Tractability-preserving transformations of global cost functions

Infrared: a declarative tree decomposition-powered framework for bioinformatics

MOTIVATION

Many bioinformatics problems can be approached as optimization or controlled sampling tasks, and solved exactly and efficiently using Dynamic Programming (DP). However, such exact methods are typically tailored towards specific settings, complex to develop, and hard to implement and adapt to problem variations.

METHODS

We introduce the Infrared framework to overcome such hindrances for a large class of problems. Its underlying paradigm is tailored toward problems that can be declaratively formalized as sparse feature networks, a generalization of constraint networks. Classic Boolean constraints specify a search space, consisting of putative solutions whose evaluation is performed through a combination of features. Problems are then solved using generic cluster tree elimination algorithms over a tree decomposition of the feature network. Their overall complexities are linear on the number of variables, and only exponential in the treewidth of the feature network. For sparse feature networks, associated with low to moderate treewidths, these algorithms allow to find optimal solutions, or generate controlled samples, with practical empirical efficiency.

RESULTS

Implementing these methods, the Infrared software allows Python programmers to rapidly develop exact optimization and sampling applications based on a tree decomposition-based efficient processing. Instead of directly coding specialized algorithms, problems are declaratively modeled as sets of variables over finite domains, whose dependencies are captured by constraints and functions. Such models are then automatically solved by generic DP algorithms. To illustrate the applicability of Infrared in bioinformatics and guide new users, we model and discuss variants of bioinformatics applications. We provide reimplementations and extensions of methods for RNA design, RNA sequence-structure alignment, parsimony-driven inference of ancestral traits in phylogenetic trees/networks, and design of coding sequences. Moreover, we demonstrate multidimensional Boltzmann sampling. These applications of the framework-together with our novel results-underline the practical relevance of Infrared. Remarkably, the achieved complexities are typically equivalent to the ones of specialized algorithms and implementations.

AVAILABILITY

Infrared is available at https://amibio.gitlabpages.inria.fr/Infrared with extensive documentation, including various usage examples and API reference; it can be installed using Conda or from source.

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.

MPE Computation in Bayesian Networks Using Mini-Bucket and Probability Trees Approximation

Given a set of uncertain discrete variables with a joint probability distribution and a set of observations for some of them, the most probable explanation is a set or configuration of values for non-observed variables maximizing the conditional probability of these variables given the observations. This is a hard problem which can be solved by a deletion algorithm with max marginalization, having a complexity similar to the one of computing conditional probabilities. When this approach is unfeasible, an alternative is to carry out an approximate deletion algorithm, which can be used to guide the search of the most probable explanation, by using A* or branch and bound (the approximate+search approach). The most common approximation procedure has been the mini-bucket approach. In this paper it is shown that the use of probability trees as representation of potentials with a pruning of branches with similar values can improve the performance of this procedure. This is corroborated with an experimental study in which computation times are compared using randomly generated and benchmark Bayesian networks from UAI competitions.