Solving weighted CSP by maintaining arc consistency

iCFN: an efficient exact algorithm for multistate protein design

Motivation

Multistate protein design addresses real-world challenges, such as multi-specificity design and backbone flexibility, by considering both positive and negative protein states with an ensemble of substates for each. It also presents an enormous challenge to exact algorithms that guarantee the optimal solutions and enable a direct test of mechanistic hypotheses behind models. However, efficient exact algorithms are lacking for multistate protein design.

Results

We have developed an efficient exact algorithm called interconnected cost function networks (iCFN) for multistate protein design. Its generic formulation allows for a wide array of applications such as stability, affinity and specificity designs while addressing concerns such as global flexibility of protein backbones. iCFN treats each substate design as a weighted constraint satisfaction problem (WCSP) modeled through a CFN; and it solves the coupled WCSPs using novel bounds and a depth-first branch-and-bound search over a tree structure of sequences, substates, and conformations. When iCFN is applied to specificity design of a T-cell receptor, a problem of unprecedented size to exact methods, it drastically reduces search space and running time to make the problem tractable. Moreover, iCFN generates experimentally-agreeing receptor designs with improved accuracy compared with state-of-the-art methods, highlights the importance of modeling backbone flexibility in protein design, and reveals molecular mechanisms underlying binding specificity.

Availability and implementation

https://shen-lab.github.io/software/iCFN.

Supplementary information

Supplementary data are available at Bioinformatics online.

Deterministic Search Methods for Computational Protein Design

One main challenge in Computational Protein Design (CPD) lies in the exploration of the amino-acid sequence space, while considering, to some extent, side chain flexibility. The exorbitant size of the search space urges for the development of efficient exact deterministic search methods enabling identification of low-energy sequence-conformation models, corresponding either to the global minimum energy conformation (GMEC) or an ensemble of guaranteed near-optimal solutions. In contrast to stochastic local search methods that are not guaranteed to find the GMEC, exact deterministic approaches always identify the GMEC and prove its optimality in finite but exponential worst-case time. After a brief overview on these two classes of methods, we discuss the grounds and merits of four deterministic methods that have been applied to solve CPD problems. These approaches are based either on the Dead-End-Elimination theorem combined with A* algorithm (DEE/A*), on Cost Function Networks algorithms (CFN), on Integer Linear Programming solvers (ILP) or on Markov Random Fields solvers (MRF). The way two of these methods (DEE/A* and CFN) can be used in practice to identify low-energy sequence-conformation models starting from a pairwise decomposed energy matrix is detailed in this review.

Fast search algorithms for computational protein design

One of the main challenges in computational protein design (CPD) is the huge size of the protein sequence and conformational space that has to be computationally explored. Recently, we showed that state-of-the-art combinatorial optimization technologies based on Cost Function Network (CFN) processing allow speeding up provable rigid backbone protein design methods by several orders of magnitudes. Building up on this, we improved and injected CFN technology into the well-established CPD package Osprey to allow all Osprey CPD algorithms to benefit from associated speedups. Because Osprey fundamentally relies on the ability of A* to produce conformations in increasing order of energy, we defined new A* strategies combining CFN lower bounds, with new side-chain positioning-based branching scheme. Beyond the speedups obtained in the new A*-CFN combination, this novel branching scheme enables a much faster enumeration of suboptimal sequences, far beyond what is reachable without it. Together with the immediate and important speedups provided by CFN technology, these developments directly benefit to all the algorithms that previously relied on the DEE/ A* combination inside Osprey* and make it possible to solve larger CPD problems with provable algorithms.

Fast gap-free enumeration of conformations and sequences for protein design

Despite significant successes in structure-based computational protein design in recent years, protein design algorithms must be improved to increase the biological accuracy of new designs. Protein design algorithms search through an exponential number of protein conformations, protein ensembles, and amino acid sequences in an attempt to find globally optimal structures with a desired biological function. To improve the biological accuracy of protein designs, it is necessary to increase both the amount of protein flexibility allowed during the search and the overall size of the design, while guaranteeing that the lowest-energy structures and sequences are found. DEE/A*-based algorithms are the most prevalent provable algorithms in the field of protein design and can provably enumerate a gap-free list of low-energy protein conformations, which is necessary for ensemble-based algorithms that predict protein binding. We present two classes of algorithmic improvements to the A* algorithm that greatly increase the efficiency of A*. First, we analyze the effect of ordering the expansion of mutable residue positions within the A* tree and present a dynamic residue ordering that reduces the number of A* nodes that must be visited during the search. Second, we propose new methods to improve the conformational bounds used to estimate the energies of partial conformations during the A* search. The residue ordering techniques and improved bounds can be combined for additional increases in A* efficiency. Our enhancements enable all A*-based methods to more fully search protein conformation space, which will ultimately improve the accuracy of complex biomedically relevant designs.

SUBMODULARITY-BASED DECOMPOSING FOR VALUED CSP

Many combinatorial problems can be formulated as Valued Constraint Satisfaction Problems (VCSPs). In this framework, the constraints are defined by means of valuation functions to reflect several degrees of coherence. Despite the NP-hardness of the VCSP, tractable versions can be obtained by forcing the allowable valuation functions to have specific features. This is the case for submodular VCSPs, i.e. VCSPs that involve submodular valuation functions only.

In this paper, we propose a problem decomposition scheme for binary VCSPs that takes advantage of submodular functions even when the studied problem is not submodular. The proposed scheme consists in decomposing the problem to be solved into a set of submodular, then tractable, subproblems. The decomposition scheme combines two techniques that where already used in the framework of constraint-based reasoning, but in separate manner. These techniques are domain partitioning and value permutation.

Searching RNA motifs and their intermolecular contacts with constraint networks

MOTIVATION

Searching RNA gene occurrences in genomic sequences is a task whose importance has been renewed by the recent discovery of numerous functional RNA, often interacting with other ligands. Even if several programs exist for RNA motif search, none exists that can represent and solve the problem of searching for occurrences of RNA motifs in interaction with other molecules.

RESULTS

We present a constraint network formulation of this problem. RNA are represented as structured motifs that can occur on more than one sequence and which are related together by possible hybridization. The implemented tool MilPat is used to search for several sRNA families in genomic sequences. Results show that MilPat allows to efficiently search for interacting motifs in large genomic sequences and offers a simple and extensible framework to solve such problems. New and known sRNA are identified as H/ACA candidates in Methanocaldococcus jannaschii.

AVAILABILITY

http://carlit.toulouse.inra.fr/MilPaT/MilPat.pl.