Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment.

In the absence of input energy, a chemical reaction in a closed system ineluctably relaxes toward an equilibrium state governed by a Boltzmann distribution. The addition of a catalyst to the system provides a way for more rapid equilibration toward this distribution, but the catalyst can never, in and of itself, drive the system away from equilibrium. In the presence of external fluctuations, however, a macromolecular catalyst (e.g., an enzyme) can absorb energy and drive the formation of a steady state between reactant and product that is not determined solely by their relative energies. Due to the ubiquity of non-equilibrium steady states in living systems, the development of a theory for the effects of external fluctuations on chemical systems has been a longstanding focus of non-equilibrium thermodynamics. The theory of stochastic pumping has provided insight into how a non-equilibrium steady-state can be formed and maintained in the presence of dissipation and kinetic asymmetry. This effort has been greatly enhanced by a confluence of experimental and theoretical work on synthetic molecular machines designed explicitly to harness external energy to drive non-equilibrium transport and self-assembly.

How molecular motors work - insights from the molecular machinist's toolbox: the Nobel prize in Chemistry 2016.

The Nobel prize in Chemistry for 2016 was awarded to Jean Pierre Sauvage, Sir James Fraser Stoddart, and Bernard (Ben) Feringa for their contributions to the design and synthesis of molecular machines. While this field is still in its infancy, and at present there are no commercial applications, many observers have stressed the tremendous potential of molecular machines to revolutionize technology. However, perhaps the most important result so far accruing from the synthesis of molecular machines is the insight provided into the fundamental mechanisms by which molecular motors, including biological motors such as kinesin, myosin, FoF1 ATPase, and the flagellar motor, function. The ability to "tinker" with separate components of molecular motors allows asking, and answering, specific questions about mechanism, particularly with regard to light driven vs. chemistry driven molecular motors.

Optical vs. chemical driving for molecular machines.

Molecular machines use external energy to drive transport, to do mechanical, osmotic, or electrical work on the environment, and to form structure. In this paper the fundamental difference between the design principles necessary for a molecular machine to use light or external modulation of thermodynamic parameters as an energy source vs. the design principle for using an exergonic chemical reaction as a fuel will be explored. The key difference is that for catalytically-driven motors microscopic reversibility must hold arbitrarily far from equilibrium. Applying the constraints of microscopic reversibility assures that a coarse grained model is consistent with an underlying model for motion on a single time-independent potential energy surface. In contrast, light-driven processes, and processes driven by external modulation of the thermodynamic parameters of a system cannot in general be described in terms of motion on a single time-independent potential energy surface, and the rate constants are not constrained by microscopic reversibility. The results presented here call into question the value of the so-called power stroke model as an explanation of the function of autonomous chemically-driven molecular machines such as are commonly found in biology.

Asymmetric pore distribution and loss of membrane lipid in electroporated DOPC vesicles.

An externally applied electric field across vesicles leads to transient perforation of the membrane. The distribution and lifetime of these pores was examined using 1,2-di-oleoyl-sn-glycero-3-phosphocholine (DOPC) phospholipid vesicles using a standard fluorescent microscope. The vesicle membrane was stained with a fluorescent membrane dye, and upon field application, a single membrane pore as large as approximately 7 microm in diameter was observed at the vesicle membrane facing the negative electrode. At the anode-facing hemisphere, large and visible pores are seldom found, but formation of many small pores is implicated by the data. Analysis of pre- and post-field fluorescent vesicle images, as well as images from negatively stained electron micrographs, indicate that pore formation is associated with a partial loss of the phospholipid bilayer from the vesicle membrane. Up to approximately 14% of the membrane surface could be lost due to pore formation. Interestingly, despite a clear difference in the size distribution of the pores observed, the effective porous areas at both hemispheres was approximately equal. Ca(2+) influx measurements into perforated vesicles further showed that pores are essentially resealed within approximately 165 ms after the pulse. The pore distribution found in this study is in line with an earlier hypothesis (E. Tekle, R. D. Astumian, and P. B. Chock, 1994, Proc. Natl. Acad. Sci. U.S.A. 91:11512--11516) of asymmetric pore distribution based on selective transport of various fluorescent markers across electroporated membranes.

Towards a chemically driven molecular electron pump.

Charge can be pumped through a tiny gated portal from a reservoir at low electrochemical potential to one at the same or higher electrochemical potential by cyclically modulating the portal and gate energies. A theoretically and experimentally well established mechanism is Thouless adiabatic pumping, achieved by a precisely timed out-of-phase modulation of at least two parameters of the system. Here we show that stochastic modulation between two configurations of gate and portal energies can drive efficient pumping by a different, nonadiabatic, mechanism that may provide a basis for chemically driven electron pumping through a molecular wire.

Nonlinearly coupled flows.

We study energy flows that are coupled at a higher than linear order. A number of examples are presented where a force brings about a flow in the perpendicular direction. In some cases the symmetry of the system is such that coupling can only take place at even orders. We apply the theory to recently proposed two-dimensional devices that separate colloidal particles by ratcheting the different particles in different directions.

Surfactant sealing of membranes permeabilized by ionizing radiation.

Acute tissue injury and subsequent inflammation, including tissue edema and erythema, can be caused by sufficiently high levels of exposure to gamma radiation. The mechanism of this tissue injury is related to the generation of reactive oxygen intermediates (ROI) which chemically alter biological molecules and cell physiology. Cell membrane lipids are vulnerable to ROI-mediated lipid peroxidation that then leads to many of the acute tissue effects. We hypothesize that increased cell membrane permeability leading to osmotic swelling and vascular transudation is one of these effects. Thus we used adult postmitotic rhabdomyocytes in culture and microscopic fluorescence techniques to quantify radiation-induced changes in cell membrane permeability. Based on time-resolved dye flux measurements, a characteristic lag time of 34 +/- 3 min was determined between exposure to 160 Gy of gamma radiation and the decrease in membrane permeability. Administration of 0.1 mM nonionic surfactant Poloxamer 188 added to the cell medium after irradiation completely inhibited the dye loss over the time course of 2 h. Thus a reproducible model was developed for studying the mechanism of acute radiation injury and the efficacy of membrane-sealing agents. As only supportive measures now exist for treating the acute, nonlethal injuries from high-dose radiation exposure, agents that can restore cell membrane function after radiation damage may offer an important tool for therapy.

The role of thermal activation in motion and force generation by molecular motors.

The currently accepted mechanism for ATP-driven motion of kinesin is called the hand-over-hand model, where some chemical transition during the ATP hydrolysis cycle stretches a spring, and motion and force production result from the subsequent relaxation. It is essential in this mechanism for the moving head of kinesin to dissociate, while the other head remains firmly attached to the microtubule. Here we propose an alternative Brownian motor model where the action of ATP modulates the interaction potential between kinesin and the microtubule rather than a spring internal to the kinesin molecule alone. In this model neither head need dissociate (which predicts that under some circumstances a single-headed kinesin can display processive motion) and the transitions by which the motor moves are best described as thermally activated steps. This model is consistent with a wide range of experimental data on the force-velocity curves, the one ATP to one-step stoichiometry observed at small load, and the stochastic properties of the stepping.

Biological sensing of small field differences by magnetically sensitive chemical reactions.

There is evidence that animals can detect small changes in the Earth's magnetic field by two distinct mechanisms, one using the mineral magnetite as the primary sensor and one using magnetically sensitive chemical reactions. Magnetite responds by physically twisting, or even reorienting the whole organism in the case of some bacteria, but the magnetic dipoles of individual molecules are too small to respond in the same way. Here we assess whether reactions whose rates are affected by the orientation of reactants in magnetic fields could form the basis of a biological compass. We use a general model, incorporating biological components and design criteria, to calculate realistic constraints for such a compass. This model compares a chemical signal produced owing to magnetic field effects with stochastic noise and with changes due to physiological temperature variation. Our analysis shows that a chemically based biological compass is feasible with its size, for any given detection limit, being dependent on the magnetic sensitivity of the rate constant of the chemical reaction.

A chemically reversible Brownian motor: application to kinesin and Ncd.

Kinesin and nonclaret disjunctional protein (ncd) are two microtubule-based molecular motors that use energy from ATP hydrolysis to drive motion in opposite directions. They are structurally very similar and bind with similar orientations on microtubule. What is the origin of the different directionality? Is it some subtle feature of the structure of the motor domains, not apparent in x-ray diffraction studies, or possibly some difference near the neck regions far from the microtubule binding site? Perhaps because the motors function as dimers, the explanation involves differences in the strength of the interaction between the two motor monomers themselves. Here we present another possibility, based on a Brownian ratchet, in which the direction of motion of the motor is controlled by the chemical mechanism of ATP hydrolysis and is an inherent property of a single head. In contrast to conventional power stroke models, dissociation of the individual heads is not obligatory in the chemomechanical cycle, and the steps during which motion and force generation occurs are best described as one-dimensional thermally activated transitions that take place while both heads are attached to the microtubule. We show that our model is consistent with experiments on kinesin in which the velocity is measured as a function of external force and with the observed stiochiometry of one ATP/8-nm step at low load. Further, the model provides a way of understanding recent experiments on the ATP dependence of the variance (randomness) of the distance moved in a given time.

Intrawell relaxation of overdamped Brownian particles.

We consider an overdamped Brownian particle in a well. When the particle escapes, it does so as an instanton, i.e., in one run and without dwelling anywhere on the way from the bottom of the well to the top of the barrier. For a sufficiently steep slope the instanton time equals the time it takes the particle to deterministically slide down the same slope. We show that the instanton time is also the relaxation time for the escape rate after the barrier changes shape.

Efficiency of Brownian heat engines.

We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle.

Fluctuation driven transport and models of molecular motors and pumps.

Non-equilibrium fluctuations can drive vectorial transport along an anisotropic structure in an isothermal medium by biasing the effect of thermal noise (kBT). Mechanisms based on this principle are often called Brownian ratchets and have been invoked as a possible explanation for the operation of biomolecular motors and pumps. We discuss the thermodynamics and kinetics for the operation of microscopic ratchet motors under conditions relevant to biology, showing how energy provided by external fluctuations or a non-equilibrium chemical reaction can cause unidirectional motion or uphill pumping of a substance. Our analysis suggests that molecular pumps such as Na,K-ATPase and molecular motors such as kinesin and myosin may share a common underlying mechanism.

Theoretical limits on the threshold for the response of long cells to weak extremely low frequency electric fields due to ionic and molecular flux rectification.

Understanding exposure thresholds for the response of biological systems to extremely low frequency (ELF) electric and magnetic fields is a fundamental problem of long-standing interest. We consider a two-state model for voltage-gated channels in the membrane of an isolated elongated cell (Lcell = 1 mm; rcell = 25 micron) and use a previously described process of ionic and molecular flux rectification to set lower bounds for a threshold exposure. A key assumption is that it is the ability of weak physical fields to alter biochemistry that is limiting, not the ability of a small number of molecules to alter biological systems. Moreover, molecular shot noise, not thermal voltage noise, is the basis of threshold estimates. Models with and without stochastic resonance are used, with a long exposure time, texp = 10(4) s. We also determined the dependence of the threshold on the basal transport rate. By considering both spherical and elongated cells, we find that the lowest bound for the threshold is Emin approximately 9 x 10(-3) V m-1 (9 x 10(-5) V cm-1). Using a conservative value for the loop radius rloop = 0.3 m for induced current, the corresponding lower bound in the human body for a magnetic field exposure is Bmin approximately 6 x 10(-4) T (6 G). Unless large, organized, and electrically amplifying multicellular systems such as the ampullae of Lorenzini of elasmobranch fish are involved, these results strongly suggest that the biophysical mechanism of voltage-gated macromolecules in the membranes of cells can be ruled out as a basis of possible effects of weak ELF electric and magnetic fields in humans.

Optimal modulation of a Brownian ratchet and enhanced sensitivity to a weak external force.

We studied the dynamics of a Brownian particle moving in a spatially anisotropic potential acted on by multiplicative temporal modulations so that V(x,t) = g(t)U(x). Using the concept of the "thermodynamic action," we show that the class of modulation that maximizes the flow is a square-wave in time. We also show that adding a weak, homogenous force F in synergy with the square-wave modulation can cause particles of slightly different size to move in opposite directions. The synergetic change in velocity caused by F can be much greater than the drift velocity that would be caused by F alone.

Thermodynamics and kinetics of a Brownian motor.

Nonequilibrium fluctuations, whether generated externally or by a chemical reaction far from equilibrium, can bias the Brownian motion of a particle in an anisotropic medium without thermal gradients, a net force such as gravity, or a macroscopic electric field. Fluctuation-driven transport is one mechanism by which chemical energy can directly drive the motion of particles and macromolecules and may find application in a wide variety of fields, including particle separation and the design of molecular motors and pumps.

The physicochemical basis for thermal and non-thermal 'burn' injuries.

One of the most basic problems of burn science may well be the confusing nomenclature we use. The word 'burn' is used to identify several different mechanisms of tissue injury. This article describes the problem of accurately characterizing and defining the various burn injuries on the basis of molecular events. The most important objective is to distinguish between the various physicochemical injuries on the basis of differences in their fundamental physicochemical mechanisms and physiological consequences. Also, pathophysiologically important biophysical processes such as the central importance of cell membrane permeabilization in acute cellular necrosis, which different types of burn injury have in common, are emphasized. The biophysics of membrane formation and permeabilization is presented to clarify the conditions for membrane damage as well as to discuss the potential for therapeutic intervention. Where feasible, plausible new strategies to reverse the molecular alterations caused by injury are hypothesized.

Mechanochemical coupling of the motion of molecular motors to ATP hydrolysis.

The typical biochemical paradigm for coupling between hydrolysis of ATP and the performance of chemical or mechanical work involves a well-defined sequence of events (a kinetic mechanism) with a fixed stoichiometry between the number of ATP molecules hydrolyzed and the turnover of the output reaction. Recent experiments show, however, that such a deterministic picture of coupling may not be adequate to explain observed behavior of molecular motor proteins in the presence of applied forces. Here we present a general model in which the binding of ATP and release of ADP serve to modulate the binding energy of a motor protein as it travels along a biopolymer backbone. The mechanism is loosely coupled--the average number of ATPs hydrolyzed to cause a single step from one binding site to the next depends strongly on the magnitude of an applied force and on the effective viscous drag force. The statistical mechanical perspective described here offers insight into how local anisotrophy along the "track" for a molecular motor, combined with an energy-releasing chemical reaction to provide a source of nonequilibrium fluctuations, can lead to macroscopic motion.