Soft arc consistency revisited

Seven Amino Acid Types Suffice to Create the Core Fold of RNA Polymerase

The extant complex proteins must have evolved from ancient short and simple ancestors. The double-ψ β-barrel (DPBB) is one of the oldest protein folds and conserved in various fundamental enzymes, such as the core domain of RNA polymerase. Here, by reverse engineering a modern DPBB domain, we reconstructed its plausible evolutionary pathway started by "interlacing homodimerization" of a half-size peptide, followed by gene duplication and fusion. Furthermore, by simplifying the amino acid repertoire of the peptide, we successfully created the DPBB fold with only seven amino acid types (Ala, Asp, Glu, Gly, Lys, Arg, and Val), which can be coded by only GNN and ARR (R = A or G) codons in the modern translation system. Thus, the DPBB fold could have been materialized by the early translation system and genetic code.

Guaranteed Diversity and Optimality in Cost Function Network Based Computational Protein Design Methods

Proteins are the main active molecules of life. Although natural proteins play many roles, as enzymes or antibodies for example, there is a need to go beyond the repertoire of natural proteins to produce engineered proteins that precisely meet application requirements, in terms of function, stability, activity or other protein capacities. Computational Protein Design aims at designing new proteins from first principles, using full-atom molecular models. However, the size and complexity of proteins require approximations to make them amenable to energetic optimization queries. These approximations make the design process less reliable, and a provable optimal solution may fail. In practice, expensive libraries of solutions are therefore generated and tested. In this paper, we explore the idea of generating libraries of provably diverse low-energy solutions by extending cost function network algorithms with dedicated automaton-based diversity constraints on a large set of realistic full protein redesign problems. We observe that it is possible to generate provably diverse libraries in reasonable time and that the produced libraries do enhance the Native Sequence Recovery, a traditional measure of design methods reliability.

Development and applications of artificial symmetrical proteins

Since the determination of the first molecular models of proteins there has been interest in creating proteins artificially, but such methods have only become widely successful in the last decade. Gradual improvements over a long period of time have now yielded numerous examples of non-natural proteins, many of which are built from repeated elements. In this review we discuss the design of such symmetrical proteins and their various applications in chemistry and medicine.

Positive multistate protein design

Motivation

Structure-based computational protein design (CPD) plays a critical role in advancing the field of protein engineering. Using an all-atom energy function, CPD tries to identify amino acid sequences that fold into a target structure and ultimately perform a desired function. The usual approach considers a single rigid backbone as a target, which ignores backbone flexibility. Multistate design (MSD) allows instead to consider several backbone states simultaneously, defining challenging computational problems.

Results

We introduce efficient reductions of positive MSD problems to Cost Function Networks with two different fitness definitions and implement them in the Pompd (Positive Multistate Protein design) software. Pompd is able to identify guaranteed optimal sequences of positive multistate full protein redesign problems and exhaustively enumerate suboptimal sequences close to the MSD optimum. Applied to nuclear magnetic resonance and back-rubbed X-ray structures, we observe that the average energy fitness provides the best sequence recovery. Our method outperforms state-of-the-art guaranteed computational design approaches by orders of magnitudes and can solve MSD problems with sizes previously unreachable with guaranteed algorithms.

Availability and implementation

https://forgemia.inra.fr/thomas.schiex/pompd as documented Open Source.

Supplementary information

Supplementary data are available at Bioinformatics online.

Computational design of symmetrical eight-bladed β-propeller proteins

β-Propeller proteins form one of the largest families of protein structures, with a pseudo-symmetrical fold made up of subdomains called blades. They are not only abundant but are also involved in a wide variety of cellular processes, often by acting as a platform for the assembly of protein complexes. WD40 proteins are a subfamily of propeller proteins with no intrinsic enzymatic activity, but their stable, modular architecture and versatile surface have allowed evolution to adapt them to many vital roles. By computationally reverse-engineering the duplication, fusion and diversification events in the evolutionary history of a WD40 protein, a perfectly symmetrical homologue called Tako8 was made. If two or four blades of Tako8 are expressed as single polypeptides, they do not self-assemble to complete the eight-bladed architecture, which may be owing to the closely spaced negative charges inside the ring. A different computational approach was employed to redesign Tako8 to create Ika8, a fourfold-symmetrical protein in which neighbouring blades carry compensating charges. Ika2 and Ika4, carrying two or four blades per subunit, respectively, were found to assemble spontaneously into a complete eight-bladed ring in solution. These artificial eight-bladed rings may find applications in bionanotechnology and as models to study the folding and evolution of WD40 proteins.

Maximum Persistency via Iterative Relaxed Inference in Graphical Models

We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some labels of the considered graphical model either as (i) optimal, meaning that they belong to all optimal solutions of the inference problem; (ii) non-optimal if they provably do not belong to any solution. With access to an exact solver of a linear programming relaxation to the MAP-inference problem, our algorithm marks the maximal possible (in a specified sense) number of labels. We also present a version of the algorithm, which has access to a suboptimal dual solver only and still can ensure the (non-)optimality for the marked labels, although the overall number of the marked labels may decrease. We propose an efficient implementation, which runs in time comparable to a single run of a suboptimal dual solver. Our method is well-scalable and shows state-of-the-art results on computational benchmarks from machine learning and computer vision.

Marginal Consistency: Upper-Bounding Partition Functions over Commutative Semirings

Many inference tasks in pattern recognition and artificial intelligence lead to partition functions in which addition and multiplication are abstract binary operations forming a commutative semiring. By generalizing max-sum diffusion (one of convergent message passing algorithms for approximate MAP inference in graphical models), we propose an iterative algorithm to upper bound such partition functions over commutative semirings. The iteration of the algorithm is remarkably simple: change any two factors of the partition function such that their product remains the same and their overlapping marginals become equal. In many commutative semirings, repeating this iteration for different pairs of factors converges to a fixed point when the overlapping marginals of every pair of factors coincide. We call this state marginal consistency. During that, an upper bound on the partition function monotonically decreases. This abstract algorithm unifies several existing algorithms, including max-sum diffusion and basic constraint propagation (or local consistency) algorithms in constraint programming. We further construct a hierarchy of marginal consistencies of increasingly higher levels and show than any such level can be enforced by adding identity factors of higher arity (order). Finally, we discuss instances of the framework for several semirings, including the distributive lattice and the max-sum and sum-product semirings.

Universality of the Local Marginal Polytope

We show that solving the LP relaxation of the min-sum labeling problem (also known as MAP inference problem in graphical models, discrete energy minimization, or valued constraint satisfaction) is not easier than solving any linear program. Precisely, every polytope is linear-time representable by a local marginal polytope and every LP can be reduced in linear time to a linear optimization (allowing infinite costs) over a local marginal polytope. The reduction can be done (though with a higher time complexity) even if the local marginal polytope is restricted to have a planar structure.