquantitative accounting for the macroscopic features of excitation-contraction coupling. It was possible to restore stability to a model based on a bilayer-derived gating scheme, by introducing allosteric interactions between nearest-neighbor RyRs so as to stabilize the inactivated state and produce cooperativity among calcium binding sites on different RyRs. Such allosteric coupling between RyRs may be a function of the foot process and lattice array, explaining their conservation during evolution. (+info)
Quantal amplitude and quantal variance of strontium-induced asynchronous EPSCs in rat dentate granule neurons.
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1. Excitatory postsynaptic currents (EPSCs) were recorded from granule cells of the dentate gyrus in acute slices of 17- to 21-day-old rats (22-25 C) using tissue cuts and minimal extracellular stimulation to selectively activate a small number of synaptic contacts. 2. Adding millimolar Sr2+ to the external solution produced asynchronous EPSCs (aEPSCs) lasting for several hundred milliseconds after the stimulus. Minimally stimulated aEPSCs resembled miniature EPSCs (mEPSCs) recorded in the same cell but differed from them in ways expected from the greater range of dendritic filtering experienced by mEPSCs. aEPSCs had the same stimulus threshold as the synchronous EPSCs (sEPSCs) that followed the stimulus with a brief latency. aEPSCs following stimulation of distal inputs had a slower mean rise time than those following stimulation of proximal inputs. These results suggest that aEPSCs arose from the same synapses that generated sEPSCs. 3. Proximally elicited aEPSCs had a mean amplitude of 6.7 +/- 2.2 pA (+/- s.d., n = 23 cells) at -70 mV and an amplitude coefficient of variation of 0. 46 +/- 0.08. 4. The amplitude distributions of sEPSCs never exhibited distinct peaks. 5. Monte Carlo modelling of the shapes of aEPSC amplitude distributions indicated that our data were best explained by an intrasite model of quantal variance. 6. It is concluded that Sr2+-evoked aEPSCs are uniquantal events arising at synaptic terminals that were recently invaded by an action potential, and so provide direct information about the quantal amplitude and quantal variance at those terminals. The large quantal variance obscures quantization of the amplitudes of evoked sEPSCs at this class of excitatory synapse. (+info)
Bayesian inference on biopolymer models.
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MOTIVATION: Most existing bioinformatics methods are limited to making point estimates of one variable, e.g. the optimal alignment, with fixed input values for all other variables, e.g. gap penalties and scoring matrices. While the requirement to specify parameters remains one of the more vexing issues in bioinformatics, it is a reflection of a larger issue: the need to broaden the view on statistical inference in bioinformatics. RESULTS: The assignment of probabilities for all possible values of all unknown variables in a problem in the form of a posterior distribution is the goal of Bayesian inference. Here we show how this goal can be achieved for most bioinformatics methods that use dynamic programming. Specifically, a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition is given. In addition, full Bayesian inference algorithms for sequence alignment are described. AVAILABILITY: Software and a set of transparencies for a tutorial describing these ideas are available at http://www.wadsworth.org/res&res/bioinfo/ (+info)
A hierarchical approach to protein molecular evolution.
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Biological diversity has evolved despite the essentially infinite complexity of protein sequence space. We present a hierarchical approach to the efficient searching of this space and quantify the evolutionary potential of our approach with Monte Carlo simulations. These simulations demonstrate that nonhomologous juxtaposition of encoded structure is the rate-limiting step in the production of new tertiary protein folds. Nonhomologous "swapping" of low-energy secondary structures increased the binding constant of a simulated protein by approximately 10(7) relative to base substitution alone. Applications of our approach include the generation of new protein folds and modeling the molecular evolution of disease. (+info)
The topomer-sampling model of protein folding.
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Clearly, a protein cannot sample all of its conformations (e.g., approximately 3(100) approximately 10(48) for a 100 residue protein) on an in vivo folding timescale (<1 s). To investigate how the conformational dynamics of a protein can accommodate subsecond folding time scales, we introduce the concept of the native topomer, which is the set of all structures similar to the native structure (obtainable from the native structure through local backbone coordinate transformations that do not disrupt the covalent bonding of the peptide backbone). We have developed a computational procedure for estimating the number of distinct topomers required to span all conformations (compact and semicompact) for a polypeptide of a given length. For 100 residues, we find approximately 3 x 10(7) distinct topomers. Based on the distance calculated between different topomers, we estimate that a 100-residue polypeptide diffusively samples one topomer every approximately 3 ns. Hence, a 100-residue protein can find its native topomer by random sampling in just approximately 100 ms. These results suggest that subsecond folding of modest-sized, single-domain proteins can be accomplished by a two-stage process of (i) topomer diffusion: random, diffusive sampling of the 3 x 10(7) distinct topomers to find the native topomer ( approximately 0.1 s), followed by (ii) intratopomer ordering: nonrandom, local conformational rearrangements within the native topomer to settle into the precise native state. (+info)
Testing the fit of a quantal model of neurotransmission.
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Many studies of synaptic transmission have assumed a parametric model to estimate the mean quantal content and size or the effect upon them of manipulations such as the induction of long-term potentiation. Classical tests of fit usually assume that model parameters have been selected independently of the data. Therefore, their use is problematic after parameters have been estimated. We hypothesized that Monte Carlo (MC) simulations of a quantal model could provide a table of parameter-independent critical values with which to test the fit after parameter estimation, emulating Lilliefors's tests. However, when we tested this hypothesis within a conventional quantal model, the empirical distributions of two conventional goodness-of-fit statistics were affected by the values of the quantal parameters, falsifying the hypothesis. Notably, the tests' critical values increased when the combined variances of the noise and quantal-size distributions were reduced, increasing the distinctness of quantal peaks. Our results support two conclusions. First, tests that use a predetermined critical value to assess the fit of a quantal model after parameter estimation may operate at a differing unknown level of significance for each experiment. Second, a MC test enables a valid assessment of the fit of a quantal model after parameter estimation. (+info)