J. Miguel Rubi

Heat transfer in protein-water interfaces.

We investigate using transient non-equilibrum molecular dynamics simulation the temperature relaxation process of three structurally different proteins in water, namely; myoglobin, green fluorescence protein (GFP) and two conformations of the Ca(2+)-ATPase protein. By modeling the temperature relaxation process using the solution of the heat diffusion equation we compute the thermal conductivity and thermal diffusivity of the proteins, as well as the thermal conductance of the protein-water interface. Our results indicate that the temperature relaxation of the protein can be described using a macroscopic approach. The protein-water interface has a thermal conductance of the order of 100-270 MW K(-1) m(-2), characteristic of water-hydrophilic interfaces. The thermal conductivity of the proteins is of the order of 0.1-0.2 W K(-1) m(-1) as compared with approximately 0.6 W K(-1) m(-1) for water, suggesting that these proteins can develop temperature gradients within the biomolecular structures that are larger than those of aqueous solutions. We find that the thermal diffusivity of the transmembrane protein, Ca(2+)-ATPase is about three times larger than that of myoglobin or GFP. Our simulation shows that the Kapitza length of these structurally different proteins is of the order of 1 nm, showing that the protein-water interface should play a major role in defining the thermal relaxation of biomolecules.

Inferring the in vivo looping properties of DNA

The free energy of looping DNA by proteins and protein complexes determines to what extent distal DNA sites can affect each other. We inferred its in vivo value through a combined computational-experimental approach for different lengths of the loop and found that, in addition to the intrinsic periodicity of the DNA double helix, the free energy has an oscillatory component of about half the helical period. Moreover, the oscillations have such an amplitude that the effects of regulatory molecules become strongly dependent on their precise DNA positioning and yet easily tunable by their cooperative interactions. These unexpected results can confer to the physical properties of DNA a more prominent role at shaping the properties of gene regulation than previously thought.

Failure of the Work-Hamiltonian Connection for Free-Energy Calculations

Extensions of statistical mechanics are routinely being used to infer free energies from the work performed over single-molecule nonequilibrium trajectories. A key element of this approach is the ubiquitous expression dW/dt=partial differentialH(x,t)/partial differentialt, which connects the microscopic work W performed by a time-dependent force on the coordinate x with the corresponding Hamiltonian H(x,t) at time t. Here we show that this connection, as pivotal as it is, cannot be used to estimate free-energy changes. We discuss the implications of this result for single-molecule experiments and atomistic molecular simulations and point out possible avenues to overcome these limitations.

Energy dissipation in slipping biological pumps

We describe active transport in slipping biological pumps, using mesoscopic nonequilibrium thermodynamics. The pump operation is characterised by its stochastic nature and energy dissipation. We show how heating as well as cooling effects can be associated with pump operation. We use as an example the well studied active transport of Ca2+ across a biological membrane by means of its ATPase, and use published data to find values for the transport coefficients of the pump under various conditions. Most of the transport coefficients of the pump, including those that relate ATP hydrolysis or synthesis to thermal effects, are estimated. This can give a quantitative description of thermogenesis. We show by calculation that all of these coupling coefficients are significant.

Confined Brownian ratchets

We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situations where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phenomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.

Khinchin theorem and anomalous diffusion.

A recent Letter [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, (Dover, New York, 1949)] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a generalized Langevin equation the Khinchin theorem holds.

Entropic transport in confined media: a challenge for computational studies in biological and soft-matter systems

Transport in small-scale biological and soft-matter systems typically occurs under confinement conditions in which particles proceed through obstacles and irregularities of the boundaries that may significantly alter their trajectories. A transport model that assimilates the confinement to the presence of entropic barriers provides an efficient approach to quantify its effect on the particle current and the diffusion coefficient. We review the main peculiarities of entropic transport and treat two cases in which confinement effects play a crucial role, with the appearance of emergent properties. The presence of entropic barriers modifies the mean first-passage time distribution and therefore plays a very important role in ion transport through micro- and nano-channels. The functionality of molecular motors, modeled as Brownian ratchets, is strongly affected when the motor proceeds in a confined medium that may constitute another source of rectification. The interplay between ratchet and entropic rectification gives rise to a wide variety of dynamical behaviors, not observed when the Brownian motor proceeds in an unbounded medium. Entropic transport offers new venues of transport control and particle manipulation and new ways to engineer more efficient devices for transport at the nanoscale.

Some conceptual thoughts toward nanoscale oriented friction in a model of articular cartilage.

This work presents a conceptual framework as to how a deficit in the synovial-fluid content, exemplified by hyaluronan or any other amphiphilic species, is capable of decisively altering the complex lubrication and wear conditions observed clinically in articular cartilage. The effect is revealed in (non)stationary regimes if the cartilage is subjected to some normal periodic load, revealing over its exploitation time increasingly dissipative, in general entropy-addressing, characteristics. It can be hypothesized that a Grotthuss-type proton transport physiology-concerning mechanism in channel-like, phospholipid-water cartilages articulating nanospaces will be responsible for the expression of the lubrication mode. The corresponding wear involving overall change is then manifested adequately in the stationary regime, and in a viable system-parametric correlation with its lubrication counterpart. Certain analytic formulae for the nanoscale oriented coefficient of friction, involving generically H-bonds breaking mechanism, and pointing to some local-viscosity context, have been proposed for fitting the experimental data and clinical observations involving proton management at articular cartilage surfaces.

Heat exchange between two interacting nanoparticles beyond the fluctuation-dissipation regime.

We show that the observed nonmonotonic behavior of the thermal conductance between two nanoparticles when they are brought into contact is originated by an intricate phase space dynamics. Here it is assumed that this dynamics results from the thermally activated jumping through a rough energy landscape. A hierarchy of relaxation times plays the key role in the description of this complex phase space behavior. Our theory enables us to analyze the heat transfer just before and at the moment of contact.

Energy Transduction in Biological Systems: A Mesoscopic Non-Equilibrium Thermodynamics Perspective

Abstract We review recent efforts aimed at analyzing energy transduction processes in biological systems from the perspective of mesoscopic non-equilibrium thermodynamics. The inherent nonlinear nature of many of these systems, which undergo activated processes, has over the years impeded the use of classical non-equilibrium thermodynamics for their description, because this theory accounts only for the linear regime of these processes. The diffculty of putting non-equilibrium thermodynamics methods into a broader scope has recently been overcome. It has been shown that if one assumes local equilibrium at short time and length scales, in the mesoscale domain, the limitation of only providing linear laws can be removed and Arrhenius type nonlinear laws can be derived. The new theory proposed here provides a scenario under which transformations taking place in chemical and biological processes can be studied. We show in this paper how the theory can be applied to describe energy conversion processes in molecular motors and pumps and conclude that both systems can be studied by means of this common framework.