Development of an extended simulated annealing method: Application to the modeling of complementary determining regions of immunoglobulins

Abstract

An extended simulated annealing process (ESAP) has been developed in order to obtain an ensemble of conformations of a peptide segment from a protein fluctuating at a given temperature. The annealing process was performed with a fast Monte Carlo method using the scaled collective variables developed by Noguti and Go. The system was divided into two parts: one consists of one or more peptide segments and is flexible around the main-chain and side-chain torsional angles; the other represents the rest of the molecule and was maintained fixed at the atomic positions determined by x-ray experiments. The target function included the nonbonding atomic interactions and a distance function to anchor the N and C terminal ends of each segment to the fixed part. Three systems of complementary determining regions (CDR) of antibodies were tested and compared to x-ray data: L2 loop (7 residues) of the light chain of lambda-type Bence-Jones protein, H1 and the H2 loops (14 residues) of McPC603, and H1 and H2 loops (12 residues) of HyHEL-5. Each state of CDR conformations was characterized at room temperature by the average of their coordinates (average conformation) and the internal energy. With a limited number of annealing processes (10), starting from the extended conformation, we have obtained states with conformations close to the observed x-ray structures, from 1.1 to 1.7 A root mean square deviation (rmsd) of main-chain atoms depending on the system. These states were identical or within 0.25 A rmsd of those of lowest internal energy. For unknown CDR structures the criteria of lowest internal energies from ESAP can be used to predict hypervariable loop structures in antibodies with an accuracy comparable to other methods.

Modeling of protein loops by simulated annealing

“…The ESAP method of Higo et al (1992) has already been found to be more accurate for modeling hypervariable loops of immunoglobulins than the conformational search methods (Gibrat et al, 1992), and the results for the two hypervariable loops of McPC603 confirmed these findings. The accuracy of the modeling of the bovine pancreatic trypsin inhibitor (BPTI) and trypsin loops in Table 2 were very similar to the accuracy found for the hypervariable loops even if some of them contain residues in regular secondary structure such as those of B2, B3, and BS.…”

“…Ensemble averages of the energies and coordinates have been considered by Higo et al (1992) as the best approximation to compare the modeled hypervariable loops of antibodies with X-ray data. Comparison was made between the X-ray coordinates without regularization of the X-ray structure with the rigid geometry and without a least-squared superposition of the modeled loop.…”

“…The ESAP method developed by Higo et al (1992) for modeling hypervariable loops of immunoglobulins has been found to be a method applicable to loops or peptide segments of similar length from different proteins with a comparable accuracy, about an rmsd backbone of 1 A and an all-atom rmsd of 2.3 A. Could one expect better accuracy?…”

“…The simulated annealing was performed as described by Higo et al (1992). The gradual decrease of temperature was obtained by increasing the X values of Equation 1, keeping the temperature at 300 K. The effective temperatures were 300/X.…”

“…We want to report here the results of a Monte Carlo method for the modeling of loops of medium size, six to nine amino acid residues from an initial extended conformation. These loops were taken from different proteins in order to ascertain the generality of a method that has previously only been applied to the modeling of hypervariable loops of immunoglobulins (Gibrat et al, 1992;Higo et al, 1992). The results shown below indicate an accuracy very similar to the accuracy of modeling of the immunoglobulin loops without the difficulties linked to conformational search algorithms such as that used by Bruccoleri et al (1988) in which the search space increases exponentially with the number of amino acids in the loop.…”