Theorizing how the brain encodes consciousness based on negentropic entanglement.

The physicality of subjectivity is explained through a theoretical conceptualization of guidance waves informing meaning in negentropically entangled non-electrolytic brain regions. Subjectivity manifests its influence at the microscopic scale of matter originating from de Broglie 'hidden' thermodynamics as action of guidance waves. The preconscious experienceability of subjectivity is associated with a nested hierarchy of microprocesses, which are actualized as a continuum of patterns of discrete atomic microfeels (or "qualia"). The mechanism is suggested to be through negentropic entanglement of hierarchical thermodynamic transfer of information as thermo-qubits originating from nonpolarized regions of actin-binding proteinaceous structures of nonsynaptic spines. The resultant continuous stream of intrinsic information entails a negentropic action (or experiential flow of thermo-quantum internal energy that results in a negentropic force) which is encoded through the non-zero real component of the mean approximation of the negentropic force as a 'consciousness code'. Consciousness consisting of two major subprocesses: (1) preconscious experienceability and (2) conscious experience. Both are encapsulated by nonreductive physicalism and panexperiential materialism. The subprocess (1) governing "subjectivity" carries many microprocesses leading to the actualization of discrete atomic microfeels by the 'consciousness code'. These atomic microfeels constitute internal energy that results in the transfer intrinsic information in terms of thermo-qubits. These thermo-qubits are realized as thermal entropy and sensed by subprocess (2) governing "self-awareness" in conscious experience.

Nonsynaptic plasticity model of long-term memory engrams.

Using steady-state electrical properties of non-ohmic dendrite based on cable theory, we derive electrotonic potentials that do not change over time and are localized in space. We hypothesize that clusters of such stationary, local and permanent pulses are the electrical signatures of enduring memories which are imprinted through nonsynaptic plasticity, encoded through epigenetic mechanisms, and decoded through electrotonic processing. We further hypothesize how retrieval of an engram is made possible by integration of these permanently imprinted standing pulses in a neural circuit through neurotransmission in the extracellular space as part of conscious recall that acts as a guiding template in the reconsolidation of long-term memories through novelty characterized by uncertainty that arises when new fragments of memories reinstate an engram by way of nonsynaptic plasticity that permits its destabilization. Collectively, these findings seem to reinforce this hypothesis that electrotonic processing in non-ohmic dendrites yield insights into permanent electrical signatures that could reflect upon enduring memories as fragments of long-term memory engrams.

Induced mitochondrial membrane potential for modeling solitonic conduction of electrotonic signals.

A cable model that includes polarization-induced capacitive current is derived for modeling the solitonic conduction of electrotonic potentials in neuronal branchlets with microstructure containing endoplasmic membranes. A solution of the nonlinear cable equation modified for fissured intracellular medium with a source term representing charge 'soakage' is used to show how intracellular capacitive effects of bound electrical charges within mitochondrial membranes can influence electrotonic signals expressed as solitary waves. The elastic collision resulting from a head-on collision of two solitary waves results in localized and non-dispersing electrical solitons created by the nonlinearity of the source term. It has been shown that solitons in neurons with mitochondrial membrane and quasi-electrostatic interactions of charges held by the microstructure (i.e., charge 'soakage') have a slower velocity of propagation compared with solitons in neurons with microstructure, but without endoplasmic membranes. When the equilibrium potential is a small deviation from rest, the nonohmic conductance acts as a leaky channel and the solitons are small compared when the equilibrium potential is large and the outer mitochondrial membrane acts as an amplifier, boosting the amplitude of the endogenously generated solitons. These findings demonstrate a functional role of quasi-electrostatic interactions of bound electrical charges held by microstructure for sustaining solitons with robust self-regulation in their amplitude through changes in the mitochondrial membrane equilibrium potential. The implication of our results indicate that a phenomenological description of ionic current can be successfully modeled with displacement current in Maxwell's equations as a conduction process involving quasi-electrostatic interactions without the inclusion of diffusive current. This is the first study in which solitonic conduction of electrotonic potentials are generated by polarization-induced capacitive current in microstructure and nonohmic mitochondrial membrane current.

Erratum: Solitonic conduction of electrotonic signals in neuronal branchlets with polarized microstructure.

A correction to this article has been published and is linked from the HTML version of this paper. The error has been fixed in the paper.

Solitonic conduction of electrotonic signals in neuronal branchlets with polarized microstructure.

A model of solitonic conduction in neuronal branchlets with microstructure is presented. The application of cable theory to neurons with microstructure results in a nonlinear cable equation that is solved using a direct method to obtain analytical approximations of traveling wave solutions. It is shown that a linear superposition of two oppositely directed traveling waves demonstrate solitonic interaction: colliding waves can penetrate through each other, and continue fully intact as the exact pulses that entered the collision. These findings indicate that microstructure when polarized can sustain solitary waves that propagate at a constant velocity without attenuation or distortion in the absence of synaptic transmission. Solitonic conduction in a neuronal branchlet arising from polarizability of its microstructure is a novel signaling mode of electrotonic signals in thin processes (<0.5 µm diameter).

A fuzzy integral method based on the ensemble of neural networks to analyze fMRI data for cognitive state classification across multiple subjects.

The huge number of voxels in fMRI over time poses a major challenge to for effective analysis. Fast, accurate, and reliable classifiers are required for estimating the decoding accuracy of brain activities. Although machine-learning classifiers seem promising, individual classifiers have their own limitations. To address this limitation, the present paper proposes a method based on the ensemble of neural networks to analyze fMRI data for cognitive state classification for application across multiple subjects. Similarly, the fuzzy integral (FI) approach has been employed as an efficient tool for combining different classifiers. The FI approach led to the development of a classifiers ensemble technique that performs better than any of the single classifier by reducing the misclassification, the bias, and the variance. The proposed method successfully classified the different cognitive states for multiple subjects with high accuracy of classification. Comparison of the performance improvement, while applying ensemble neural networks method, vs. that of the individual neural network strongly points toward the usefulness of the proposed method.

The Two-Brains Hypothesis: Towards a guide for brain-brain and brain-machine interfaces.

Great advances have been made in signaling information on brain activity in individuals, or passing between an individual and a computer or robot. These include recording of natural activity using implants under the scalp or by external means or the reverse feeding of such data into the brain. In one recent example, noninvasive transcranial magnetic stimulation (TMS) allowed feeding of digitalized information into the central nervous system (CNS). Thus, noninvasive electroencephalography (EEG) recordings of motor signals at the scalp, representing specific motor intention of hand moving in individual humans, were fed as repetitive transcranial magnetic stimulation (rTMS) at a maximum intensity of 2.0[Formula: see text]T through a circular magnetic coil placed flush on each of the heads of subjects present at a different location. The TMS was said to induce an electric current influencing axons of the motor cortex causing the intended hand movement: the first example of the transfer of motor intention and its expression, between the brains of two remote humans. However, to date the mechanisms involved, not least that relating to the participation of magnetic induction, remain unclear. In general, in animal biology, magnetic fields are usually the poor relation of neuronal current: generally "unseen" and if apparent, disregarded or just given a nod. Niels Bohr searched for a biological parallel to complementary phenomena of physics. Pertinently, the two-brains hypothesis (TBH) proposed recently that advanced animals, especially man, have two brains i.e., the animal CNS evolved as two fundamentally different though interdependent, complementary organs: one electro-ionic (tangible, known and accessible), and the other, electromagnetic (intangible and difficult to access) - a stable, structured and functional 3D compendium of variously induced interacting electro-magnetic (EM) fields. Research on the CNS in health and disease progresses including that on brain-brain, brain-computer and brain-robot engineering. As they grow even closer, these disciplines involve their own unique complexities, including direction by the laws of inductive physics. So the novel TBH hypothesis has wide fundamental implications, including those related to TMS. These require rethinking and renewed research engaging the fully complementary equivalence of mutual magnetic and electric field induction in the CNS and, within this context, a new mathematics of the brain to decipher higher cognitive operations not possible with current brain-brain and brain-machine interfaces. Bohr may now rest.

A hybrid method for classifying cognitive states from fMRI data.

Functional magnetic resonance imaging (fMRI) makes it possible to detect brain activities in order to elucidate cognitive-states. The complex nature of fMRI data requires under-standing of the analyses applied to produce possible avenues for developing models of cognitive state classification and improving brain activity prediction. While many models of classification task of fMRI data analysis have been developed, in this paper, we present a novel hybrid technique through combining the best attributes of genetic algorithms (GAs) and ensemble decision tree technique that consistently outperforms all other methods which are being used for cognitive-state classification. Specifically, this paper illustrates the combined effort of decision-trees ensemble and GAs for feature selection through an extensive simulation study and discusses the classification performance with respect to fMRI data. We have shown that our proposed method exhibits significant reduction of the number of features with clear edge classification accuracy over ensemble of decision-trees.

Neuronal models in infinite-dimensional spaces and their finite-dimensional projections: Part II.

Application of comparison theorem is used to examine the validitiy of the "lumped parameter assumption" in describing the behavior of solutions of the continuous cable equation U(t) = DU(xx)+f(U) with the discrete cable equation dV(n)/dt = d*(V(n+1) - 2V(n) + V(n-1)) + f(V(n)), where f is a nonlinear functional describing the internal diffusion of electrical potential in single neurons. While the discrete cable equation looks like a finite difference approximation of the continuous cable equation, solutions of the two reveal significantly different behavior which imply that the compartmental models (spiking neurons) are poor quantifiers of neurons, contrary to what is commonly accepted in computational neuroscience.

Intracellular capacitive effects of polarized proteins in dendrites.

Passive dendrites become active as a result of electrostatic interactions by dielectric polarization in proteins in a segment of a dendrite. The resultant nonlinear cable equation for a cylindrical volume representation of a dendritic segment is derived from Maxwell's equations under assumptions: (i) the electric field is restricted longitudinally along the cable length; (ii) extracellular isopotentiality; (iii) quasi-electrostatic conditions; (iv) isotropic membrane and homogeneous medium with constant conductivity; and (v) protein polarization contributes to intracellular capacitive effects through a well defined nonlinear capacity-voltage characteristic; (vi) intracellular resistance and capacitance in parallel are connected to the membrane in series. Under the above hypotheses, traveling wave solutions of the cable equation are obtained as propagating fronts of electrical excitation associated with capacitive charge-equalization and dispersion of continuous polarization charge densities in an Ohmic cable. The intracellular capacitative effects of polarized proteins in dendrites contribute to the conduction process.

Associable representations as field of influence for dynamic cognitive processes.

In earlier models, synaptic plasticity forms the basis for cellular signaling underlying learning and memory. However, synaptic computation of learning and memory in the brain remains controversial. In this paper, we discuss ways in which synaptic plasticity remodels subcellular networks by deflecting trajectories in neuronal state-space as regulating patterns for the synthesis of dynamic continuity that form cognitive networks of associable representations through endogenous dendritic coding to consolidate memory.

Analytical solution of reaction-diffusion equations for calcium wave propagation in a starburst amacrine cell.

A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 µm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.

Cellular inhibitory behavior underlying the formation of retinal direction selectivity in the starburst network.

Optical imaging of dendritic calcium signals provided evidence of starburst amacrine cells exhibiting calcium bias to somatofugal motion. In contrast, it has been impractical to use a dual-patch clamp technique to record membrane potentials from both proximal dendrites and distal varicosities of starburst amacrine cells in order to unequivocally prove that they are directionally sensitive to voltage, as was first suggested almost two decades ago. This paper aims to extend the passive cable model to an active cable model of a starburst amacrine cell that is intrinsically dependent on the electrical properties of starburst amacrine cells, whose various macroscopic currents are described quantitatively. The coupling between voltage and calcium just below the membrane results in a voltage-calcium system of coupled nonlinear Volterra integral equations whose solutions must be integrated into a prescribed model for example, for a synaptic couplet of starburst amacrine cells. Networks of starburst amacrine cells play a fundamental role in the retinal circuitry underlying directional selectivity. It is suggested that the dendritic plexus of starburst amacrine cells provides the substrate for the property of directional selectivity, while directional selectivity is a property of the exclusive layerings and confinement of their interconnections within the sublaminae of the inner plexiform layer involving cone bipolar cells and directionally selective ganglion cells.

A dendritic cable model for the amplification of synaptic potentials by an ensemble average of persistent sodium channels.

The persistent sodium current density (I(NaP)) at the soma measured with the 'whole-cell' patch-clamp recording method is linearized about the resting state and used as a current source along the dendritic cable (depicting the spatial distribution of voltage-dependent persistent sodium ionic channels). This procedure allows time-dependent analytical solutions to be obtained for the membrane depolarization. Computer simulated response to a dendritic current injection in the form of synaptically-induced voltage change located at a distance from the recording site in a cable with unequally distributed persistent sodium ion channel densities per unit length of cable (the so-called 'hot-spots') is used to obtain conclusions on the density and distribution of persistent sodium ion channels. It is shown that the excitatory postsynaptic potentials (EPSPs) are amplified if hot-spots of persistent sodium ion channels are spatially distributed along the dendritic cable, with the local density of I(NaP) with respect to the recording site shown to specifically increase the peak amplitude of the EPSP for a proximally placed synaptic input, while the spatial distribution of I(NaP) serves to broaden the time course of the amplified EPSP. However, in the case of a distally positioned synaptic input, both local and nonlocal densities yield an approximately identical enhancement of EPSPs in contradiction to the computer simulations performed by Lipowsky et al. [J. Neurophysiol. 76 (1996) 2181]. The results indicate that persistent sodium channels produce EPSP amplification even when their distribution is relatively sparse (i.e. , approximately 1-2% of the transient sodium channels are found in dendrites of CA1 hippocampal pyramidal neurons). This gives a strong impetus for the use of the theory as a novel approach in the investigation of synaptic integration of signals in active dendrites represented as ionic cables.

Theoretical analysis of the amplification of synaptic potentials by small clusters of persistent sodium channels in dendrites.

We extend on the work developed by R.R. Poznanski and J. Bell from a linearized somatic persistent sodium current source to a non-linear representation of the dendritic Na(+)P current source associated with a small number of persistent sodium channels. The main objective is to investigate the modulation in the amplification of excitatory postsynaptic potentials (EPSPs) in dendrites studded with persistent sodium channels. The relation between membrane potential (V) and persistent sodium current density (I(NaP)) is approximated heuristically with a sigmoidal function and the resultant cable equation is solved analytically using a regular perturbation expansion and Green's function techniques. The transient simulated (non-evoked) response is found as a result of current injection in the form of synaptically induced voltage change located at a distance from the recording site in a cable with a uniform distribution of ion channel densities per unit length of cable (the so-called 'hot-spots') and with the conductance of each hot-spot (i.e., number of channels per hot-spot) assumed to be a constant. The results show an amplification in the observed EPSPs to be compatible with the experimentally derived estimates, and in addition a saturation in the amplification is observed indicating an optimum number of ionic channels.

Syncytial integration by a network of coupled bipolar cells in the retina.

A model system for syncytial integration is the outer vertebrate retina, where graded signals or electrotonic potentials interact laterally via gap junctions to form an integrated response that is relayed by chemical synapses to the next layer of interconnected cells. Morphological and physiological experiments confirm that bipolar cells form quasisyncytial lattices, and so this review will aim to address two important issues: the function of coupling in visual information processing and the construction of a robust mathematical model that can adequately simulate signal spread in the bipolar cell syncytium. It is shown that the role of coupling in bipolar cells differs from that associated in the presynaptic networks, namely, loss in spatial resolution in order to increase the signal-to-noise ratio. The intrinsic membrane properties of bipolar cells which give rise to voltage-dependent currents are inactive over the normal in vivo operating range of membrane potential and may be shunted as a direct result of electrotonic coupling, suppressing any possibility of action potential propagation in the bipolar cell syncytium. It is therefore speculated that the mechanisms underlying processing of information in bipolar networks are dependent on the structure of bipolar cells and in particular, on the presence of gap junctions. It is proposed that a three-dimensional model which incorporates the spatial properties of each bipolar cell in the network in the form of a leaky cable is the most likely model to simulate signal spread in the bipolar cell syncytium in vivo. This is because discrete network models represent each bipolar cell in the syncytium as isopotential units without any spatial structure, and thus are unable to reproduce the temporal characteristics of electrotonic potential spread within the central receptive field of bipolar cells.

Subthreshold response to white-noise current input in a tapering cable model of a neuron.

The expectation (mean) and variance of the depolarization in the absence of a threshold for action-potential generation is obtained in a neuron model represented by a tapering equivalent cable with a random (white noise) synaptic input current at a point along the dendrites. The results show that the introduction of a taper in the equivalent-cable representation of the neuron produces larger values for both the expectation and variance which are neither insensitive nor symmetrical with respect to the location of the input. It is also shown that taper extends the invariance of the variability in the steady-state somatic response to proximally located random inputs, implying that only small changes in the noisiness of the somatic response occur for a random input located in the dendrites.

Transient response in a tapering cable model with somatic shunt.

Transient voltage responses (charging transients) to current stimulation are presented for a non-linearly tapering cable model of a neurone with a shunt at the soma. Exact expressions are given for the time constants of exponential decay expressed in terms of the passive membrane time constant and the taper rate constant. The effect of a somatic shunt on the membrane potential transients at the soma is shown to result in a more rapid final decay of the membrane potential than simple passive decay with membrane time constant. The theoretical analysis should be of use to electrophysiologists wishing to interpret their experimentally observed charging transients recorded at the some in terms of cable properties of neurones in vivo.

Electrotonic coupling between two CA3 hippocampal pyramidal neurons: a distributed cable model with somatic gap-junction.

A model of a pair of electrotonically coupled CA3 hippocampal pyramidal neurons is presented. Each neuron is represented by a tapered equivalent cable attached to an isopotential soma. The synaptic potential in a neuron soma is determined as a consequence of electrical coupling to another soma that receives a synaptic input on its dendritic tree. Estimates of the coupling resistances, soma input resistances and soma-to-dendritic tree conductance ratio show that a substantial current may arise in a neuron as a consequence of synaptic activity in a neuron coupled to it. The small increase in decay time due to coupling in the model indicates that actual coupling is between more than just pairs of neurons.

Extracellular current flow and potential during quantal transmission from varicosities in a smooth muscle syncytium.

A discrete model has been developed that describes the extracellular current that flows in a smooth muscle syncytium upon the secretion of a quantum of transmitter onto a smooth muscle cell in the syncytium. This allows a description to be given of the current (called the excitatory junctional current (EJC)) recorded by an electrode of given diameter placed on the surface of the muscle, during synaptic transmission from a varicosity situated anywhere in the muscle. The EJC is of maximum negative amplitude when the varicosity is at the surface of the muscle near the inside rim of the electrode and decreases as the varicosity moves to the centre of the electrode. It is of maximum positive amplitude when the varicosity is at the surface near the outside rim of the electrode and declines rapidly in amplitude as the varicosity is removed further from the outside rim. Smaller diameter electrodes give larger EJCs than larger diameter electrodes for most positions of the varicosity on the surface of the muscle. The EJC amplitude declines for varicosities beneath the electrode that are not on the surface of the muscle, but deep in the tissue. The rate of this decline is greater the smaller the diameter of the electrode. The time-course of the EJC is largely invariant under changes in the position of the varicosity with respect to the recording electrode. Changes in the polarity of the current flow during a single EJC can occur, however, if two varicosities secrete transmitter simultaneously, one inside the electrode and one outside, and the time-course of the currents due to the individual varicosities is either the same or slightly different. This theoretical work has been used to interpret a number of recent experimental studies of extracellular current flow during autonomic neuromuscular transmission.