Math Biology Seminar: Mattia Bacca

We propose a mathematical model based on non-equilibrium thermodynamics to describe the mechanical behavior of an active polymer gel created by the inclusion of molecular motors in its solvent. When activated, these motors attach to the chains of the polymer network and shorten them creating a global contraction of the gel, which mimics the active behavior of a cytoskeleton. The power generated by these motors is obtained by ATP hydrolysis reaction, which transduces chemical energy into mechanical work. The model is based on the Flory and Rehner theory for polymer network swelling and considers species diffusion to describe the transient passive behavior of the gel. The active behavior is modeled defining a volumetric density of mechanical power generated by the motors, through ATP hydrolysis, which increases the strain energy of the polymer network. The latter is depicted by an increment of the crosslink density in the polymer network, reducing the entropy of the polymer network. The model is finally adapted to the problem of uniaxial contraction of a slab of gel and compared with experimental results, showing good agreement.