Origin of Scaling Behavior of Protein Packing Density: A Sequential Monte Carlo Study of Compact Long Chain Polymers

Single domain proteins are thought to be tightly packed. The introduction of voids by mutations is often regarded as destabilizing. In this study we show that packing density for single domain proteins decreases with chain length. We find that the radius of gyration provides poor description of protein packing but the alpha contact number we introduce here characterize proteins well. We further demonstrate that protein-like scaling relationship between packing density and chain length is observed in off-lattice self-avoiding walks. A key problem in studying compact chain polymer is the attrition problem: It is difficult to generate independent samples of compact long self-avoiding walks. We develop an algorithm based on the framework of sequential Monte Carlo and succeed in generating populations of compact long chain off-lattice polymers up to length $N=2,000$. Results based on analysis of these chain polymers suggest that maintaining high packing density is only characteristic of short chain proteins. We found that the scaling behavior of packing density with chain length of proteins is a generic feature of random polymers satisfying loose constraint in compactness. We conclude that proteins are not optimized by evolution to eliminate packing voids.Comment: 9 pages, 10 figures. Accepted by J. Chem. Phy

Protein Design Using Continuous Rotamers

Optimizing amino acid conformation and identity is a central problem in computational protein design. Protein design algorithms must allow realistic protein flexibility to occur during this optimization, or they may fail to find the best sequence with the lowest energy. Most design algorithms implement side-chain flexibility by allowing the side chains to move between a small set of discrete, low-energy states, which we call rigid rotamers. In this work we show that allowing continuous side-chain flexibility (which we call continuous rotamers) greatly improves protein flexibility modeling. We present a large-scale study that compares the sequences and best energy conformations in 69 protein-core redesigns using a rigid-rotamer model versus a continuous-rotamer model. We show that in nearly all of our redesigns the sequence found by the continuous-rotamer model is different and has a lower energy than the one found by the rigid-rotamer model. Moreover, the sequences found by the continuous-rotamer model are more similar to the native sequences. We then show that the seemingly easy solution of sampling more rigid rotamers within the continuous region is not a practical alternative to a continuous-rotamer model: at computationally feasible resolutions, using more rigid rotamers was never better than a continuous-rotamer model and almost always resulted in higher energies. Finally, we present a new protein design algorithm based on the dead-end elimination (DEE) algorithm, which we call iMinDEE, that makes the use of continuous rotamers feasible in larger systems. iMinDEE guarantees finding the optimal answer while pruning the search space with close to the same efficiency of DEE. Availability: Software is available under the Lesser GNU Public License v3. Contact the authors for source code

Computational Design of a PDZ Domain Peptide Inhibitor that Rescues CFTR Activity

The cystic fibrosis transmembrane conductance regulator (CFTR) is an epithelial chloride channel mutated in patients with cystic fibrosis (CF). The most prevalent CFTR mutation, ΔF508, blocks folding in the endoplasmic reticulum. Recent work has shown that some ΔF508-CFTR channel activity can be recovered by pharmaceutical modulators (“potentiators” and “correctors”), but ΔF508-CFTR can still be rapidly degraded via a lysosomal pathway involving the CFTR-associated ligand (CAL), which binds CFTR via a PDZ interaction domain. We present a study that goes from theory, to new structure-based computational design algorithms, to computational predictions, to biochemical testing and ultimately to epithelial-cell validation of novel, effective CAL PDZ inhibitors (called “stabilizers”) that rescue ΔF508-CFTR activity. To design the “stabilizers”, we extended our structural ensemble-based computational protein redesign algorithm to encompass protein-protein and protein-peptide interactions. The computational predictions achieved high accuracy: all of the top-predicted peptide inhibitors bound well to CAL. Furthermore, when compared to state-of-the-art CAL inhibitors, our design methodology achieved higher affinity and increased binding efficiency. The designed inhibitor with the highest affinity for CAL (kCAL01) binds six-fold more tightly than the previous best hexamer (iCAL35), and 170-fold more tightly than the CFTR C-terminus. We show that kCAL01 has physiological activity and can rescue chloride efflux in CF patient-derived airway epithelial cells. Since stabilizers address a different cellular CF defect from potentiators and correctors, our inhibitors provide an additional therapeutic pathway that can be used in conjunction with current methods

A Generic Program for Multistate Protein Design

Some protein design tasks cannot be modeled by the traditional single state design strategy of finding a sequence that is optimal for a single fixed backbone. Such cases require multistate design, where a single sequence is threaded onto multiple backbones (states) and evaluated for its strengths and weaknesses on each backbone. For example, to design a protein that can switch between two specific conformations, it is necessary to to find a sequence that is compatible with both backbone conformations. We present in this paper a generic implementation of multistate design that is suited for a wide range of protein design tasks and demonstrate in silico its capabilities at two design tasks: one of redesigning an obligate homodimer into an obligate heterodimer such that the new monomers would not homodimerize, and one of redesigning a promiscuous interface to bind to only a single partner and to no longer bind the rest of its partners. Both tasks contained negative design in that multistate design was asked to find sequences that would produce high energies for several of the states being modeled. Success at negative design was assessed by computationally redocking the undesired protein-pair interactions; we found that multistate design's accuracy improved as the diversity of conformations for the undesired protein-pair interactions increased. The paper concludes with a discussion of the pitfalls of negative design, which has proven considerably more challenging than positive design

A Measure of the Promiscuity of Proteins and Characteristics of Residues in the Vicinity of the Catalytic Site That Regulate Promiscuity

Promiscuity, the basis for the evolution of new functions through ‘tinkering’ of residues in the vicinity of the catalytic site, is yet to be quantitatively defined. We present a computational method Promiscuity Indices Estimator (PROMISE) - based on signatures derived from the spatial and electrostatic properties of the catalytic residues, to estimate the promiscuity (PromIndex) of proteins with known active site residues and 3D structure. PromIndex reflects the number of different active site signatures that have congruent matches in close proximity of its native catalytic site, the quality of the matches and difference in the enzymatic activity. Promiscuity in proteins is observed to follow a lognormal distribution (μ = 0.28, σ = 1.1 reduced chi-square = 3.0E-5). The PROMISE predicted promiscuous functions in any protein can serve as the starting point for directed evolution experiments. PROMISE ranks carboxypeptidase A and ribonuclease A amongst the more promiscuous proteins. We have also investigated the properties of the residues in the vicinity of the catalytic site that regulates its promiscuity. Linear regression establishes a weak correlation (R2∼0.1) between certain properties of the residues (charge, polar, etc) in the neighborhood of the catalytic residues and PromIndex. A stronger relationship states that most proteins with high promiscuity have high percentages of charged and polar residues within a radius of 3 Å of the catalytic site, which is validated using one-tailed hypothesis tests (P-values∼0.05). Since it is known that these characteristics are key factors in catalysis, their relationship with the promiscuity index cross validates the methodology of PROMISE

Computational Treatment of Metalloproteins

Metalloproteins present a considerable challenge for modeling, especially when the starting point is far from thermodynamic equilibrium. Examples include formidable problems such as metalloprotein folding and structure prediction upon metal addition, removal, or even just replacement; metalloenzyme design, where stabilization of a transition state of the catalyzed reaction in the specific binding pocket around the metal needs to be achieved; docking to metal-containing sites and design of metalloenzyme inhibitors. Even more conservative computations, such as elucidations of the mechanisms and energetics of the reaction catalyzed by natural metalloenzymes, are often nontrivial. The reason is the vast span of time and length scales over which these proteins operate, and thus the resultant difficulties in estimating their energies and free energies. It is required to perform extensive sampling, properly treat the electronic structure of the bound metal or metals, and seamlessly merge the required techniques to assess energies and entropies, or their changes, for the entire system. Additionally, the machinery needs to be computationally affordable. Although a great advancement has been made over the years, including some of the seminal works resulting in the 2013 Nobel Prize in chemistry, many aforementioned exciting applications remain far from reach. We review the methodology on the forefront of the field, including several promising methods developed in our lab that bring us closer to the desired modern goals. We further highlight their performance by a few examples of applications

Computational protein design as a cost function network optimization problem

Proteins are chains of simple molecules called amino acids. The three-dimensional shape of a protein and its amino acid composition define its biological function. Over millions of years, living organisms have evolved and produced a large catalog of proteins. By exploring the space of possible amino-acid sequences, protein engineering aims at similarly designing tailored proteins with specific desirable properties. In Computational Protein Design (CPD), the challenge of identifying a protein that performs a given task is defined as the combinatorial optimization problem of a complex energy function over amino acid sequences. In this paper, we introduce the CPD problem and some of the main approaches that have been used to solve it. We then show how this problem directly reduces to Cost Function Network (CFN) and 0/1LP optimization problems. We construct di erent real CPD instances to evaluate CFN and 0/1LP algorithms as implemented in the toulbar2 and cplex solvers. We observe that CFN algorithms bring important speedups compared to the CPD platform osprey but also to cplex

Engineered antibody Fc variants with enhanced effector function

Antibody-dependent cell-mediated cytotoxicity, a key effector function for the clinical efficacy of monoclonal antibodies, is mediated primarily through a set of closely related Fcγ receptors with both activating and inhibitory activities. By using computational design algorithms and high-throughput screening, we have engineered a series of Fc variants with optimized Fcγ receptor affinity and specificity. The designed variants display >2 orders of magnitude enhancement of in vitro effector function, enable efficacy against cells expressing low levels of target antigen, and result in increased cytotoxicity in an in vivo preclinical model. Our engineered Fc regions offer a means for improving the next generation of therapeutic antibodies and have the potential to broaden the diversity of antigens that can be targeted for antibody-based tumor therapy