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Biochemical reaction systems in a cell exhibit stochastic behaviour, owing to the unpredictable nature of the molecular interactions. The fluctuations at the molecular level may lead to a different behaviour than that predicted by the deterministic model of the reaction rate equations, when some reacting species have low population numbers. As a result, stochastic models are vital to accurately describe system dynamics. Sensitivity analysis is an important method for studying the influence of the variations in various parameters on the output of a biochemical model. We propose a finite-difference strategy for approximating second-order parametric sensitivities for stochastic discrete models of biochemically reacting systems. This strategy utilizes adaptive tau-leaping schemes and coupling of the perturbed and nominal processes for an efficient sensitivity estimation. The advantages of the new technique are demonstrated through its application to several biochemical system models with practical significance. [ABSTRACT FROM AUTHOR]

Sequence similarity is of paramount importance in biology, as similar sequences tend to have similar function and share common ancestry. Scoring matrices, such as PAM or BLOSUM, play a crucial role in all bioinformatics algorithms for identifying similarities, but have the drawback that they are fixed, independent of context. We propose a new scoring method for amino acid similarity that remedies this weakness, being contextually dependent. It relies on recent advances in deep learning architectures that employ self-supervised learning in order to leverage the power of enormous amounts of unlabelled data to generate contextual embeddings, which are vector representations for words. These ideas have been applied to protein sequences, producing embedding vectors for protein residues. We propose the E-score between two residues as the cosine similarity between their embedding vector representations. Thorough testing on a wide variety of reference multiple sequence alignments indicate that the alignments produced using the new |$E$| -score method, especially ProtT5-score, are significantly better than those obtained using BLOSUM matrices. The new method proposes to change the way alignments are computed, with far-reaching implications in all areas of textual data that use sequence similarity. The program to compute alignments based on various |$E$| -scores is available as a web server at e-score.csd.uwo.ca. The source code is freely available for download from github.com/lucian-ilie/E-score. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Abstract Background The most frequently used tools in bioinformatics are those searching for similarities, or local alignments, between biological sequences. Since the exact dynamic programming algorithm is quadratic, linear-time heuristics such as BLAST are used. Spaced seeds are much more sensitive than the consecutive seed of BLAST and using several seeds represents the current state of the art in approximate search for biological sequences. The most important aspect is computing highly sensitive seeds. Since the problem seems hard, heuristic algorithms are used. The leading software in the common Bernoulli model is the SpEED program. Findings SpEED uses a hill climbing method based on the overlap complexity heuristic. We propose a new algorithm for this heuristic that improves its speed by over one order of magnitude. We use the new implementation to compute improved seeds for several software programs. We compute as well multiple seeds of the same weight as MegaBLAST, that greatly improve its sensitivity. Conclusion Multiple spaced seeds are being successfully used in bioinformatics software programs. Enabling researchers to compute very fast high quality seeds will help expanding the range of their applications.

Abstract Background DNA oligonucleotides are a very useful tool in biology. The best algorithms for designing good DNA oligonucleotides are filtering out unsuitable regions using a seeding approach. Determining the quality of the seeds is crucial for the performance of these algorithms. Results We present a sound framework for evaluating the quality of seeds for oligonucleotide design. The F - score is used to measure the accuracy of each seed. A number of natural candidates are tested: contiguous (BLAST-like), spaced, transitions-constrained, and multiple spaced seeds. Multiple spaced seeds are the best, with more seeds providing better accuracy. Single spaced and transition seeds are very close whereas, as expected, contiguous seeds come last. Increased accuracy comes at the price of reduced efficiency. An exception is that single spaced and transitions-constrained seeds are both more accurate and more efficient than contiguous ones. Conclusions Our work confirms another application where multiple spaced seeds perform the best. It will be useful in improving the algorithms for oligonucleotide design.

Stochastic modeling is essential for an accurate description of the biochemical network dynamics at the level of a single cell. Biochemically reacting systems often evolve on multiple time-scales, thus their stochastic mathematical models manifest stiffness. Stochastic models which, in addition, are stiff and computationally very challenging, therefore the need for developing effective and accurate numerical methods for approximating their solution. An important stochastic model of well-stirred biochemical systems is the chemical Langevin Equation. The chemical Langevin equation is a system of stochastic differential equation with multidimensional non-commutative noise. This model is valid in the regime of large molecular populations, far from the thermodynamic limit. In this paper, we propose a variable time-stepping strategy for the numerical solution of a general chemical Langevin equation, which applies for any level of randomness in the system. Our variable stepsize method allows arbitrary values of the time-step. Numerical results on several models arising in applications show significant improvement in accuracy and efficiency of the proposed adaptive scheme over the existing methods, the strategies based on halving/doubling of the stepsize and the fixed step-size ones. [ABSTRACT FROM AUTHOR]

Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes. [ABSTRACT FROM AUTHOR]