Accelerating molecular simulations of proteins using Bayesian inference on weak information

Abstract

Atomistic molecular dynamics (MD) simulations of protein molecules are too computationally expensive to predict most native structures from amino acid sequences. Here, we integrate "weak" external knowledge into folding simulations to predict protein structures, given their sequence. For example, we instruct the computer "to form a hydrophobic core," "to form good secondary structures," or "to seek a compact state." This kind of information has been too combinatoric, nonspecific, and vague to help guide MD simulations before. Within atomistic replica-exchange molecular dynamics (REMD), we develop a statistical mechanical framework, modeling using limited data with coarse physical insight(s) (MELD + CPI), for harnessing weak information. As a test, we apply MELD + CPI to predict the native structures of 20 small proteins. MELD + CPI samples to within less than 3.2 Å from native for all 20 and correctly chooses the native structures (<4 Å) for 15 of them, including ubiquitin, a millisecond folder. MELD + CPI is up to five orders of magnitude faster than brute-force MD, satisfies detailed balance, and should scale well to larger proteins. MELD + CPI may be useful where physics-based simulations are needed to study protein mechanisms and populations and where we have some heuristic or coarse physical knowledge about states of interest.protein folding | molecular dynamics | integrative structural biology | Bayesian inference C omputer modeling is an important source of insights into the properties of protein molecules. There are two main approaches, each with different main areas of applicability: comparative modeling and atomistic molecular dynamics (MD) simulations. Comparative modeling draws inferences from a database of the more than 100,000 known native structures of proteins (1); it is an information-centric approach. A key area of applicability is in predicting the native structures of previously unknown proteins. These methods are often tested in the community-wide blind event for predicting native protein structures, called community assessment of structure prediction (2, 3). In contrast, physics-based atomistic simulations are aimed at computing proper relative populations of the many different states of a system; this type of modeling is an energy-centric approach. Computing proper populations (or, correspondingly, free energies) is essential for elucidating stabilities, motions, and mechanistic actions of protein molecules.Physical simulations offer important advantages in the long run, providing a principled and transferrable basis for understanding properties; the capability to go beyond just native structures alone to dynamics, binding, folding, and mechanisms; applicability where databases are limited, including membrane proteins or other foldable polymers, such as peptoids (4); and extensibility to other temperatures, solvents, and binding conditions, for example. A proper physical model requires a plausible physical energy function that can accurately predict native structures (validation); that app...

Advances in free-energy-based simulations of protein folding and ligand binding

“…Recently, an approach called MELD (Modeling Employing Limited Data), has been developed to find and sample important states efficiently by “melding” structural or heuristic information into MD simulations [14,15]. MELD is able to use combinatorically vague and generic instructives such as: “make a hydrophobic core” or “make secondary structures that are consistent with those provided by webservers” or “make a compact structure.” MELD accelerates conformational searching substantially, while at the same time preserving its critically important ability to give free energies.…”

“…MELD is able to use combinatorically vague and generic instructives such as: “make a hydrophobic core” or “make secondary structures that are consistent with those provided by webservers” or “make a compact structure.” MELD accelerates conformational searching substantially, while at the same time preserving its critically important ability to give free energies. For example, MELD finds and samples well native structures (better than 4 Å RMSD) for 15 out of 20 small proteins, up to 92-mers, starting from fully extended states [15]. The speed advantage of MELD over brute-force MD is shown in Figure 2A.…”

“…In earlier protein-folding modeling, force fields were systematically unbalanced between different types of secondary structures. Newer models have much better balance, as shown by recent studies where a variety of protein structures can be folded with a single force field [51,52] [6,10,15]. There remain challenges in capturing the secondary structure propensities of different amino acids and accurately modeling unfolded or disordered proteins [53,54] – a research area receiving recent attention [55,56,57].…”

“…Simulation times for finding native states as a function of protein size, by unrestrained MD, and by MELD, which uses generic directives as restraints. Data from [10,15]. Figure 2B.…”

Constraint methods that accelerate free-energy simulations of biomolecules

“…4. Figure 5 shows the predictions of MELD of the folded states of 20 small proteins, 40 based on 4 CPIs: (1) secondary structure web server predictions, (2) globular proteins have hydrophobic cores, (3) beta-strands pair up, and (4) globular proteins are compact. We run REMD for 500 ns with these heuristic constraints.…”