Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed.

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Empirical force fields for biological macromolecules: overview and issues.

The term molecular mechanics (MM) refers to the use of simple potential-energy functions (e.g., harmonic oscillator or Coulombic potentials) to model molecular systems. Molecular mechanics approaches are widely applied in molecular structure refinement, molecular dynamics (MD) simulations, Monte Carlo (MC) simulations, and ligand-docking simulations.

Typically, molecular mechanics models consist of spherical atoms connected by springs which represent bonds. Internal forces experienced in the model structure are described using simple mathematical functions. For example, Hooke’s law is commonly used to describe bonded interactions, and the nonbonded atoms might be treated as inelastic hard spheres or may interact according to a Lennard-Jones potential. Using these simple models, a molecular dynamics simulation numerically solves Newton’s equations of motion, thus allowing structural fluctuations to be observed with respect to time.

Dynamic simulation methods are widely used to obtain information on the time evolution of conformations of proteins and other biological macromolecules1–4 and also kinetic and thermodynamic information. Simulations can provide fine detail concerning the motions of individual particles as a function of time. They can be utilized to quantify the properties of a system at a precision and on a time scale that is otherwise inaccessible, and simulation is, therefore, a valuable tool in extending our understanding of model systems. Theoretical consideration of a system additionally allows one to investigate the specific contributions to a property through “computational alchemy”,5 that is, modifying the simulation in a way that is nonphysical but nonetheless allows a model’s characteristics to be probed. One particular example is the artificial conversion of the energy function from that representing one system to that of another during a simulation. This is an important technique in free-energy calculations.6 Thus, molecular dynamics simulations, along with a range of complementary computational approaches, have become valuable tools for investigating the basis of protein structure and function.

This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool. This review then covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role. The range of studies in which MD has played a considerable or pivotal role is immense, and this review cannot do justice to them; MD simulations of biomedical importance were recently reviewed.4 Particular emphasis will be placed on the study of dynamic aspects of protein recognition, an area where molecular dynamics has scope to provide broad and far-ranging insights. This review concludes with a brief discussion of the future potential offered to advancement of the biological and biochemical sciences and the remaining issues that must be overcome to allow the full extent of this potential to be realized.

1.1. Historical Background
MD methods were originally conceived within the theoretical physics community during the 1950s. In 1957, Alder and Wainwright7 performed the earliest MD simulation using the so-called hard-sphere model, in which the atoms interacted only through perfect collisions. Rahman8 subsequently applied a smooth, continuous potential to mimic real atomic interactions. During the 1970s, as computers became more widespread, MD simulations were developed for more complex systems, culminating in 1976 with the first simulation of a protein9,10 using an empirical energy function constructed using physics-based first-principles assumptions. MD simulations are now widely and routinely applied and especially popular in the fields of materials science11,12 and biophysics.

As will be discussed later in this review, a variety of experimental conditions may be simulated with modern theories and algorithms. The initial simulations only considered single molecules in vacuo. Over time, more realistic or at least biologically relevant simulations could be performed. This trend is continuing today.

The initial protein MD simulation, of the small bovine pancreatic trypsin inhibitor (BPTI), covered only 9.2 ps of simulation time. Modern simulations routinely have so-called equilibration periods much longer than that, and production simulations of tens of nanoseconds are routine, with the first microsecond MD simulation being reported in 1998.13 In addition, the original BPTI simulation included only about 500 atoms rather than the 104-106 atoms that are common today. While much of this advancement results from an immense increase in availability of computing power, major theoretical and methodological developments also contribute significantly.

The number of publications regarding MD theory and application of MD to biological systems is growing at an extraordinary pace. A single review cannot do justice to the recent applications of MD. Using data from ISI Web of Science, the authors estimate that during 2005 at least 800 articles will be published that discuss molecular dynamics and proteins. The historical counts are shown in Figure 1.






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Figure 1


Articles matching ISI Web of Science query “TS=(protein) AND TS=(molecular dynamics)”.

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Molecular dynamics: survey of methods for simulating the activity of proteins.

We present a new shape-based method, LigandFit, for accurately docking ligands into protein active sites. The method employs a cavity detection algorithm for detecting invaginations in the protein as candidate active site regions. A shape comparison filter is combined with a Monte Carlo conformational search for generating ligand poses consistent with the active site shape. Candidate poses are minimized in the context of the active site using a grid-based method for evaluating protein-ligand interaction energies. Errors arising from grid interpolation are dramatically reduced using a new non-linear interpolation scheme. Results are presented for 19 diverse protein-ligand complexes. The method appears quite promising, reproducing the X-ray structure ligand pose within an RMS of 2A in 14 out of the 19 complexes. A high-throughput screening study applied to the thymidine kinase receptor is also presented in which LigandFit, when combined with LigScore, an internally developed scoring function, yields very good hit rates for a ligand pool seeded with known actives.

LigandFit: a novel method for the shape-directed rapid docking of ligands to protein active sites

Empirical force fields commonly used to describe the condensed phase properties of complex systems such as biological macromolecules are continuously being updated. Improvements in quantum mechanical (QM) methods used to generate target data, availability of new experimental target data, incorporation of new classes of compounds and new theoretical developments (eg. polarizable methods) make force-field development a dynamic domain of research. Accordingly, a number of improvements and extensions of the CHARMM force fields have occurred over the years. The objective of the present review is to provide an up-to-date overview of the CHARMM force fields. A limited presentation on the historical aspects of force fields will be given, including underlying methodologies and principles, along with a brief description of the strategies used for parameter development. This is followed by information on the CHARMM additive and polarizable force fields, including examples of recent applications of those force fields.

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Recent Developments and Applications of the CHARMM force fields.

Molecular dynamics simulations of nucleic acid-protein complexes.

A class II valence force field covering a broad range of organic molecules has been derived employing ab initio quantum mechanical "observables." The procedure includes selecting representative molecules and molecular structures, and systematically sampling their energy surfaces as described by energies and energy first and second derivatives with respect to molecular deformations. In this article the procedure for fitting the force field parameters to these energies and energy derivatives is briefly reviewed. The application of the methodology to the derivation of a class II quantum mechanical force field (QMFF) for 32 organic functional groups is then described. A training set of 400 molecules spanning the 32 functional groups was used to parameterize the force field. The molecular families comprising the functional groups and, within each family, the torsional angles used to sample different conformers, are described. The number of stationary points (equilibria and transition states) for these molecules is given for each functional group. This set contains 1324 stationary structures, with 718 minimum energy structures and 606 transition states. The quality of the fit to the quantum data is gauged based on the deviations between the ab initio and force field energies and energy derivatives. The accuracy with which the QMFF reproduces the ab initio molecular bond lengths, bond angles, torsional angles, vibrational frequencies, and conformational energies is then given for each functional group. Consistently good accuracy is found for these computed properties for the various types of molecules. This demonstrates that the methodology is broadly applicable for the derivation of force field parameters across widely differing types of molecular structures. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1782-1800, 2001

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds.

The compounds can bind selectively to G-quadruplex DNA and result in a strong turn-on red fluorescence response, and it is also a potential fluorescence probe for G-quadruplex DNA in the living cells. 

Haiying Li

Papers

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds.

Benzothiazole Derivatives Targeting G‐Quadruplex DNA: Synthesis, DNA Interaction and Living Cell Imaging