Roles of subcellular Na+ channel distributions in the mechanism of cardiac conduction

The gap junction and voltage-gated Na⁺ channel play an important role in the action potential propagation. The purpose of this study was to elucidate the roles of subcellular Na⁺ channel distribution in action potential propagation. To achieve this, we constructed the myocardial strand model, which can calculate the current via intercellular cleft (electric-field mechanism) together with gap-junctional current (gap-junctional mechanism). We conducted simulations of action potential propagation in a myofiber model where cardiomyocytes were electrically coupled with gap junctions alone or with both the gap junctions and the electric field mechanism. Then we found that the action potential propagation was greatly affected by the subcellular distribution of Na⁺ channels in the presence of the electric field mechanism. The presence of Na⁺ channels in the lateral membrane was important to ensure the stability of propagation under conditions of reduced gap-junctional coupling. In the poorly coupled tissue with sufficient Na⁺ channels in the lateral membrane, the slowing of action potential propagation resulted from the periodic and intermittent dysfunction of the electric field mechanism. The changes in the subcellular Na⁺ channel distribution might be in part responsible for the homeostatic excitation propagation in the diseased heart.     

Calcium movements during each heart beat

Transsarcolemmal calcium movements are closely related to force generation in the heart. It is important to understand the transport pathways that control these movements of calcium across the sarcolemmal membrane. In the normal, beating heart, sodium-calcium exchange appears to be an important mechanism for the extrusion of calcium from the cell. The kinetics of this exchange are dependent upon the characteristics of the cell action potential. Calcium efflux via sodium-calcium exchange may be sufficient to balance calcium entry through calcium channels during the action potential.     

Mechanism of RecA-mediated homologous recombination revisited by single molecule nanomanipulation

The mechanisms of RecA-mediated three-strand homologous recombination are investigated at the single-molecule level, using magnetic tweezers. Probing the mechanical response of DNA molecules and nucleoprotein filaments in tension and in torsion allows a monitoring of the progression of the exchange in real time, both from the point of view of the RecA-bound single-stranded DNA and from that of the naked double-stranded DNA (dsDNA). We show that strand exchange is able to generate torsion even along a molecule with freely rotating ends. RecA readily depolymerizes during the reaction, a process presenting numerous advantages for the cell's 'protein economy' and for the management of topological constraints. Invasion of an untwisted dsDNA by a nucleoprotein filament leads to an exchanged duplex that remains topologically linked to the exchanged single strand, suggesting multiple initiations of strand exchange on the same molecule. Overall, our results seem to support several important assumptions of the monomer redistribution model.     

Measurements of calcium transients in ventricular cells during discontinuous action potential conduction

The L-type calcium current (I(Ca)) is important in sustaining propagation during discontinuous conduction. In addition, I(Ca) is altered during discontinuous conduction, which may result in changes in the intracellular calcium transient. To study this, we have combined the ability to monitor intracellular calcium concentration ([Ca(2+)](i)) in an isolated cardiac cell using confocal scanning laser fluorescence microscopy with our "coupling clamp" technique, which allows action potential propagation from the real cell to a real-time simulation of a model cell. Coupling a real cell to a model cell with a value of coupling conductance (G(C) = 8 nS) just above the critical value for action potential propagation results in both an increased amplitude and an increased rate of rise of the calcium transient. Similar but smaller changes in the calcium transient are caused by increasing G(C) to 20 nS. The increase of [Ca(2+)](i) by discontinuous conduction is less than the increase of I(Ca), which may indicate that much of [Ca(2+)](i) is the result of calcium released from the sarcoplasmic reticulum rather than the integration of I(Ca).     

A free energy principle for the brain.

By formulating Helmholtz's ideas about perception, in terms of modern-day theories, one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts: using constructs from statistical physics, the problems of inferring the causes of sensory input and learning the causal structure of their generation can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory input is caused. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of cortical organisation and responses. In this paper, we show these perceptual processes are just one aspect of emergent behaviours of systems that conform to a free energy principle. The free energy considered here measures the difference between the probability distribution of environmental quantities that act on the system and an arbitrary distribution encoded by its configuration. The system can minimise free energy by changing its configuration to affect the way it samples the environment or change the distribution it encodes. These changes correspond to action and perception respectively and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment assumes that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at the models entailed by the brain and how minimisation of its free energy can explain its dynamics and structure.     

Hydrophobic potential of mean force as a solvation function for protein structure prediction

We have developed a solvation function that combines a Generalized Born model for polarization of protein charge by the high dielectric solvent, with a hydrophobic potential of mean force (HPMF) as a model for hydrophobic interaction, to aid in the discrimination of native structures from other misfolded states in protein structure prediction. We find that our energy function outperforms other reported scoring functions in terms of correct native ranking for 91% of proteins and low Z scores for a variety of decoy sets, including the challenging Rosetta decoys. This work shows that the stabilizing effect of hydrophobic exposure to aqueous solvent that defines the HPMF hydration physics is an apparent improvement over solvent-accessible surface area models that penalize hydrophobic exposure. Decoys generated by thermal sampling around the native-state basin reveal a potentially important role for side-chain entropy in the future development of even more accurate free energy surfaces.     

Dynamics of pore growth in membranes and membrane stability.

Pores can form and grow in biomembranes because of factors such as thermal fluctuation, transmembrane electrical potential, and cellular environment. We propose a new statistical physics model of the pore growth treated as a non-Markovian stochastic process, with a free energy barrier and memory friction from the membrane matrix treated as a quasi-two-dimensional viscoelastic and dielectric fluid continuum. On the basis of the modern theory of activated barrier crossing, an analytical expression for membrane lifetime and the phase diagram for membrane stability are obtained. The memory effect due to membrane viscoelasticity and the elasticity due to cytoskeletal network are found to induce sharp transitions to membrane stability against pore growth and compete with other factors to manifest rich dynamic transitions over the membrane lifetime.     

An eikonal-curvature equation for action potential propagation in myocardium

We derive an eikonal-curvature equation to describe the propagation of action potential wavefronts in myocardium. This equation is used to study the effects of fiber orientation on propagation in the myocardial wall. There are significant computational advantages to the use of an eikonal-curvature equation over a full ionic model of action potential spread. With this model, it is shown that the experimentally observed misalignment of spreading action potential ellipses from fiber orientation in level myocardial surfaces is adequately explained by the rotation of fiber orientation through the myocardial wall. Additionally, it is shown that apparently high propagation velocities on the epicardial and endocardial surfaces are the result of propagation into the midwall region and acceleration along midwall fibers before reemergence at an outer surface at a time preceding what could be accomplished with propagation along the surface alone.Research was supported in part by NSF Grant DMS-8801446     

Gap junctions in excitable cells

Gap junction channels are an integral part of the conduction or propagation of an action potential from cell to cell. Gap junctions have rather unique gating and permeability properties which permit the movement of molecules from cell to cell. These molecules may not be directly linked to action potentials but can alter nonjunctional processes within cells, which in turn can affect conduction velocity. The data described in this review reveal that, for the majority of excitable cells, there are two limiting factors, with respect to gap junctions, that affect the conduction/propagation of action potentials. These are (1) the total number of channels and (2) the selective permeability of the channels. Interestingly, voltage dependence and the time course of voltage inactivation (kinetics) are not rate limiting steps under normal physiological conditions for any of the connexins studied so far. Only specialized rectifying electrical synapses utilize strong voltage dependence and rapid kinetics to permit or deny the continued propagation of an action potential.     

Energy exchange between subject and belt during treadmill walking

Treadmill walking aims to simulate overground walking, but intra-stride belt speed variations of treadmills result in some interaction between treadmill and subject, possibly obstructing this aim. Especially in self-paced treadmill walking, in which the belt speed constantly adjusts to the subject, these interactions might affect the gait pattern significantly. The aim of this study was to quantify the energy exchange between subject and treadmill, during the fixed speed (FS) and self-paced (SP) modes of treadmill walking. Eighteen subjects walked on a dual-belt instrumented treadmill at both modes. The energy exchange was calculated as the integration of the product of the belt speed deviation and the fore-aft ground reaction force over the stride cycle. The total positive energy exchange was 0.44 J/stride and the negative exchange was 0.11 J/stride, which was both less than 1.6% of the performed work on the center of mass. Energy was mainly exchanged from subject to treadmill during both the braking and propulsive phase of gait. The two treadmill modes showed a similar pattern of energy exchange, with a slightly increased energy exchange during the braking phase of SP walking. It is concluded that treadmill walking is only mildly disturbed by subject-belt interactions when using instrumented treadmills with adequate belt control.     

The propagation potential. An axonal response with implications for scalp-recorded EEG

An electrophysiological response of axons, referred to as the "propagation potential," was investigated. The propagation potential is a sustained voltage that lasts as long as an action potential propagates between two widely spaced electrodes. The sign of the potential depends on the direction of action potential propagation. The electrode towards which the action potential is propagating is positive with respect to the electrode from which it is receding. For normal frog sciatic nerves the magnitude of the propagation potential was 17% of the peak of the extracellular action potential; TEA increased it to 32%. For normal earthworm median or lateral giant fibers it was 30%. A ripple pattern on the propagation potential was attributed to variation in resistance along the length of the worm. Cooling increased the duration of the propagation potential and attenuated the higher frequency components of the ripple pattern. Differential records from two widely spaced intracellular microelectrodes in the same axon differed from the propagation potential. The amplitude of the plateau relative to the peak was smaller, it decreased as the action potential propagated from one electrode site to the other, and the potential did not return to zero as rapidly as for extracellular records. When propagation was blocked by heat, the propagation potential slowly decayed. There was no ripple pattern during the decay. In a volume conductor, electrodes contacting the worm did not show the typical propagation potential, but electrodes located a few centimeters away from the worm did. Simple core-conductor models based on classical action potential theory did not reproduce the propagation potential. More complex, modified core-conductor models were needed to accurately simulate it. The results suggest that long, slowly conducting fibers can contribute to the scalp-recorded EEG.     

Muscle mechanical work requirements during normal walking: the energetic cost of raising the body's center-of-mass is significant

Inverted pendulum models of walking predict that little muscle work is required for the exchange of body potential and kinetic energy in single-limb support. External power during walking (product of the measured ground reaction force and body center-of-mass (COM) velocity) is often analyzed to deduce net work output or mechanical energetic cost by muscles. Based on external power analyses and inverted pendulum theory, it has been suggested that a primary mechanical energetic cost may be associated with the mechanical work required to redirect the COM motion at the step-to-step transition. However, these models do not capture the multi-muscle, multi-segmental properties of walking, co-excitation of muscles to coordinate segmental energetic flow, and simultaneous production of positive and negative muscle work. In this study, a muscle-actuated forward dynamic simulation of walking was used to assess whether: (1). potential and kinetic energy of the body are exchanged with little muscle work; (2). external mechanical power can estimate the mechanical energetic cost for muscles; and (3.) the net work output and the mechanical energetic cost for muscles occurs mostly in double support. We found that the net work output by muscles cannot be estimated from external power and was the highest when the COM moved upward in early single-limb support even though kinetic and potential energy were exchanged, and muscle mechanical (and most likely metabolic) energetic cost is dominated not only by the need to redirect the COM in double support but also by the need to raise the COM in single support.     

Thermal fluctuation spectroscopy of DNA thermal denaturation

We have developed the technique of thermal fluctuation spectroscopy to measure the thermal fluctuations in a system. This technique is particularly useful to study the denaturation dynamics of biomolecules like DNA. Here we present a study of the thermal fluctuations during the thermal denaturation (or melting) of double-stranded DNA. We find that the thermal denaturation of heteropolymeric DNA is accompanied by large, non-Gaussian thermal fluctuations. The thermal fluctuations show a two-peak structure as a function of temperature. Calculations of enthalpy exchanged show that the first peak comes from the denaturation of AT rich regions and the second peak from denaturation of GC rich regions. The large fluctuations are almost absent in homopolymeric DNA. We suggest that bubble formation and cooperative opening and closing dynamics of basepairs causes the additional fluctuation at the first peak and a large cooperative transition from a partially molten DNA to a completely denatured state causes the additional fluctuation at the second peak.     

Oligodendrocyte-derived transcellular signaling regulates axonal energy metabolism

The unique morphology and functionality of central nervous system (CNS) neurons necessitate specialized mechanisms to maintain energy metabolism throughout long axons and extensive terminals. Oligodendrocytes (OLs) enwrap CNS axons with myelin sheaths in a multilamellar fashion. Apart from their well-established function in action potential propagation, OLs also provide intercellular metabolic support to axons by transferring energy metabolites and delivering exosomes consisting of proteins, lipids, and RNAs. OL-derived metabolic support is crucial for the maintenance of axonal integrity; its dysfunction has emerged as an important player in neurological disorders that are associated with axonal energy deficits and degeneration. In this review, we discuss recent advances in how these transcellular signaling pathways maintain axonal energy metabolism in health and neurological disorders.     

Where's the evidence?

Science is in large part the art of careful measurement, and a fixed measurement scale is the sine qua non of this art. It is obvious to us that measurement devices lacking fixed units and constancy of scale across applications are problematic, yet we seem oddly laissez faire in our approach to measurement of one critically important quantity: statistical evidence. Here I reconsider problems with reliance on p values or maximum LOD scores as measures of evidence, from a measure-theoretic perspective. I argue that the lack of an absolute scale for evidence measurement is every bit as problematic for modern biological research as was lack of an absolute thermal scale in pre-thermodynamic physics. Indeed, the difficulty of establishing properly calibrated evidence measures is strikingly similar to the problem 19th century physicists faced in deriving an absolute scale for the measurement of temperature. I propose that the formal relationship between the two problems might enable us to apply the mathematical foundations of thermodynamics to establish an absolute scale for the measurement of evidence, in statistical applications and possibly other areas of mathematical modeling as well. Here I begin to sketch out what such an endeavor might look like.     

Empirical Study of an Adaptive Multiscale Model for Simulating Cardiac Conduction

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and the waveform, including both upstroke and recovery, of fully microscale models. They also reveal that perfect alignment between myocytes and the macroscale grid is not necessary to reproduce the dynamics of a traveling action potential. Further, our simulations suggest that the macroscale grid spacing used in an adaptive multiscale model need not be much finer than the spatial width of an action potential. These results are demonstrated to hold under high, low, and zero gap-junctional coupling regimes.     

No evidence for a forced-unfolding mechanism during ATP/GroES binding to substrate-bound GroEL: no observable protection of metastable Rubisco intermediate or GroEL-bound Rubisco from tritium exchange

In tritium-hydrogen exchange experiments, the large GroEL substrate Rubisco was unfolded and exchanged in urea/acid/tritiated water, then diluted into either protic buffer or protic buffer containing GroEL. The respective Rubisco metastable folding intermediate or Rubisco-GroEL binary complex was then separated from residual tritium after varying times of exchange by centrifugation through P-10 or G-25 resin. No significant tritium was recovered in either case, in contrast to an earlier report. Thus, although the earlier-proposed forced unfolding mechanism for the action of GroEL on a bound polypeptide, occurring during ATP/GroES binding, remains an attractive hypothesis, the data here do not provide any indication that it is involved in the folding of Rubisco.     

Solitary waves in soybean induced by localized thermal stress

Action potentials in higher plants are believed to be the information carriers in intercellular and intracellular communication in the presence of an environmental stressor. Plant electrophysiologists have recorded long distance electrical signaling in higher plants during the last two hundred years. Reproducing the duration, speed of propagation, and the shape of the action potential is challenging. Early measurements revealed that the speed of action potential propagation in plants is extremely slow - from 0.1 mm/s to 20 cm/s, although many faster plant responses to stress have been recorded as well. We hypothesized that this discrepancy is most likely due to the artifacts of aliasing from slow registration systems. In this study, we employ real time measurements using modern data acquisition techniques to detect ultra fast action potentials in green plants induced by localized heat stress. Thermal shock or heat stress is the most common environmental stress. Based on more sophisticated measuring techniques, we show that plants transmit solitary waves and that the speed of action potential propagation in green plants is similar to the speed of action potentials in mammalians, varying from a few meters per second up to 105 m/s. Possible pathways for electrical signal propagation in vascular plants are discussed.Key words: Action potential, plant electrophysiology, electrical signaling, localized heat stress, excitability     

Protein-mediated exchange of synthetic phosphatidylcholines into synaptosomal membranes

A phosphatidylcholine (PC) exchange protein from bovine liver was used to exchange endogenous synaptosomal membrane PC's with PC's of defined fatty-acid composition from phospholipid vesicles. Up to 50% of the total synaptosomal PC could be exchanged during a 3 h incubation with PC's which were in the liquid-crystalline state at the temperature of incubation (dimyristoyl-, dioleoyl- and dielaidoyl-PC). The biphasic kinetics of the exchange of 14C-labeled 1-palmitoyl-2-oleoyl-PC into isolated synaptic plasma membrane vesicles indicated that the half-time for transbilayer equilibrium of PC in these membranes was about 10 h. Hence, the observed 50% exchange of total synaptosomal PC probably represented nearly complete exchange of PC in the outer face of the synaptosomal plasma membrane. This extensive exchange was accomplished without apparent loss of synaptosomal function, including membrane potential and high-affinity uptake of choline and gamma-aminobutyric acid. PC's in the gel state (dipalmitoyl- and distearoyl-PC) could not be exchanged extensively into the synaptosomal membranes. However, from within gel-state distearoyl-PC liposomes, a trace amount of fluid 1-palmitoyl-2-oleoyl-PC (Tm less than 10 degrees C) could be preferentially exchanged into the synaptosomes at 32 degrees C with little transfer of the saturated PC.