Abstract
In this work, we consider a microfluidic mixer that uses hydrodynamic diffusion stream to induce the beginning of the folding process of a certain protein. To perform these molecular changes, the concentration of the denaturant, which is introduced into the mixer together with the protein, has to be diminished until a given value in a short period of time, known as mixing time. In this context, this article is devoted to optimize the design of the mixer, focusing on its shape and its flow parameters with the aim of minimizing its mixing time. First, we describe the involved physical phenomena through a mathematical model that allows us to obtain the mixing time for a considered device. Then, we formulate an optimization problem considering the mixing time as the objective function and detailing the design parameters related to the shape and the flow of the mixer. For dealing with this problem, we propose an enhanced optimization algorithm based on the hybridization of two techniques: a genetic algorithm as a core method and a multi-layer line search methodology based on the secant, which aims to improve the initialization of the core method. More precisely, in our hybrid approach, the core optimization is implemented as a sub-problem to be solved at each iteration of the multi-layer algorithm starting from the initial conditions that it provides. Before applying it to the mixer design problem, we validate this methodology by considering a set of benchmark problems and, then, compare its results to those obtained with other classical global optimization methods. As shown in the comparison, for the majority of those problems, our methodology needs fewer evaluations of the objective function, has higher success rates and is more accurate than the other considered algorithms. For those reasons, it has been selected for solving the computationally expensive problem of optimizing the mixer design. The obtained optimized device shows a great reduction in its mixing time with respect to the state-of-the-art mixers.
Highlights
Proteins are bio-molecules composed of one or more long chains of amino acids
That particular list of benchmark problems is considered as a good enough representation of low dimensional optimization problems (i.e., ≈10 variables) because it illustrates a wide and diverse set of difficulties that can be found in real problems [19, 36]
When the Genetic Multi-Layer Algorithm (GMA) ends, its solution is improved by performing 10 iterations of the Steepest Descent (SD) algorithm, in which the descent step size ρ is determined using 10 iterations of a dichotomy method starting from ρ0 = 1
Summary
Proteins are bio-molecules composed of one or more long chains of amino acids. Protein folding refers to the processes by which these amino acids interact with each other and produce a well-defined three-dimensional structure, called folded protein, able to performIvorra et al Journal of Mathematics in Industry (2018) 8:4a wide range of biological functions [1]. Protein folding can be initiated, for instance, by inducing changes in chemical potential (e.g. changes in the concentration of a chemical specie). This kind of micromixer enables a fast and effective laminar mixing of unfolding proteins and a chemical denaturant, favoring the folding process. The objective is to rapidly decrease the denaturant concentration to initiate protein folding in the outlet channel. Since the publication of Brody et al, various researchers have aimed to improve the micromixer performances [3,4,5], either by reducing the consumption rate of reactants or by minimizing the so called mixing time, i.e. the time required to attain a desired denaturant concentration The primary mixer of Brody et al [2] exhibited mixing times larger than 10 μs, while Hertzog et al [3] reported mixing times of 1.2 μs
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