Open Problems In Computational Biology Research Articles

Distilling identifiable and interpretable dynamic models from biological data.

Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam's razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable.

Characterizing Star-PCGs

A graph $G$ is called a pairwise compatibility graph (PCG, for short) if it admits a tuple $(T,w, d_{\min},d_{\max})$ of a tree $T$ whose leaf set is equal to the vertex set of $G$, a non-negative edge weight $w$, and two non-negative reals $d_{\min}\leq d_{\max}$ such that $G$ has an edge between two vertices $u,v\in V$ if and only if the distance between the two leaves $u$ and $v$ in the weighted tree $(T,w)$ is in the interval $[d_{\min}, d_{\max}]$. The tree $T$ is also called a witness tree of the PCG $G$. The problem of testing if a given graph is a PCG is not known to be NP-hard yet. To obtain a complete characterization of PCGs is a wide open problem in computational biology and graph theory. In literature, most witness trees admitted by known PCGs are stars and caterpillars. In this paper, we give a complete characterization for a graph to be a star-PCG (a PCG that admits a star as its witness tree), which provides us the first polynomial-time algorithm for recognizing star-PCGs.

Protein Sequence Alignment Analysis by Local Covariation: Coevolution Statistics Detect Benchmark Alignment Errors

The use of sequence alignments to understand protein families is ubiquitous in molecular biology. High quality alignments are difficult to build and protein alignment remains one of the largest open problems in computational biology. Misalignments can lead to inferential errors about protein structure, folding, function, phylogeny, and residue importance. Identifying alignment errors is difficult because alignments are built and validated on the same primary criteria: sequence conservation. Local covariation identifies systematic misalignments and is independent of conservation. We demonstrate an alignment curation tool, LoCo, that integrates local covariation scores with the Jalview alignment editor. Using LoCo, we illustrate how local covariation is capable of identifying alignment errors due to the reduction of positional independence in the region of misalignment. We highlight three alignments from the benchmark database, BAliBASE 3, that contain regions of high local covariation, and investigate the causes to illustrate these types of scenarios. Two alignments contain sequential and structural shifts that cause elevated local covariation. Realignment of these misaligned segments reduces local covariation; these alternative alignments are supported with structural evidence. We also show that local covariation identifies active site residues in a validated alignment of paralogous structures. Loco is available at https://sourceforge.net/projects/locoprotein/files/

Modeling Structures and Motions of Loops in Protein Molecules

Unlike the secondary structure elements that connect in protein structures, loop fragments in protein chains are often highly mobile even in generally stable proteins. The structural variability of loops is often at the center of a protein’s stability, folding, and even biological function. Loops are found to mediate important biological processes, such as signaling, protein-ligand binding, and protein-protein interactions. Modeling conformations of a loop under physiological conditions remains an open problem in computational biology. This article reviews computational research in loop modeling, highlighting progress and challenges. Important insight is obtained on potential directions for future research.

A hybrid approach to protein folding problem integrating constraint programming with local search

BackgroundThe protein folding problem remains one of the most challenging open problems in computational biology. Simplified models in terms of lattice structure and energy function have been proposed to ease the computational hardness of this optimization problem. Heuristic search algorithms and constraint programming are two common techniques to approach this problem. The present study introduces a novel hybrid approach to simulate the protein folding problem using constraint programming technique integrated within local search.ResultsUsing the face-centered-cubic lattice model and 20 amino acid pairwise interactions energy function for the protein folding problem, a constraint programming technique has been applied to generate the neighbourhood conformations that are to be used in generic local search procedure. Experiments have been conducted for a few small and medium sized proteins. Results have been compared with both pure constraint programming approach and local search using well-established local move set. Substantial improvements have been observed in terms of final energy values within acceptable runtime using the hybrid approach.ConclusionConstraint programming approaches usually provide optimal results but become slow as the problem size grows. Local search approaches are usually faster but do not guarantee optimal solutions and tend to stuck in local minima. The encouraging results obtained on the small proteins show that these two approaches can be combined efficiently to obtain better quality solutions within acceptable time. It also encourages future researchers on adopting hybrid techniques to solve other hard optimization problems.

Classification of co-expressed genes from DNA regulatory regions

The analysis of non-coding DNA regulatory regions is one of the most challenging open problems in computational biology. In this paper we investigate whether we can predict functional information about genes by using information extracted from their sequences together with expression data. We formalize this problem as a classification problem, and we apply Support Vector Machines (SVMs) with non-linear kernels to predict classes of co-expressed genes obtained from clustering procedures. SVMs are trained using information about selected motifs extracted from DNA regulatory regions through combinatorial and statistical methods. In our experiments, we show that functional classes of genes can be predicted from biological sequence data in Saccharomices cerevisiae, achieving results competitive with those recently presented in the literature.

Approximate protein folding in the HP side chain model on extended cubic lattices

One of the most important open problems in computational biology is the prediction of the conformation of a protein based on its amino acid sequence. In this paper, we design approximation algorithms for protein structure prediction in the so-called HP side chain model. The major drawback of the standard HP side chain model is the bipartiteness of the cubic lattice. To eliminate this drawback, we introduce the extended cubic lattice that extends the cubic lattice by diagonals in the plane. For this lattice, we present two linear algorithms with approximation ratios of 59/70 and 37/42, respectively. The second algorithm is designed for a ‘natural’ subclass of proteins, which covers more than 99.5% of all sequenced proteins. This is the first time that a protein structure prediction algorithm is designed for a ‘natural’ subclass of all combinatorial possible sequences.