Improved prediction of MHC-peptide binding using protein language models.

Major histocompatibility complex Class I (MHC-I) molecules bind to peptides derived from intracellular antigens and present them on the surface of cells, allowing the immune system (T cells) to detect them. Elucidating the process of this presentation is essential for regulation and potential manipulation of the cellular immune system. Predicting whether a given peptide binds to an MHC molecule is an important step in the above process and has motivated the introduction of many computational approaches to address this problem.

Improved cluster ranking in protein-protein docking using a regression approach.

We develop a method to rank clusters of similar protein complex conformations generated by an underlying docking program. The method leverages robust regression to predict the relative quality difference between any pair or clusters and combines these pairwise assessments to form a ranked list of clusters, from higher to lower quality. We apply RRPCC to clusters produced by the automated docking server ClusPro and, depending on the training/validation strategy, we show improvement by 24-100% in ranking acceptable or better quality clusters first, and by 15-100% in ranking medium or better quality clusters first.

Focused grid-based resampling for protein docking and mapping.

The fast Fourier transform (FFT) sampling algorithm has been used with success in application to protein-protein docking and for protein mapping, the latter docking a variety of small organic molecules for the identification of binding hot spots on the target protein. Here we explore the local rather than global usage of the FFT sampling approach in docking applications. If the global FFT based search yields a near-native cluster of docked structures for a protein complex, then focused resampling of the cluster generally leads to a substantial increase in the number of conformations close to the native structure.

Energy Minimization on Manifolds for Docking Flexible Molecules.

In this paper, we extend a recently introduced rigid body minimization algorithm, defined on manifolds, to the problem of minimizing the energy of interacting flexible molecules. The goal is to integrate moving the ligand in six dimensional rotational/translational space with internal rotations around rotatable bonds within the two molecules. We show that adding rotational degrees of freedom to the rigid moves of the ligand results in an overall optimization search space that is a manifold to which our manifold optimization approach can be extended.

A Subspace Semi-Definite programming-based Underestimation (SSDU) method for stochastic global optimization in protein docking.

We propose a new stochastic global optimization method targeting protein docking problems. The method is based on finding a general convex polynomial underestimator to the binding energy function in a permissive subspace that possesses a funnel-like structure. We use Principal Component Analysis (PCA) to determine such permissive subspaces.

Optimization on the space of rigid and flexible motions: an alternative manifold optimization approach.

In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose.

The impact of side-chain packing on protein docking refinement.

We study the impact of optimizing the side-chain positions in the interface region between two proteins during the process of binding. Mathematically, the problem is similar to side-chain prediction, which has been extensively explored in the process of protein structure prediction. The protein-protein docking application, however, has a number of characteristics that necessitate different algorithmic and implementation choices.

Efficient Maintenance and Update of Nonbonded Lists in Macromolecular Simulations.

Molecular mechanics and dynamics simulations use distance based cutoff approximations for faster computation of pairwise van der Waals and electrostatic energy terms. These approximations traditionally use a precalculated and periodically updated list of interacting atom pairs, known as the "nonbonded neighborhood lists" or nblists, in order to reduce the overhead of finding atom pairs that are within distance cutoff. The size of nblists grows linearly with the number of atoms in the system and superlinearly with the distance cutoff, and as a result, they require significant amount of memory for large molecular systems.

Encounter complexes and dimensionality reduction in protein-protein association.

An outstanding challenge has been to understand the mechanism whereby proteins associate. We report here the results of exhaustively sampling the conformational space in protein-protein association using a physics-based energy function. The agreement between experimental intermolecular paramagnetic relaxation enhancement (PRE) data and the PRE profiles calculated from the docked structures shows that the method captures both specific and non-specific encounter complexes.

Rigid Body Energy Minimization on Manifolds for Molecular Docking.

Virtually all docking methods include some local continuous minimization of an energy/scoring function in order to remove steric clashes and obtain more reliable energy values. In this paper, we describe an efficient rigid-body optimization algorithm that, compared to the most widely used algorithms, converges approximately an order of magnitude faster to conformations with equal or slightly lower energy. The space of rigid body transformations is a nonlinear manifold, namely, a space which locally resembles a Euclidean space.

A New Distributed Algorithm for Side-Chain Positioning in the Process of Protein Docking.

is an important component of computational protein docking methods. Existing SCP methods and available software have been designed for protein folding applications where side-chain positioning is also important. As a result they do not take into account significant special structure that SCP for docking exhibits.

Flexible Refinement of Protein-Ligand Docking on Manifolds.

Our work is motivated by energy minimization of biological macromolecules, an essential step in computational docking. By allowing some ligand flexibility, we generalize a recently introduced novel representation of rigid body minimization as an optimization on the [Formula: see text] manifold, rather than on the commonly used Special Euclidean group (3). We show that the resulting flexible docking can also be formulated as an optimization on a Lie group that is the direct product of simpler Lie groups for which geodesics and exponential maps can be easily obtained.

A New Approach to Rigid Body Minimization with Application to Molecular Docking.

Our work is motivated by energy minimization in the space of rigid affine transformations of macromolecules, an essential step in computational protein-protein docking. We introduce a novel representation of rigid body motion that leads to a natural formulation of the energy minimization problem as an optimization on the [Formula: see text] manifold, rather than the commonly used (3). The new representation avoids the complications associated with optimization on the (3) manifold and provides additional flexibilities for optimization not available in that formulation.

A Message Passing Approach to Side Chain Positioning with Applications in Protein Docking Refinement.

We introduce a message-passing algorithm to solve the problem. SCP is a crucial component of , which is a key step of an important class of problems in computational structural biology called . We model SCP as a combinatorial optimization problem and formulate it as a problem.

Protein docking by the underestimation of free energy funnels in the space of encounter complexes.

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling.

Protein-protein docking with reduced potentials by exploiting multi-dimensional energy funnels.

We propose a new computational approach for protein docking exploiting energy funnels in the 6-dimensional space of translations and rotations of the ligand with respect to the receptor. Our approach consists of a series of translational and orientational moves of the ligand towards the receptor. Each move is performed using a global optimization method we have developed - the semi-definite underestimation (SDU) method - which can exploit a funnel-like energy function.

SDU: A Semidefinite Programming-Based Underestimation Method for Stochastic Global Optimization in Protein Docking.

This paper introduces a new stochastic global optimization method targeting protein-protein docking problems, an important class of problems in computational structural biology. The method is based on finding general convex quadratic underestimators to the binding energy function that is funnel-like. Finding the optimum underestimator requires solving a semidefinite programming problem, hence the name semidefinite programming-based underestimation (SDU).