Sean L. Seyler

Sampling large conformational transitions: adenylate kinase as a testing ground

A fundamental problem in computational biophysics is to deduce the function of a protein from the structure. Many biological macromolecules such as enzymes, molecular motors or membrane transport proteins perform their function by cycling between multiple conformational states. Understanding such conformational transitions, which typically occur on the millisecond to second time scale, is central to understanding protein function. Molecular dynamics (MD) computer simulations have become an important tool to connect molecular structure to function, but equilibrium MD simulations are rarely able to sample on time scales longer than a few microseconds – orders of magnitudes shorter than the time scales of interest. A range of different simulation methods have been proposed to overcome this time-scale limitation. These include calculations of the free energy landscape and path sampling methods to directly sample transitions between known conformations. All these methods solve the problem to sample infrequently occupied but important regions of configuration space. Many path-sampling algorithms have been applied to the closed open transition of the enzyme adenylate kinase (AdK), which undergoes a large, clamshell-like conformational transition between an open and a closed state. Here we review approaches to sample macromolecular transitions through the lens of AdK. We focus our main discussion on the current state of knowledge – both from simulations and experiments – about the transition pathways of ligand-free AdK, its energy landscape, transition rates and interactions with substrates. We conclude with a comparison of the discussed approaches with a view towards quantitative evaluation of path-sampling methods.

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA was applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

Structure of the SLC4 transporter Bor1p in an inward-facing conformation.

Bor1p is a secondary transporter in yeast that is responsible for boron transport. Bor1p belongs to the SLC4 family which controls bicarbonate exchange and pH regulation in animals as well as borate uptake in plants. The SLC4 family is more distantly related to members of the Amino acid‐Polyamine‐organoCation (APC) superfamily, which includes well studied transporters such as LeuT, Mhp1, AdiC, vSGLT, UraA, SLC26Dg. Their mechanism generally involves relative movements of two domains: a core domain that binds substrate and a gate domain that in many cases mediates dimerization. To shed light on conformational changes governing transport by the SLC4 family, we grew helical membrane crystals of Bor1p from Saccharomyces mikatae and determined a structure at ∼6 Å resolution using cryo‐electron microscopy. To evaluate the conformation of Bor1p in these crystals, a homology model was built based on the related anion exchanger from red blood cells (AE1). This homology model was fitted to the cryo‐EM density map using the Molecular Dynamics (MD) Flexible Fitting method and then relaxed by all‐atom MD simulation in explicit solvent and membrane. Mapping of water accessibility indicates that the resulting structure represents an inward‐facing conformation. Comparisons of the resulting Bor1p model with the X‐ray structure of AE1 in an outward‐facing conformation, together with MD simulations of inward‐facing and outward‐facing Bor1p models, suggest rigid body movements of the core domain relative to the gate domain. These movements are consistent with the rocking‐bundle transport mechanism described for other members of the APC superfamily.