Conduction in bundles of demyelinated nerve fibers: computer simulation

This study presents a model of action potential propagation in bundles of myelinated nerve fibers. The model combines the single-cable formulation of Goldman and Albus (1967) with a basic representation of the ephaptic interaction among the fibers. We analyze first the behavior of the conduction velocity (CV) under the change of the various conductance parameters and temperature. The main parameter influencing the CV is the fast sodium conductance, and the dependence of CV on the temperature is linear up to 30 degrees C. The increase of myelin thickness above its normal value (5 microm) gives a slight increase in CV. The CV of the single fiber decreases monotonically with the disruption of myelin, but the breakdown is abrupt. There is always conduction until the thickness is larger than 2% of its original value, at which with at this point a sharp transition of CV to zero occurs. Also, the increase of temperature can block conduction. At 5% of the original thickness there is still spike propagation, but an increase of 2 degrees C causes conduction block. These results are consistent with clinical observations. Computer simulations are performed to show how the CV is affected by local damage to the myelin sheath, temperature alterations, and increased ephaptic coupling (i.e., coupling of electrical origin due to the electric neutrality of all the nerve) in the case of fiber bundles. The ephaptic interaction is included in the model. Synchronous impulse transmission and the formation of "condensed" pulse states are found. Electric impulses with a delay of 0.5 ms are presented to the system, and the numerical results show that, for increasing coupling, the impulses tend to adjust their speed and become synchronized. Other interesting phenomena are that spurious spikes are likely to be generated when ephaptic interaction is raised and that damaged axons suffering conduction block can be brought into conduction by the normal functioning fibers surrounding them. This is seen also in the case of a large number of fibers (N=500). When all the fibers are stimulated simultaneously, the conduction velocity is found to be strongly dependent on the level of ephaptic coupling and a sensible reduction is observed with respect to the propagation along an isolated axon even for low coupling level. As in the case of three fibers, spikes tend to lock and form collective impulses that propagate slowly in the nerve. On the other hand, if only 10% of fibers are stimulated by an external input, the conduction velocity is only 2% less than that along a single axon. We found a threshold value for the ephaptic coupling such that for lower values it is impossible to recruit the damaged fibers into conduction, for values of the coupling equal to this threshold only one fiber can be restored by the nondamaged fibers, and for values larger than the threshold an increasing number of fibers can return to normal functioning. We get values of the ephaptic coupling such that 25% of axons can be damaged without change of the collective conduction.     

Raman spectroscopy of nerve fibers. A study of membrane lipids under steady state conditions.

The molecular structures of different nerve fibers kept in good physiological conditions were studied by laser Raman spectroscopy. For myelinated nerves like the rat sciatic nerve, the Raman spectrum is dominated by bands due to the lipid component of the myelin sheath. The temperature dependence of these bands does not reveal any thermotropic phase transition between 0 and 40 degrees C. There is, however, with temperature, a linear increase in the intermolecular disorder that is accompanied by an increase in the number of gauche bonds of the phospholipid acyl chains. For unmyelinated nerves such as the lobster leg nerve, the C-H stretching region of the Raman spectrum is covered by bands arising from the protein component of the axoplasm. However, for the garfish olfactory nerve that has a high density of excitable membranes, phospholipid bands are observed and can be used as intrinsic structural probes of the excitable membranes. The relative intensity of these bands is also temperature dependent.     

Modelled temperature-dependent excitability behaviour of a generalised human peripheral sensory nerve fibre

The objective of this study was to determine if a recently developed human Ranvier node model, which is based on a modified version of the Hodgkin–Huxley model, could predict the excitability behaviour in human peripheral sensory nerve fibres with diameters ranging from 5.0 to 15.0 μm. The Ranvier node model was extended to include a persistent sodium current and was incorporated into a generalised single cable nerve fibre model. Parameter temperature dependence was included. All calculations were performed in Matlab. Sensory nerve fibre excitability behaviour characteristics predicted by the new nerve fibre model at different temperatures and fibre diameters compared well with measured data. Absolute refractory periods deviated from measured data, while relative refractory periods were similar to measured data. Conduction velocities showed both fibre diameter and temperature dependence and were underestimated in fibres thinner than 12.5 μm. Calculated strength–duration time constants ranged from 128.5 to 183.0 μs at 37°C over the studied nerve fibre diameter range, with chronaxie times about 30% shorter than strength–duration time constants. Chronaxie times exhibited temperature dependence, with values overestimated by a factor 5 at temperatures lower than body temperature. Possible explanations include the deviated absolute refractory period trend and inclusion of a nodal strangulation relationship. At the time of this research J. E. Smit was with the University of Pretoria.     

Fluorescence anisotropy and myelin structure. III. Effect of temperature changes on the orientation of dye molecules in nerve fibers]

The temperature dependence of fluorescence polarization of stained nerve fibres has been studied. As has been previously demonstrated by the authors, the dependence of fluorescence polarization on the angle between the electrical vector of exciting light and the fibre axis (azimuth characteristics) is associated with the molecular orientation of dyes adsorbed on the membranes of the myelin sheath. This permits an indirect conclusion to be made about the structure and structural changes of an adsorbent. The experiments with changing temperature show that the molecular orientation of dyes decreases with decline of temperature from the room temperature to the freezing point of the Ringer solution. The structure of myelin membranes is suggested to be stabilized through hydrophobic interaction.     

The combined effects of reactant kinetics and enzyme stability explain the temperature dependence of metabolic rates

A mechanistic understanding of the response of metabolic rate to temperature is essential for understanding thermal ecology and metabolic adaptation. Although the Arrhenius equation has been used to describe the effects of temperature on reaction rates and metabolic traits, it does not adequately describe two aspects of the thermal performance curve (TPC) for metabolic rate—that metabolic rate is a unimodal function of temperature often with maximal values in the biologically relevant temperature range and that activation energies are temperature dependent. We show that the temperature dependence of metabolic rate in ectotherms is well described by an enzyme‐assisted Arrhenius (EAAR) model that accounts for the temperature‐dependent contribution of enzymes to decreasing the activation energy required for reactions to occur. The model is mechanistically derived using the thermodynamic rules that govern protein stability. We contrast our model with other unimodal functions that also can be used to describe the temperature dependence of metabolic rate to show how the EAAR model provides an important advance over previous work. We fit the EAAR model to metabolic rate data for a variety of taxa to demonstrate the model's utility in describing metabolic rate TPCs while revealing significant differences in thermodynamic properties across species and acclimation temperatures. Our model advances our ability to understand the metabolic and ecological consequences of increases in the mean and variance of temperature associated with global climate change. In addition, the model suggests avenues by which organisms can acclimate and adapt to changing thermal environments. Furthermore, the parameters in the EAAR model generate links between organismal level performance and underlying molecular processes that can be tested for in future work.     

Axonal Transport in the Garfish Optic Nerve: Comparison with the Olfactory System

Fast and slow axonal transports were studied in the optic nerve of the garfish and compared with previous studies on the olfactory nerve. The composition of fast-transport proteins was very similar in the two nerves. Although the velocity of fast transport was slightly lower in the optic nerve, there was a linear increase in velocity with temperature in both nerves. As in the olfactory nerve, only a single wave of slow-transport protein radioactivity moves along the nerve. The velocity of slow transport also increased linearly with temperature, but the coefficient was less than in the olfactory system. The composition of slow transport in the optic nerve was significantly different from that in the olfactory nerve, a finding reflecting the different cytoskeletal constituents of the two types of axons. The slow wave could be differentiated into several subcomponents, with the order of velocities being a 105-kilodalton protein and actin greater than tubulins and clathrin greater than fodrin much greater than neurofilaments. It can be concluded that the temperature dependence of fast and slow axonal transport in different nerves reflects the influence of temperature on the individual polypeptides constituting the various transport phases. The garfish optic nerve preparation may be advantageous for studies of axonal transport in retinal ganglion cell axons, because its great length avoids the complications of having to study transport in the optic tract or in material accumulating at the tectum.     

Temperature dependence of the disulfide perturbation to the triplet state of tryptophan

Variability in the temperature dependence of disulfide quenching of the tryptophan phosphorescence of globular proteins in rigid glasses is illustrated with lysozyme and α-bungarotoxin. A laser-pulsed phosphorescence study of this short-range interaction with a model indole-disulfide system is described. The perturbation of secondary dibutyl disulfide on the triplet state of the indole moiety in 2-(3-indolyl)ethyl phenyl ketone in rigid media is found to display a bimodal temperature dependence. The quenching rate constant at contact between chromophore and perturber is observed to be temperature independent below 30 K, but to increase with temperature between 30 and 100 K with an activation energy of ~200 cm^-1. The results suggest that the underlying quenching interaction involves a photo-induced one-electron transfer from the excited state of indole to the disulfide.     

Free volume model for lipid lateral diffusion coefficients. Assessment of the temperature dependence in phosphatidylcholine and phosphatidylethanolamine bilayers

The lipid lateral diffusion coefficients, DT, in fluid-phase phosphatidylcholine and phosphatidylethanolamine bilayers have been analysed in terms of the free-volume diffusion model by fitting the expression: DT = AT exp[- B/(T - T0)] to the observed temperature dependence, where A, B and T0 are the parameters to be optimized. Application of an unconstrained optimization procedure to data obtained from excimer formation (Galla et al. (1979) J. Membrane Biol. 48, 215-236) and from fluorescence photobleaching (Vaz et al. (1985) Biochemistry 24, 781-786) provides statistical evidence for a free-volume model as opposed to a simple Stokes-Einstein model (T0 = 0), only in certain cases. In the instances for which the parameter T0 can be determined with a reasonable degree of accuracy, it is found that this characteristic temperature at which the free volume extrapolates to zero lies below the bilayer gel-to-fluid phase transition temperature and does not coincide with the pre-transition temperature for phosphatidylcholines.     

Reactor Performance in the Presence of Catalyst Deactivation

The main variable of enzymatic processes is often found to be the operating temperature. An increase in temperature leads to higher rates for the catalytic transformation. However, beyond a certain temperature catalyst deactivation is winning the game. Therefore, processes should be optimized in order to determine the temperature which leads to a minimal demand of enzyme preparation. For the prediction of such optimal reactor operation, modeling of the temperature dependence of the process has to be performed. Examples of such modeling are given for the hydrolysis of lactose in UHT milk by means of three different β‐galactosidases – those from Aspergillus oryzae, Kluyveromyces lactis, and Escherichia coli. The reaction kinetics for a constant initial lactose concentration can be described by a model of two parameters, of which only one depends on temperature. For the lactase of E. coli the reaction can be described as a simple reaction with first order kinetics. The deactivation mechanism includes a reversible as well as an irreversible path of denaturation. The temperature dependent parameters follow Arrhenius' and van't Hoff's law, respectively. On the basis of their particular reaction models all three enzymes can be compared with respect to their optimum use. The models have been verified under laboratory conditions and have shown their usefulness for the prediction of optimum operating variables. Quite remarkable features have been found for the lactase of E. coli.     

Possible effects of the influence of dynamic disorder of biological systems on characteristics of intramolecular mobility, determined by Mossbauer spectroscopy]

A model for describing dynamic properties of proteins is proposed. The model involves the distribution over amplitudes and correlation times of intramolecular dynamics. It has been shown that distribution parameters and its temperature dependence have a great influence upon the values of experimental dynamic characteristics. Besides the discrepancy between the real and experimental temperature, dependence of characteristics on intramolecular dynamics can be observed.     

Inferring the temperature dependence of population parameters: the effects of experimental design and inference algorithm

Understanding and quantifying the temperature dependence of population parameters, such as intrinsic growth rate and carrying capacity, is critical for predicting the ecological responses to environmental change. Many studies provide empirical estimates of such temperature dependencies, but a thorough investigation of the methods used to infer them has not been performed yet. We created artificial population time series using a stochastic logistic model parameterized with the Arrhenius equation, so that activation energy drives the temperature dependence of population parameters. We simulated different experimental designs and used different inference methods, varying the likelihood functions and other aspects of the parameter estimation methods. Finally, we applied the best performing inference methods to real data for the species Paramecium caudatum. The relative error of the estimates of activation energy varied between 5% and 30%. The fraction of habitat sampled played the most important role in determining the relative error; sampling at least 1% of the habitat kept it below 50%. We found that methods that simultaneously use all time series data (direct methods) and methods that estimate population parameters separately for each temperature (indirect methods) are complementary. Indirect methods provide a clearer insight into the shape of the functional form describing the temperature dependence of population parameters; direct methods enable a more accurate estimation of the parameters of such functional forms. Using both methods, we found that growth rate and carrying capacity of Paramecium caudatum scale with temperature according to different activation energies. Our study shows how careful choice of experimental design and inference methods can increase the accuracy of the inferred relationships between temperature and population parameters. The comparison of estimation methods provided here can increase the accuracy of model predictions, with important implications in understanding and predicting the effects of temperature on the dynamics of populations.     

A study of the quadrupolar NMR splittings of 7Li+, 23Na+, and 133Cs+ counterions in macroscopically oriented DNA fibers.

The hydration and temperature dependencies of the 23Na+, 133Cs+, and 7Li+ quadrupolar splitting have been determined in hydrated, macroscopically oriented DNA fibers. At low water contents the quadrupolar splitting is found to decrease as the water content increases, regardless of counterion, while at high water contents the hydration dependence is reversed. The 23Na+ and 133Cs+ quadrupolar splittings decrease as the temperature increases, while the 7Li+ splitting shows the opposite behavior. At high water contents the 23Na+ and 133Cs+ splittings decrease, and then, after passing zero splitting, increase as the temperature increases. The interpretation of the temperature dependence is discussed in terms of a two-site model (free and bound ions) and a three-site model (free ions and specifically or nonspecifically bound ions). It is suggested that a three-site model is more consistent with the data for the present system. At high water contents, the temperature dependence of the 7Li+ splitting vanishes, indicating counterion condensation. The behavior of the 7Li+ splitting is confirmed by measurements on DNA fibers in equilibrium with a C2H5OD-D2O-LiCl solution. The salt dependence in this system is weak. The counterion quadrupolar splitting is seen to be very sensitive to structural transitions in double-helical DNA.     

Application of the primary hydration shell approach to locally enhanced sampling simulated annealing: computer simulation of thyrotropin-releasing hormone in water

A unified model of simulated annealing with locally enhanced sampling (LES) in a primary hydration shell (PHS) aqueous environment is developed and tested by predicting the structure of the tripeptide thyrotropin-releasing hormone (TRH) in solution. The model extends the formulation of the restraining force in the PHS method as a function of temperature, number of copies in the LES method, and shell thickness. The dependence of the restraining force on temperature can be shown to follow the relationship c(1)T - c(2), which can be derived from the expression for kinetic energy in molecular dynamics simulations. The calibration of the restraining force for different simulation conditions reveals the dependence of c(1) and c(2) on the number of copies in the LES method and the thickness of the PHS. The predicted structure of TRH is in very good agreement with results from NMR experiments and from a 10-ns PHS simulation at 300 K. The method promises to be useful in predicting structure of peptides and proteins in an aqueous environment.     

Autoimmune sympathectomy in fetal rabbits

An autoimmune model for in utero immunosympathectomy of fetal rabbits was developed. Non-pregnant, female rabbits were injected with purified nerve growth factor and then bred after confirmation of high titers of anti-nerve growth factor antiserum. Fetuses were delivered and sacrificed at 27 and 31 days gestation and tissue norepinephrine concentration was used as an index of sympathetic innervation. There were significant reductions in tissue norepinephrine at both gestational ages. At 31 days there was a 32% reduction in lung norepinephrine concentration, 46% in the heart and 60% in brown adipose tissue. Corresponding reductions at 27 days were 68% for lung, 44% for heart and 49% for brown adipose tissue. Adrenal catecholamine content was unaffected but para-aortic gland catecholamines were slightly increased. Pulmonary beta adrenergic receptors showed a 30% up regulation in response to dennervation. Carcass weight was reduced 15% to 11% in the dennervated animals. These results demonstrate that dependence of organ sympathetic innervation on nerve growth factor can be demonstrated as early as 27 days gestation. This is a useful model to study the timing and dependence of organ sympathetic innervation on nerve growth factor and the factors which regulate this dependence.     

Poly- and mononeuronal innervation in a model for the development of neuromuscular connections

In the normal development of connections between motor neurons and muscle fibres, an initial stage of polyneuronal innervation is followed by withdrawal of connections until each muscle fibre is innervated by a single axon. However, polyneuronal innervation has been found to persist after prolonged nerve conduction block, in spite of the resumption of normal neuromuscular activity. Here we analyse in detail a model proposed for the withdrawal of nerve connections in developing muscle, based on competition between nerve terminals. The model combines competition for a pre-synaptic resource with competition for a post-synaptic resource. Using bifurcation and phase space analysis, we show that polyneuronal innervation, as well as mononeuronal innervation, can be stable. The model accounts for the development of mononeuronal innervation and for persistent polyneuronal innervation after prolonged nerve conduction block, which appears as a consequence of the general competitive interactions operating during normal development.     

AMINO ACID TRANSPORT IN PERIPHERAL NERVE: ENERGY AND SODIUM DEPENDENCE

Abstract— The energy and sodium dependence of the several carrier-mediated mechanisms for amino acid uptake have been studied in frog sciatic nerve. The different transport mechanisms are found to be variable in their dependence on sodium and metabolic energy. Saturable uptakes of lysine, phenylalanine and valine are relatively independent of the presence or absence of sodium in the incubation medium, indicating that uptakes by those mechanisms subserving basic, large neutral amino acids, and those amino acids containing aromatic or heterocyclic ring structures are largely sodium independent. Saturable uptakes of glutamic acid, proline, glycine and β-alanine are considerably reduced in the absence of sodium; thus carrier mechanisms for uptake of acidic, small neutral amino acids, β-alanine and proline are highly sodium dependent. The efficacies of several cations in substituting for sodium is variable; greatest inhibitions are found when potassium is used to replace sodium.
With the exception of proline, those mechanisms found to be sodium dependent are also found to be energy dependent, since they are inhibited by both DNP and lowered temperature. Although proline uptake is sodium dependent, proline uptake is stimulated by DNP and relatively insensitive to lowered temperature.     

An implantable nerve cooler for the exercising dog

An implantable nerve cooler has been constructed to block cervical vago-sympathetic activity in the exercising dog reversibly. An insulated gilt brass container implanted around the nerve is perfused with cooled alcohol via silicone tubes. The flow of alcohol is controlled by an electromagnetic valve to keep nerve temperature at the required value. Nerve temperature is measured by a thermistor attached to the housing and in contact with the nerve. It is shown that, during cooling, temperature at this location differs less than 2 degrees C from nerve core temperature. Measurement of changes in heart rate revealed that complete vagal block in the conscious animal is obtained at a nerve temperature of 2 degrees C and can be achieved within 50 s. During steady-state cooling in the exercising animal nerve temperature varied less than 0.5 degree C. When the coolers after 2 weeks of implantation were removed they showed no oxydation and could be used again.     

Differential scanning calorimetry of lobster haemocyanin

Differential scanning calorimetry has been performed with Palinurus vulgaris haemocyanin monomers and hexamers. The denaturation of the protein is irreversible. Both the temperature of the transition maximum and the enthalpy are lower for the monomer than for the hexamer. A scan rate dependence of the temperature of the maxima is found for both the monomer and the hexamer; for the hexamer at least, this can be explained in terms of a two-state kinetic model. Some comments are made as to the use of equilibrium thermodynamics in the analysis of irreversible scanning calorimetric traces.     

Theoretical analysis of the firing pattern of a neuron with stationary N-shaped current voltage characteristic of its dendritic membrane

To confirm the hypothesis of the N-shaped current-voltage characteristic curve of slow ionic currents of the dendritic membrane the role of processes taking place on that membrane in organization of the firing pattern of the nerve cells was examined. On a mathematical model dependence of discharge frequency on strength of depolarizing current can be divided into two ranges. The second range of sharply increased steepness of the curve of discharge frequency versus current can be explained by transitions of the distal parts of the dendrites from resting potential to persistent depolarization. The possibility of hysteresis of the frequency-current curve is postulated and the spontaneous discharge of neurons as an off-response to strong depolarization is explained.