Simulation method for calculating the entropy and free energy of peptides and proteins

Bacterial surface capsular polysaccharides (CPS) that are similar in carbohydrate sequence may differ markedly in immunogenicity and antigenicity. The structural origin of these phenomena is poorly understood. Such a case is presented by the Gram-positive bacteria Streptococcus agalactiae (Group B Streptococcus; GBS) type III (GBSIII) and Streptococcus pneumoniae (Pn) type 14 (Pn14), which share closely related CPS sequences. Nevertheless, antibodies (Abs) against GBSIII rarely cross-react with the CPS from Pn14. To establish the origin for the variation in CPS antigenicity, models for the immune complexes of CPS fragments from GBSIII and Pn14, with the variable fragment (Fv) of a GBS-specific mAb (mAb 1B1), are presented. The complexes are generated through a combination of comparative Ab modeling and automated ligand docking, followed by explicitly solvated 10-ns molecular dynamics simulations. The relationship between carbohydrate sequence and antigenicity is further quantified through the computation of interaction energies using the Molecular Mechanics-Generalized Born Surface Area (MM-GBSA) method, augmented by conformational entropy estimates. Despite the electrostatic differences between Pn14 and GBSIII CPS, analysis indicates that entropic penalties are primarily responsible for the loss of affinity of the highly flexible Pn14 CPS for mAb 1B1. The similarity of the solution conformation of the relatively rigid GBSIII CPS with that in the immune complex characterizes the previously undescribed 3D structure of the conformational epitope. The analysis provides a comprehensive interpretation for a large body of biochemical and immunological data related to Ab recognition of bacterial polysaccharides and should be applicable to other Ab-carbohydrate interactions. S treptococcus agalactiae [Group B Streptococcus (GBS)] andStreptococcus pneumoniae (Pn) are responsible for the majority of life-threatening cases of septicemia, meningitis, and pneumonia in neonates (1, 2). Gram-positive bacteria, such as GBS and Pn, are classified into serotypes according to the unique carbohydrate sequence of the bacterial surface capsular polysaccharide (CPS) and protein antigens. Serotypes vary in antigenicity, immunogenicity, virulence, and geographical distribution (3). Quantification of the structural and dynamic properties responsible for the affinity and specificity of antigenic oligosaccharide-antibody (Ab) interactions is a crucial step in furthering the understanding of the immune response to bacterial and fungal pathogens. In GBS, the CPS is a high-molecularweight polymer composed of varying sequences of ␤-D-, and sometimes L-rhamnopyranose. The glyceryl side chain of the Neu5Ac residues may also be Oacetylated (4). In all GBS strains identified to date, the Neu5Ac residues occur in the terminal position on the side-chain branches of the polymeric repeat unit of the CPS. They play an important role in defining the antigenicity and immunogenicity of the CPS (5). Variations within the CPS sequence result in the nine kno...

Section: Generation Of the Cps-fv Complexesmentioning

confidence: 99%

Understanding the bacterial polysaccharide antigenicity ofStreptococcus agalactiaeversusStreptococcus pneumoniae

Kadirvelraj

González-Outeiriño

Foley

et al. 2006

“…Therefore, in this paper we develop a method called complete HSMC that leads to the exact entropy for infinite MC sampling; this method is applied to argon systems of different size, and to a system of 64 TIP3P water molecules (18). In the companion paper (19), the complete HSMC method is extended to peptides, which ultimately makes our approach applicable to model peptideexplicit water systems. In what follows, we describe the complete HSMC method as applied to liquids.…”

mentioning

confidence: 99%

A simulation method for calculating the absolute entropy and free energy of fluids: Application to liquid argon and water

White

Meirovitch

2004

Self Cite

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy and free energy by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by adding its atoms gradually to the initially empty volume, i.e., by placing them in their positions at i using transition probabilities (TPs). At each step of the process, the volume is divided into two parts, the already visited part (the ''past'') and the ''future'' part, where obtaining the TP requires calculating partition functions over the future part in the presence of the frozen past. In recent publications, the TPs were calculated approximately by taking into account only partial future. Here we present a ''complete HSMC'' procedure, where the TPs are calculated from MC simulations carried out over the complete future. The complete HSMC method is applied to systems of liquid argon and the TIP3P model of water, and very good results for the free energy are obtained, as compared with results obtained by thermodynamic integration.T he absolute entropy, S, is a measure of order and is also a fundamental component of the absolute Helmholtz free energy, F, F ϭ E Ϫ TS, where E is the energy and T is the absolute temperature. The free energy is a key quantity as it constitutes the correct criterion of stability, which is mandatory for determining the relative populations of protein structures, for example. However, calculation of S and therefore F of a complex system, such as a peptide or a protein in water by computer simulation, is an extremely difficult problem (1-4). Using any simulation technique, it is relatively easy to calculate the energy, E i , which is ''written'' on system configuration i in terms of microscopic interactions (e.g., Lennard-Jones interactions of argon). On the other hand, calculating S Ϸ Ϫln P i B requires knowledge of the value of the Boltzmann probability, which is the sampling probability. However, P i B is not provided directly by the commonly used dynamical techniques, Metropolis Monte Carlo (MC) (5) and molecular dynamics (MD) (6 -7), therefore, F is unknown as well. In most cases, calculation of F is based on reversible thermodynamic integration (TI) techniques that provide the difference in the free energy, ⌬F m,n , between two states m and n, (e.g., helical and hairpin states of a peptide) and only when the absolute entropy of one state is known can that of the other be obtained. Although TI is a robust approach (refs. 1-4, 8, and 9 and references therein), for proteins, such integration is feasible only if the structural variance between the two states is very small; otherwise, the integration path can become prohibitively lengthy and complex. Therefore, it is important to develop methods that provide ln P i B at least approximately, enabling one to calculate the absolute F m and F n from two samples of the states m and n; in this case ⌬F m,n ϭ F m Ϫ F n can be calculated even for significa...

“…To provide a proof of principle for our reweighting approach, we will determine free energy differences ( F), between states for various test systems (15)(16)(17)(18)(19)(20)(21).…”

Section: Background and Theorymentioning

confidence: 99%

A black-box re-weighting analysis can correct flawed simulation data

Ytreberg

Zuckerman

2008

There is a great need for improved statistical sampling in a range of physical, chemical, and biological systems. Even simulations based on correct algorithms suffer from statistical error, which can be substantial or even dominant when slow processes are involved. Further, in key biomolecular applications, such as the determination of protein structures from NMR data, non-Boltzmann-distributed ensembles are generated. We therefore have developed the "blackbox" strategy for reweighting a set of configurations generated by arbitrary means to produce an ensemble distributed according to any target distribution. In contrast to previous algorithmic efforts, the black-box approach exploits the configuration-space density observed in a simulation, rather than assuming a desired distribution has been generated. Successful implementations of the strategy, which reduce both statistical error and bias, are developed for a one-dimensional system, and a 50-atom peptide, for which the correct 250-to-1 population ratio is recovered from a heavily biased ensemble.canonical sampling | free energy | non-Boltzmann | molecular simulation E nsemble averages over configurations are fundamental to the analysis of finite-temperature systems of physical, chemical, and biological interest, as well as to any statistically defined system. Yet it is well appreciated that estimates of such averages based on computer simulations can suffer from both systematic and statistical error (1, 2). We therefore ask: Given a set of previously generated configurations of uncertain quality, what is the best way to estimate ensemble averages? Our proposed answer, the "black-box reweighting" (BBRW) strategy described below, appears promising in its ability to overcome both types of error in some systems.Statistical error is a ubiquitous problem of underappreciated practical importance. Every algorithm known to the authors, including sophisticated methods (3-5), relies on repeated visits to a state (a subset of configuration space) to generate statistical reliability or precision in the population estimate for that state. If we define the simulation-and-system-specific correlation time t corr as the time required to visit all important states at least once, then statistical precision requires a long total simulation time, t sim t corr . Standard square-root-of-duration arguments (1, 2) suggest that a simulation retains a fractional imprecision of √ t corr /t sim (on a unit scale). Below, we show that BBRW dramatically cuts statistical error, avoiding the slow square-root behavior.Systematic bias is typical in some systems of great practical importance-such as full-sized proteins-where, to date, it is not clear that any atomically detailed simulation has come close to reaching t corr . Indeed, surprisingly lengthy simulations are required to obtain statistical ensembles for small peptides (6). Nevertheless, biased non-Boltzmann distributed sets of atomically detailed protein structures are regularly generated, e.g., for NMR structure determination (7) and i...