Energy dissipation in biomolecular machines

Abstract

The operation of a molecular pump, the calcium pump of sarcoplasmic reticulum is studied using mesoscopic non-equilibrium thermodynamics and molecular dynamics. The mesoscopic non-equilibrium thermodynamic description of the pump is compared to the description obtained in the framework of Hill for kinetic enzyme cycles. By comparing these two descriptions at isothermal conditions, they are found to be equivalent. This supports the validity of the mesoscopic approach. An extension of the mesoscopic non-equilibrium framework to also include a heat flux and the corresponding temperature difference is proposed. This can be used to model phenomena such as non-shivering thermogenesis, a process which lack a theoretical description in the kinetic cycle picture. Further, the heat transfer in the calcium pump is studied using molecular dynamics. This is done in order to obtain phenomenological parameters that can be used for the modeling of thermogenesis. A non-stationary non-equilibrium molecular dynamics approach is developed, which may be used to study heat transfer between a small object and the surrounding solvent. This methodology is applied to the calcium pump solvated in water. It is found that the thermal conductivity of the protein is low (0.2 W K−1 m−1) compared to water (0.6 WK−1 m−1). This means that the protein may sustain a large temperature gradient across its structure. The simulations also show that the protein-water surface is important for the heat transfer. The time scale for vibrational energy relaxation is found to be of order 10–100 ps which strengthens the local equilibrium assumption of mesoscopic non-equilibrium thermodynamics. Mesoscopic non-equilibrium thermodynamics is also applied to calculate the thermodynamic efficiency of the calcium pump embedded in lipid bilayers of varying length and from different tissues. This is done in order to show the applicability of mesoscopic non-equilibrium thermodynamics to interpret experimental data. The thermodynamic efficiency is found to be low (< 13 %) in all cases for the experimental conditions considered, which means that a large amount of the energy released from the ATP-hydrolysis is dissipated as heat. A complementary molecular dynamics study targeted on a bilayer for which the protein shows a relatively large efficiency (compared to other bilayers) shows that membrane deformation and large efficiency are not mutually exclusive. Overall, this thesis highlights the usefulness of the mesoscopic non-equilibrium thermodynamic framework applied to molecular machines and energy transduction and dissipation in these. The main result is that the mesoscopic nonequilibrium thermodynamic framework is applicable to molecular pumps and can be extended to include heat effects. This framework is general and can be applied to other molecular machines as well. Further, the results also support the notion that the calcium pump may contribute to non-shivering thermogenesis in certain tissues.