Mathematical description of protein extraction from muscle tissue of hydrobionts and determination of the effective molecular diffusion coefficient

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Elena E. Kuprina
Elena A. Rogozina
Valeria Valerevna Abramzon
Pavel Igorevich Demidov
E.I. Kiprushkina
Irina Anatolievna Shestopalova
Julia Vladimirovna Broyko
Mark Markovich Shamtsyan
B.A. Kolesnikov


mathematical description, mathematical modeling, molecular diffusion coefficient, protein extraction, waste recycling


The purpose of this work is to obtain an array of experimental data, kinetic dependences of the protein extracting from the particles of dispersed muscle tissue of hydrobionts (Alaska pollack), its mathematical description, and to find the molecular diffusion coefficients of proteins in the system of equations using solving the inverse problem of the modeling. This work’s novelty is to study swelling and protein extraction from animal tissue and its mathematical description. This study has established that the diffusion of proteins from the muscle tissue of hydrobionts during stirring suspension (raw material-extractant) occurs at a significantly higher rate than diffusion from raw materials of plant origin. It indicates the contribution of a convective component to the swelling process and dissolution of particles due to intensive blending and easy differentiability of muscular tissue particles of hydrobionts. Based on the solution of the mathematical model, the molecular diffusion coefficient of proteins from raw materials of animal origin (muscle tissue of hydrobionts) (3÷8)×10−9 m2/s, which exceeds the diffusion coefficients of carbohydrates from raw materials of plant origin (e.g., sugar 0.3×10−9 m2/s) by more than an order of magnitude. Researchers can use the obtained molecular diffusion coefficient to calculate the parameters of the diffusion process of proteins during its extraction from dispersed particles of hydrobionts.

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