The Multi-Biophysical Nature of Computation in Brain Neural Networks

Comprehending the nature of action potentials is fundamental to our understanding of the functioning of nervous systems in general. Here we consider their evolution and describe their functions of communication, modulation, and computation within nervous systems. The ionic mechanisms underlying action potentials in the squid giant axon were first described by Hodgkin and Huxley in 1952 and their findings have formed our orthodox view of how the physiological action potential functions. However, substantial evidence has now accumulated to show that the action potential is accompanied by a synchronized coupled soliton pressure pulse in the cell membrane, the action potential pulse (APPulse). Here we explore the interactions between the soliton and the ionic mechanisms known to be associated with the action potential. Computational models of the action potential usually describe it as a binary event, but we suggest that it is a quantum ternary event known as the computational action potential (CAP), whose temporal fixed point is threshold, rather than the rather plastic action potential peak used in other models. The CAP accompanies the APPulse and the physiological action potential. Therefore, we conclude that nerve impulses appear to be an ensemble of three inseparable, interdependent, concurrent states: the physiological action potential, APPulse, and CAP.

Acute temperature change can be cardioplegic to mammals, yet certain ectotherms maintain their cardiac scope over a wide temperature range. To better understand the acute effects of temperature on the ectothermic heart, we investigated the stimulus-induced change in intracellular Ca(2+) concentration ([Ca(2+)](i); cytosolic Ca(2+) transient) in isolated rainbow trout myocytes at 7 degrees C, 14 degrees C and 21 degrees C. Myocytes were voltage-clamped and loaded with Fura-2 to measure the L-type Ca(2+) channel current (I(Ca)) and [Ca(2+)](i) during physiological action potential (AP) pulses at frequencies that correspond to trout heart rates in vivo at 7 degrees C, 14 degrees C and 21 degrees C. Additionally, [Ca(2+)](i) and I(Ca) were examined with square (SQ) pulses at slow (0.2 Hz) and physiologically relevant contraction frequencies. The amplitude of [Ca(2+)](i) decreased with increasing temperature for both SQ and AP pulses, which may contribute to the well-known negative inotropic effect of warm temperature on contractile strength in trout hearts. With SQ pulses, [Ca(2+)](i) decreased from 474+/-53 nmol l(-1) at 7 degrees C to 198+/-21 nmol l(-1) at 21 degrees C, while the decrease in [Ca(2+)](i) with AP pulses was from 234+/-49 nmol l(-1) to 79+/-12 nmol l(-1), respectively. Sarcolemmal Ca(2+) influx was increased slightly at cold temperatures with AP pulses (charge transfer was 0.27+/-0.04 pC pF(-1), 0.19+/-0.03 pC pF(-1) and 0.13+/-0.03 pC pF(-1) at 7 degrees C, 14 degrees C and 21 degrees C, respectively). At all temperatures, cells were better able to maintain diastolic Ca(2+) levels at physiological frequencies with AP pulses compared with 500 ms SQ pulses. We suggest that temperature-dependent modulation of the AP is important for cellular Ca(2+) regulation during temperature and frequency change in rainbow trout heart.

At present the neurological basis of sentience is poorly understood and this problem is exacerbated by only a partial knowledge of how one of the primary elements of sentience, the action potential, actually works. This has consequences for our understanding of how communication within the brain and in artificial brain neural networks (BNNs). Reverse engineering models of brain activity assume processing works like a conventional binary computer and neglects speed of cognition, latencies, error in nerve conduction and the true dynamic structure of neural networks in the brain. Any model of nerve conduction that claims inspiration from nature must include these prerequisite parameters, but current western computer modeling of artificial BNNs assumes that the action potential is binary and binary mathematics has been assumed by force of popular acceptance to mediate computation in the brain. Here we present evidence that the action potential is a temporal compound ternary structure, described as the computational action potential (CAP). The CAP contains the refractory period, an analog third phase capable of phase-ternary computation via colliding action potentials. This would best fit a realistic BNN and provides a plausible mechanism to explain transmission, in preference to Cable Theory. The action potential pulse (APPulse), is made up of the action potential combined with a coupled synchronized soliton pressure pulse in the cell membrane. We describe a model of an ion channel in a membrane where a soliton deforms the channel sufficiently to destroy the electrostatic insulation thereby instigating a mechanical contraction across the membrane by electrostatic forces. Such a contraction has the effect of redistributing the force lengthways thereby increasing the volume of the ion channel in the membrane. Na ions, once attracted to the interior, balance the forces and the channel reforms to its original shape. A refractory period then occurs until the Na ions diffuse from the adjacent interior space. Finally, a computational model of the action potential (the CAP) is proposed with single action potentials significantly including the refractory period as a computational element capable of computation between colliding action potentials.

Rapid delayed rectifier K+ current (IKr) and late Na+ current (INaL) significantly shape the cardiac action potential (AP). Changes in their magnitudes can cause either long or short QT syndromes associated with malignant ventricular arrhythmias and sudden cardiac death. Physiological self AP-clamp was used to measure INaL and IKr during the AP in rabbit and porcine ventricular cardiomyocytes to test our hypothesis that the balance between IKr and INaL affects repolarization stability in health and disease conditions. We found comparable amount of net charge carried by IKr and INaL during the physiological AP, suggesting that outward K+ current via IKr and inward Na+ current via INaL are in balance during physiological repolarization. Remarkably, IKr and INaL integrals in each control myocyte were highly correlated in both healthy rabbit and pig myocytes, despite high overall cell-to-cell variability. This close correlation was lost in heart failure myocytes from both species. Pretreatment with E-4031 to block IKr (mimicking long QT syndrome 2) or with sea anemone toxin II to impair Na+ channel inactivation (mimicking long QT syndrome 3) prolonged AP duration (APD); however, using GS-967 to inhibit INaL sufficiently restored APD to control in both cases. Importantly, INaL inhibition significantly reduced the beat-to-beat and short-term variabilities of APD. Moreover, INaL inhibition also restored APD and repolarization stability in heart failure. Conversely, pretreatment with GS-967 shortened APD (mimicking short QT syndrome), and E-4031 reverted APD shortening. Furthermore, the amplitude of AP alternans occurring at high pacing frequency was decreased by INaL inhibition, increased by IKr inhibition, and restored by combined INaL and IKr inhibitions. Our data demonstrate that IKr and INaL are counterbalancing currents during the physiological ventricular AP and their integrals covary in individual myocytes. Targeting these ionic currents to normalize their balance may have significant therapeutic potential in heart diseases with repolarization abnormalities. Visual Overview: A visual overview is available for this article.

Conventionally it is assumed that the nerve impulse is an electrical process based upon the observation that electrical stimuli produce an action potential as defined by Hodgkin Huxley (1952) (HH). Consequently, investigations into the computation of nerve impulses have almost universally been directed to electrically observed phenomenon. However, models of computation are fundamentally flawed and assume that an undiscovered timing system exists within the nervous system. In our view it is synchronisation of the action potential pulse (APPulse) that effects computation. The APPulse, a soliton pulse, is a novel purveyor of computation and is a quantum mechanical pulse: i.e., It is a non-Turing synchronised computational event. Furthermore, the APPulse computational interactions change frequencies measured in microseconds, rather than milliseconds, producing effective efficient computation. However, the HH action potential is a necessary component for entropy equilibrium, providing energy to open ion channels, but it is too slow to be functionally computational in a neural network. Here, we demonstrate that only quantum non-electrical soliton pulses converging to points of computation are the main computational structure with synaptic transmission occurring at slower millisecond speeds. Thus, the APPulse accompanying the action potential is the purveyor of computation; a novel computational mechanism, that is incompatible with Turing timed computation and artificial intelligence (AI).

Substantial evidence has accumulated to show that the action potential is always accompanied by a synchronized coupled soliton pressure pulse in the cell membrane, the action potential pulse (APPulse). Furthermore, it has been postulated that, in computational terms, the action potential is a compound ternary structure consisting of two digital phases (the resting potential and the action potential) and a third-time dependent analogue variable, the refractory period. Together, with the APPulse, these phases are described as the computational action potential (CAP), which allows computation by phase. The nature of transmission, and thus computation across membranes, is dependent upon their structures, which have similar components from one neuron to another. Because perception and therefore sentience must be defined by the capabilities of the brain computational model, we propose that phase-ternary mathematics (PTM) is the native mathematical process underlying perception, consciousness and sentience. In this review, we take the CAP concept and apply it to the working of a well-defined neural network, the vertebrate retina. We propose an accurate working computational model of the retina and provide an explanation of computation of the neural transactions within it using PTM, and provide evidence that could form the basis of understanding neural computation within the entire nervous system. Evidence is presented of phase ternary computation (PTC), defined in phase ternary mathematics and shows an exact mathematical correlation between the activity of the amacrine cells, the bipolar cells and ganglion cells of the retina, once these cells have been activated by light falling on the cones. In this model, the computation of luminosity of multiple cones synapsed to a bipolar cell is performed by phase ternary mathematics at the points of convergence of CAPs. Redaction by the refractory periods of converging CAPs eliminates all but the leading APPulse resulting in sampling and averaging. In phase ternary analysis (PTA), the physiology of synapses defines their primary action as latency changers, changing the time taken for impulses to travel between points of convergence. This paper describes a novel type of computation, PTC, with evidence that it is the fundamental computational method used by the retina and by association the rest of the brain. By comparing the morphology of neurons it is now possible to explain their function singly and in networks. This has profound consequences both for our understanding of the brain and in clinical practice.

Influx of extracellular Ca2+ plays a major role in the activation of contraction in fish cardiac cells. The relative contributions of Na+/Ca2+ exchange and L-type Ca2+ channels to Ca2+ influx are, however, unknown. Using a physiological action potential as the command pulse in voltage-clamped heart cells, we examined sarcolemmal Ca2+ influx through Na+/Ca2+ exchange and L-type Ca2+ channels in crucian carp (Carassius carassius L.) ventricular myocytes. When other cation conductances were blocked, a Ni2+-sensitive current with the characteristic voltage- and time-dependent properties of the Na+/Ca2+ exchange current could be distinguished. At the maximum overshoot voltage of the ventricular action potential (+40 mV; [Na+]i=10 mmol l-1), the density of the Na+/Ca2+ exchange current was 2.99+/-0.27 pA pF-1 for warm-acclimated fish (23 degrees C) and 2.38+/-0.42 pA pF-1 for cold-acclimated fish (4 degrees C) (means +/- s.e.m., N=5-6; not significantly different, P=0.26). The relative contributions of the Na+/Ca2+ exchanger and L-type Ca2+ channels to Ca2+ influx were estimated using two partly different methods. Integration of the Ni2+-sensitive Na+/Ca2+ exchange current and the verapamil- and Cd2+-sensitive L-type Ca2+ current suggests that, during the action potential, approximately one-third of the activating Ca2+ comes through Na+/Ca2+ exchange and approximately two-thirds through L-type Ca2+ channels. An alternative method of analysis, using the inward tail current as a measure of the total sarcolemmal Ca2+ flux from which the Ni2+-sensitive Na+/Ca2+ exchange current was subtracted to obtain the Ca2+ influx through the channels, suggests that L-type Ca2+ channels and Na+/Ca2+ exchange are almost equally important in the activation of contraction. Furthermore, the time course of cell shortening is not adequately explained by sarcolemmal Ca2+ influx through the channels alone, but is well approximated by the sum of Ca2+ influx through the channels and the exchanger. The present results indicate that reverse Na+/Ca2+ exchange in crucian carp ventricular myocytes has sufficient capacity to trigger contraction and suggest that the exchange current makes a significant contribution to contractile Ca2+ during the physiological action potential. The relative significance of channels and exchanger molecules in sarcolemmal Ca2+ entry into crucian carp ventricular myocytes was unaffected by thermal acclimation when determined at 22 degrees C.

Chapter 5 - Membrane Potential and Action Potential

Chapter 12 - Membrane Potential and Action Potential

Effects of reduction in potassium conductance on impulse conduction were studied in squid giant axons. Internal perfusion of axons with tetraethylammonium (TEA) ions reduces G K and causes the duration of action potential to be increased up to 300 ms. This prolongation of action potentials does not change their conduction velocity. The shape of these propagating action potentials is similar to membrane action potentials in TEA. Axons with regions of differing membrane potassium conductances are obtained by perfusing the axon trunk and one of its two main branches with TEA after the second branch has been filled with normal perfusing solution. Although the latter is initially free of TEA, this ion diffuses in slowly. Up until a large amount of TEA has diffused into the second branch, action potentials in the two branches have very different durations. During this period, membrane regions with prolonged action potentials are a source of depolarizing current for the other, and repetitive activity may be initiated at transitional regions. After a single stimulus in either axon region, interactions between action potentials of different durations usually led to rebound, or a short burst, of action potentials. Complex interactions between two axon regions whose action potentials have different durations resembles electric activity recorded during some cardiac arrhythmias.

β-adrenergic regulation of late Na+ current during cardiac action potential is mediated by both PKA and CaMKII

A spherical excitable cell immersed in an electrolyte and subjected to an electric field is considered to study its behavior for Electro-Chemotherapy Treatments (ECT). The total volume is discretized with a three-dimensional lattice to which an electrical network, modeling both the passive and linear behavior of the external electrolyte and of the cytosol than the complex behavior of the ionic fluxes through the cell membrane, is associated. The Electroporation Phenomenon (EP) is considered by modeling the electrically induced pores with a voltage controlled current source governed by the dynamic of the pore density, N, and the current in a single pore. The physiological Action Potential (AP) of a Normal Rat Kidney (NRK) cell is reproduced and the EP is analyzed by looking at the transmembrane voltage (TMV) of the cell exposed to a trapezoidal Pulsed Electric Field (PEF) with a duration of 100us, a rise/fall time of 4us and amplitude of 750V/cm.

1. To obtain information about structural events that occur in axons, changes in light scattering from squid giant axons were measured during action potentials and voltage-clamp steps.2. The scattering changes were measured at several scattering angles. Because the changes in scattering divided by the resting scattering were between 10(-6) and 10(-5), signal-averaging techniques were used to increase the signal-to-noise ratio.3. The scattering changes during the action potential were different at different angles. Two types were found, one at 10-30 degrees (forward angles) and the other at 60-120 degrees (right angles).4. At forward angles, there was a transient scattering decrease during the action potential. The time course of the change was similar to that of the action potential; this change was thought to be potential-dependent.5. At right angles, there was a transient scattering increase during the action potential followed later by a second, longer-lasting increase. Indirect evidence indicated that neither component could be totally potential-dependent.6. To further analyse these effects, scattering was measured during voltage-clamp steps. The changes seen during hyperpolarizing steps were presumed to be potential-dependent; again two different changes were found, one at forward angles and one at right angles.7. The potential-dependent change at right angles occurred with a time course that could be approximated by a single exponential with a time constant tau = 24 musec. The change at forward angles required two exponentials, tau(1) = 23 musec, tau(2) = 900 musec, to represent its time course.8. The size of both potential-dependent changes was proportional to the square of potential. The change at right angles, but not that at forward angles, was increased in size by the addition of butanol or octanol to the bathing solution.

Ectothermic animals don't thrive in the cold: low temperature slows down the heart rate, which tends to decrease its output and makes animals slow and sluggish. However, some fish maintain an active lifestyle in the cold. Upon prolonged exposure to low temperature, these fish recruit compensatory mechanisms that bypass the depressive effect of cold temperature on heart rate, enabling the heart to continue to beat at a high rate and precluding an active lifestyle.The fish heart beats independent of external stimulation due to the tightly regulated firing of action potentials (APs) from a specialized set of heart muscle cells called the pacemaker. This regular firing results from coordinated ion movements in the muscle cells. The cold-induced, compensatory increase in heart rate could be due to alterations in humoral and neural regulation of cardiac pacemaker activity and/or modification of the ionic currents underlying the regular AP firing in the pacemaker.Jaako Haverinen and Matti Vornanen of the University of Joensuu, Finland,were interested in determining if and how thermal compensation of the rainbow trout (Oncorhynchus mykiss) heart occurs at the level of the primary pacemaker cells. Because the exact location of the pacemaker cells in the fish heart is not known, the researchers first located the pacemaker region of the fish heart by systematically impaling spontaneously contracting fish hearts with sharp microelectrodes to record APs. These have a specific shape depending on which heart region they are recorded from. Using this technique,and examining the heart tissue, the team discovered that the primary pacemaker in the rainbow trout heart is located in a small ring of tissue between the sinus venosus, the first chamber of a fish's heart, and the atrium.Armed with this knowledge, the team then enzymatically isolated individual pacemaker cells to find out if cold compensation occurred at the cellular level. Using patch-clamping, the team recorded APs from isolated pacemaker cells from both 4°C (cold)- and 18°C (warm)-acclimated fish at the common temperature of 11°C and found that the duration of pacemaker APs was shorter and the intrinsic pace-making rate higher in cold-compared to warm-acclimated trout, showing that at least part of the compensatory increase in heart rate is inherent to the pacemaker cells.Finally, to understand which ionic mechanisms were responsible for the cold-induced changes in pacemaker AP shape and frequency, the team compared APs recorded from spontaneously contracting pacemaker tissue preparations from warm- and cold-acclimated fish. They added chemical blockers specific to two systems: sarcoplasmic reticulum calcium ion (Ca2+) cycling and the movement of potassium ions (K+) through channels called delayed rectifier K+ channels. Both of these ionic mechanisms are implicated as being important for cardiac pacemaking in mammals and are enhanced in cold-acclimated trout.The team found that blocking sarcoplasmic reticulum Ca2+ cycling did not modify pacemaker AP shape or frequency in cold-acclimated tissue. This, they argue, eliminates the possibility that this mechanism underlies the compensatory increase of heart rate. By contrast, the team discovered that the movement of K+ increased in the cold and could be important for increasing heart rate. When they blocked the K+ channel at the common temperature of 11°C, pacemaker AP frequency and duration decreased more in warm-acclimated preparations than in cold-acclimated ones. The team explains that the greater flow of K+ in pacemaker cells of cold-acclimated trout should theoretically shorten AP duration, increase AP discharge frequency and thus increase heart rate.

Described are studies of propagation of action potentials through inhomogenous axon regions through experiments performed on squid giant axons and by computer simulations. The initial speed of propagation of the action potential is dependent upon the stimulus waveform. For a rectangular pulse of current, the action potential travel initally at a high speed that declines over the distance, reaching a constant speed of propagation at about 1-5 resting length constants; this distance depends on the stimulus strength. additional experiments studied the effects of changing the axon diameter and of introducing a temperature step. It was found that the propagated action potential suffers profound modification in shape and velocity as it reaches the region of transition. In both cases, it was possible to obtain reflected action potentials. A region of increased effective diameter was produced experimentally in the squid giant axon by insertion of an axial wire as usually employed in voltage clamps. It was found that the action potential, at the axial wire tip region, undergoes shape changes similar to those obtained tn simulations of a region of increased diameter as in a junction with the axon and soma in motor neurons. It is conducluded that the gaint axon can be used to reproduce simple electrical behaviors in other structures.-Ramón, F., R. W. Joyner and J.W. Moore. Propagation of action potentials in inhomogeneous axon regions.