Approximate solvent-accessible surface areas from tetrahedrally directed neighbor densities.

A fast analytical formula (TDND) has been derived for the calculation of approximate atomic and molecular solvent-accessible surface areas (SASA), as well as the first and second derivatives of these quantities with respect to atomic coordinates. Extending the work of Stouten et al. (Molecular Simulation, 1993, Vol. 10, pp. 97-120), as well as our own (Journal of Computational Chemistry, 1999, Vol. 20, pp. 586-596), the method makes use of a Gaussian function to calculate the neighbor density in four tetrahedral directions in three-dimensional space, sometimes twice with different orientations. SASA and first derivatives of the 2366 heavy atoms of penicillopepsin are computed in 0.13 s on an SGI R10000/194 MHz processor. When second derivatives are computed as well, the total time is 0.23 s. This is considerably faster than timings reported previously for other algorithms. Based on a parameterization set of nineteen compounds of different size (11-4346 atoms) and class (organics, proteins, DNA, and various complexes) consisting of a total 23,197 atoms, the method exhibits relative errors in the range 0.2-12.6% for total molecular surface areas and average absolute atomic surface area deviations in the range 1.7 to 3.6 A(2).

Prediction and evaluation of side-chain conformations for protein backbone structures.

A common approach to protein modeling is to propose a backbone structure based on homology or threading and then to attempt to build side chains onto this backbone. A fast algorithm using the simple criteria of atomic overlap and overall rotamer probability is proposed for this purpose. The method was first tested in the context of exhaustive searches of side chain configuration space in protein cores and was then applied to all side chains in 49 proteins of known structure, using simulated annealing to sample space. The latter procedure obtains the correct rotamer for 57% and the correct chi 1 value for 74% of the 6751 residues in the sample. When low-temperature Monte-Carlo simulations are initiated from the results of the simulated-annealing processes, consensus configurations are obtained which exhibit slightly more accurate predictions. The Monte-Carlo procedure also allows converged side chain entropies to be calculated for all residues. These prove to be accurate indicators of prediction reliability. For example, the correct rotamer is obtained for 79% and the correct chi 1 value is obtained for 84% of the half of the sample residues exhibiting the lowest entropies. Side chain entropy and predictability are nearly completely uncorrelated with solvent-accessible area. Some precedents for and implications of this observation are discussed.

Amino acid sequence determinants of beta-lactamase structure and activity.

TEM-1 beta-lactamase catalyzes the hydrolysis of beta-lactam antibiotics such as the penicillins and cephalosporins, thus providing for bacterial resistance to these compounds. To determine the amino acid residues critical for the structure and function of TEM-1 beta-lactamase, the codons for each of the 263 amino acid residues that constitute the mature form of the enzyme were randomized using a site-directed mutagenesis procedure. Functional random mutants were selected based on their ability to confer ampicillin resistance to Escherichia coli. The DNA sequence of several functional mutants was determined for each set of random mutants. It was found that 43 out of the 263 amino acid residues do not tolerate substitutions and therefore are critical for the structure and activity of the enzyme. In addition, a comparison of conserved residue positions among functional beta-lactamase mutants with conserved residues in the beta-lactamase gene family identified many positions which did not tolerate substitutions in the mutagenesis studies but are freely substituted among members of the gene family. This observation may be due to the accumulation of compensating mutations among members of the gene family. Finally, the sequence variability at residue positions among functional mutants was quantitated by calculating the effective number of substitutions at each position using information-theoretical entropy. These values were used to obtain a quantitative estimate of the correlation between the sequence variability at a position and the fractional accessible surface area of the residue. The correlation is found to be statistically significant in that buried residues tend to exhibit low variability and invariant residues tend to exhibit low solvent exposure. However, the correlation is weak because most residues are neither completely buried nor invariant.

Computer modeling of protein folding: conformational and energetic analysis of reduced and detailed protein models.

Recently we developed methods to generate low-resolution protein tertiary structures using a reduced model of the protein where secondary structure is specified and a simple potential based on a statistical analysis of the Protein Data Bank is employed. Here we present the results of an extensive analysis of a large number of detailed, all-atom structures generated from these reduced model structures. Following side-chain addition, minimization and simulated annealing simulations are carried out with a molecular mechanics potential including an approximate continuum solvent treatment. By combining reduced model simulations with molecular modeling calculations we generate energetically competitive, plausible misfolded structures which provide a more significant test of the potential function than current misfolded models based on superimposing the native sequence on the folded structures of completely different proteins. The various contributions to the total energy and their interdependence are analyzed in detail for many conformations of three proteins (myoglobin, the C-terminal fragment of the L7/L12 ribosomal protein, and the N-terminal domain of phage 434 repressor). Our analysis indicates that the all-atom potential performs reasonably well in distinguishing the native structure. It also reveals inadequacies in the reduced model potential, which suggests how this potential can be improved to yield greater accuracy. Preliminary results with an improved potential are presented.

Information-theoretical entropy as a measure of sequence variability.

We propose the use of the information-theoretical entrophy, S = -sigman pi log2 pi, as a measure of variability at a given position in a set of aligned sequences. pi stands for the fraction of times the i-th type appears at a position. For protein sequences, the sum has up to 20 terms, for nucleotide sequences, up to 4 terms, and for codon sequences, up to 61 terms. We compare S and Vs, a related measure, in detail with Vk, the traditional measure of immunoglobulin sequence variability, both in the abstract and as applied to the immunoglobulins. We conclude that S has desirable mathematical properties that Vk lacks and has intuitive and statistical meanings that accord well with the notion of variability. We find that Vk and the S-based measures are highly correlated for the immunoglobulins. We show by analysis of sequence data and by means of a mathematical model that this correlation is due to a strong tendency for the frequency of occurrence of amino acid types at a given position to be log-linear. It is not known whether the immunoglobulins are typical or atypical of protein families in this regard, nor is the origin of the observed rank-frequency distribution obvious, although we discuss several possible etiologies.

Predicting antibody hypervariable loop conformations. II: Minimization and molecular dynamics studies of MCPC603 from many randomly generated loop conformations.

We describe a method for predicting the conformations of loops in proteins and its application to four of the complementarity determining regions [CDRs] in the crystallographically determined structure of MCPC603. The method is based on the generation of a large number of randomly generated conformations for the backbone of the loop being studied, followed by either minimization or molecular dynamics followed by minimization starting from these random structures. The details of the algorithm for the generation of the loops are presented in the first paper in this series (Shenkin et al. [submitted]). The results of minimization and molecular dynamics applied to these loops is presented here. For the two shortest CDRs studied (H1 and L2, which are five and seven amino acids long), minimizations and dynamics simulations which ignore interactions of the loop amino acids beyond the carbon beta replicate the conformation of the crystal structure closely. This suggests that these loops fold independently of sequence variation. For the third CDR (L3, which is nine amino acids), those portions of the CDR near its base which are hydrogen bonded to framework are well replicated by our procedures, but the top of the loop shows significant conformational variability. This variability persists when side chain interactions for the MCPC603 sequence are included. For a fourth CDR (H3, which is 11 amino acids long), new low-energy backbone conformations are found; however, only those which are close to the crystal are compatible with the sequence when side chain interactions are taken into account. Results from minimization and dynamics on single CDRs with all other CDRs removed are presented. These allow us to explore the extent to which individual CDR conformations are determined by interactions with framework only.