Biomedical subjects

David C Sullivan

Publications and source records attributed to David C Sullivan.

4 recordsLinked to original sources

PubMed2006

Quantifying polypeptide conformational space: sensitivity to conformation and ensemble definition.

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.

Computer Simulation↗

PubMed2006

Toward absolute density of states calculations for proteins.

The density of states (DOS), which gives the number of conformations with a particular energy E, is a prerequisite in computing most thermodynamic quantities and in elucidating important biological processes such as the mechanism of protein folding. However, current methods for computing DOS of large systems such as proteins generally yield only the ratios of microstate counts for different energies, which could yield absolute conformation counts if the total number of conformations in phase space is known, thus motivating this work. Here, the total number of energy minima of 50-mer polyalanine, whose size corresponds to naturally occurring small proteins, was estimated under an all-atom potential energy function based on the cumulative distribution function (CDF) of conformational differences to be approximately 10(38). This estimate can place any DOS function, such as the Gaussian DOS distribution in the random energy model, on an absolute scale. Comparing the absolute conformational counts from a Gaussian DOS function with those from the CDF derived from quenched molecular dynamics ensembles shows that the former are far greater than the latter, indicating far fewer low-energy minima actually exist. In addition to showing how CDF and relative DOS calculations can yield absolute DOS for a discrete system, we also show how they can yield absolute DOS for continuous variable systems to a specified atomic variance. In the context of protein folding, knowing this phase-space "volume" of conformations in a DOS function, as well as characteristic transition times, constrains the set of possible folding mechanisms.

Protein Conformation↗

PubMed2004

Distributions in protein conformation space: implications for structure prediction and entropy.

By considering how polymer structures are distributed in conformation space, we show that it is possible to quantify the difficulty of structural prediction and to provide a measure of progress for prediction calculations. The critical issue is the probability that a conformation is found within a specified distance of another conformer. We address this question by constructing a cumulative distribution function (CDF) for the average probability from observations about its limiting behavior at small displacements and numerical simulations of polyalanine chains. We can use the CDF to estimate the likelihood that a structure prediction is better than random chance. For example, the chance of randomly predicting the native backbone structure of a 150-amino-acid protein to low resolution, say within 6 A, is 10(-14). A high-resolution structural prediction, say to 2 A, is immensely more difficult (10(-57)). With additional assumptions, the CDF yields the conformational entropy of protein folding from native-state coordinate variance. Or, using values of the conformational entropy change on folding, we can estimate the native state's conformational span. For example, for a 150-mer protein, equilibrium alpha-carbon displacements in the native ensemble would be 0.3-0.5 A based on T Delta S of 1.42 kcal/(mol residue).

Algorithms↗

PubMed2003

Information content of molecular structures.

For a completely enumerated set of conformers of a macromolecule or for exhaustive lattice walks of model polymers it is straightforward to use Shannon information theory to deduce the information content of the ensemble. It is also practicable to develop numerical measures of the information content of sets of exact distance constraints applied to specific conformational ensembles. We examine the effects of experimental uncertainties by considering "noisy" constraints. The introduction of noise requires additional assumptions about noise distribution and conformational clustering protocols that make the problem of measuring information content more complex. We make use of a standard concept in communication theory, the "noise sphere," to link uncertainty in measurements to information loss. Most of our numerical results are derived from two-dimensional lattice ensembles. Expressing results in terms of information per degree of freedom removes almost all of the chain length dependence. We also explore off-lattice polyalanine chains that yield surprisingly similar results.

Amino Acid Sequence↗