While extremely important for relating the protein structure to its biological function, determination of the protein conformational transition pathway upon ligand binding is made difficult due to the transient nature of intermediates, a large and rugged conformational space, and coupling between protein dynamics and ligand−protein interactions. Existing methods that rely on prior knowledge of the bound (holo) state structure are restrictive. A second concern relates to the correspondence of intermediates obtained to the metastable states on the apo → holo transition pathway. Here, we have taken the protein apo structure and ligand-binding site as only inputs and combined an elastic network model (ENM) representation of the protein Hamiltonian with linear response theory (LRT) for protein−ligand interactions to identify the set of slow normal modes of protein vibrations that have a high overlap with the direction of the protein conformational change. The structural displacement along the chosen direction was performed using excited normal modes molecular dynamics (MDeNM) simulations rather than by the direct use of LRT. Herein, the MDeNM excitation velocity was optimized on-the-fly on the basis of its coupling to protein dynamics and ligand−protein interactions. Thus, a determined set of structures was validated against crystallographic and simulation data on four protein−ligand systems, namely, adenylate kinase− di(adenosine-5′)pentaphosphate, ribose binding protein−β-D-ribopyranose, DNA β-glucosyltransferase−uridine-5′-diphosphate, and G-protein α subunit−guanosine-5′-triphosphate, which present important differences in protein conformational heterogeneity, ligand binding mechanism, viz. induced-fit or conformational selection, extent, and nonlinearity in protein conformational changes upon ligand binding, and presence of allosteric effects. The obtained set of intermediates was used as an input to path metadynamics simulations to obtain the free energy profile for the apo → holo transition.

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Prediction of ligand–induced protein conformational transitions is a challenging task due to a large and rugged conformational space, and limited knowledge of probable direction(s) of structure change. These transitions can involve a large scale, global (at the level of entire protein molecule) structural change and occur on a timescale of milliseconds to seconds, rendering application of conventional molecular dynamics simulations prohibitive even for small proteins. We have developed a computational protocol to efficiently and accurately predict these ligand–induced structure transitions solely from the knowledge of protein apo structure and ligand binding site. Our method involves a series of small scale conformational change steps, where at each step linear response theory is used to predict the direction of small scale global response to ligand binding in the protein conformational space (dLRT) followed by construction of a linear combination of slow (low frequency) normal modes (calculated for the structure from the previous step) that best overlaps with dLRT. Protein structure is evolved along this direction using molecular dynamics with excited normal modes (MDeNM) wherein excitation energy along each normal mode is determined by excitation temperature, mode frequency, and its overlap with dLRT. We show that excitation temperature (ΔT) is a very important parameter that allows limiting the extent of structural change in any one step and develop a protocol for automated determination of its optimal value at each step. We have tested our protocol for three protein–ligand systems, namely, adenylate Kinase — di(adenosine 5′)pentaphosphate, ribose binding protein — β–D ribopyranose, and DNA β–glucosyltransferase — uridine–5′–diphosphate, that incorporate important differences in type and range of structural changes upon ligand binding. We obtain very accurate prediction for not only the structure of final protein–ligand complex (holo–structure) having a large scale conformational change, but also for biologically relevant intermediates between the apo and the holo structures. Moreover, most relevant set of normal modes for conformational change at each step are an output from our method, which can be used as collective variables for determination of free energy barriers and transition timescales along the identified pathway.

The need to incorporate specific molecular-scale features for largescale structural changes in biological membranes necessitate use of a multi scale computational approach. Here, this comprises of Langevin dynamics in a normal mode space determined from an elastic network model (ENM) representation for lipid-water Hamiltonian. All atom (AA) MD simulations are used to determine model parameters, and Langevin dynamics predictions for an extensive set of bilayer properties, such as, undulation spectra, undulation relaxation rates, dynamic structure factor, and mechanical properties are validated against the data from MD simulations and experiments. The transferability of model parameters to describe dynamics of a larger lipid bilayer and a heterogeneous membrane-protein system is assessed. The developed model is coupled to the energy landscape for membrane deformations to obtain a set of generic reaction coordinates (RCs) for pore formation in two tensionless, single lipid-type bilayers, namely, 1,2-dimyristoyl-sn-glycero-3 phosphocholine (DMPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). Structure evolution is carried in an AA MD simulation wherein the generic RCs are used in a path metadynamics or an umbrella sampling simulation to investigate thermodynamics of pore formation and its molecular determinants. The transition state is characterized extensively to bring out the interplay between various bilayer motions (undulations, lateral density fluctuations, thinning, lipid tilt), lipid solvation, and lipid packing.

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