Towards an artificial brain

Three components of a brain model operating on neuromolecular computing principles are described. The first component comprises neurons whose input-output behavior is controlled by significant internal dynamics. Models of discrete enzymatic neurons, reaction-diffusion neurons operating on the basis of the cyclic nucleotide cascade, and neurons controlled by cytoskeletal dynamics are described. The second component of the model is an evolutionary learning algorithm which is used to mold the behavior of enzyme-driven neurons or small networks of these neurons for specific function, usually pattern recognition or target seeking tasks. The evolutionary learning algorithm may be interpreted either as representing the mechanism of variation and natural selection acting on a phylogenetic time scale, or as a conceivable ontogenetic adaptation mechanism. The third component of the model is a memory manipulation scheme, called the reference neuron scheme. In principle it is capable of orchestrating a repertoire of enzyme-driven neurons for coherent function. The existing implementations, however, utilize simple neurons without internal dynamics. Spatial navigation and simple game playing (using tic-tac-toe) provide the task environments that have been used to study the properties of the reference neuron model. A memory-based evolutionary learning algorithm has been developed that can assign credit to the individual neurons in a network. It has been run on standard benchmark tasks, and appears to be quite effective both for conventional neural nets and for networks of discrete enzymatic neurons. The models have the character of artificial worlds in that they map the hierarchy of processes in the brain (at the molecular, neuronal, and network levels), provide a task environment, and use this relatively self-contained setup to develop and evaluate learning and adaptation algorithms.     

A stochastic model and a functional central limit theorem for information processing in large systems of neurons

The paper deals with information transmission in large systems of neurons. We model the membrane potential in a single neuron belonging to a cell tissue by a non time-homogeneous Cox-Ingersoll-Ross type diffusion; in terms of its time-varying expectation, this stochastic process can convey deterministic signals. We model the spike train emitted by this neuron as a Poisson point process compensated by the occupation time of the membrane potential process beyond the excitation threshold. In a large system of neurons 1≤i≤N processing independently the same deterministic signal, we prove a functional central limit theorem for the pooled spike train collected from the N neurons. This pooled spike train allows to recover the deterministic signal, up to some shape transformation which is explicit.     

Microinjection of cyclic nucleotides provides evidence for a diffusional mechanism of intraneuronal control

Cyclic 3′,5′-AMP and cyclic 3′,5′-GMP injected into large neurons of the snail Helix lucorum altered neuron activity. The effect of cAMP is usually depolarizing and that of cGMP hyperpolarizing. The results are specific for 3′,5′-cyclic nucleotides. The experiments support the hypothesis that reaction-diffusion processes involving cyclic nucleotides from the basis of an intraneuronal system of information processing.     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior

The oculomotor integrator is a network that is composed of neurons in the medial vestibular nuclei and nuclei prepositus hypoglossi in the brainstem. Those neurons act approximately as fractional integrators of various orders, converting eye velocity commands into signals that are intermediate between velocity and position. The oculomotor integrator has been modeled as a network of linear neural elements, the time constants of which are lengthened by positive feedback through reciprocal inhibition. In this model, in which each neuron reciprocally inhibits its neighbors with the same Gaussian profile, all model neurons behave as identical, first-order, low-pass filters with dynamics that do not match the variable, approximately fractional-order dynamics of the neurons that compose the actual oculomotor integrator. Fractional-order integrators can be approximated by weighted sums of first-order, low-pass filters with diverse, broadly distributed time constants. Dynamic systems analysis reveals that the model integrator indeed has many broadly distributed time constants. However, only one time constant is expressed in the model due to the uniformity of its network connections. If the model network is made nonuniform by removing the reciprocal connections to and from a small number of neurons, then many more time constants are expressed. The dynamics of the neurons in the nonuniform network model are variable, approximately fractional-order, and resemble those of the neurons that compose the actual oculomotor integrator. Completely removing the connections to and from a neuron is equivalent to eliminating it, an operation done previously to demonstrate the robustness of the integrator network model. Ironically, the resulting nonuniform network model, previously supposed to represent a pathological integrator, may in fact represent a healthy integrator containing neurons with realistically variable, approximately fractional-order dynamics. Received: 8 August 1997 / Accepted in revised form: 18 June 1998     

Gamma oscillations as a mechanism for selective information transmission

In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far, concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons. The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron, the quadratic integrate and fire neuron and the Hodgkin–Huxley (HH) neuron] and that of excitatory–inhibitory coupled pairs of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information transmission is enhanced for short membrane time constants of the neuron.     

Schema design and implementation of the grasp-related mirror neuron system

 Mirror neurons within a monkey's premotor area F5 fire not only when the monkey performs a certain class of actions but also when the monkey observes another monkey (or the experimenter) perform a similar action. It has thus been argued that these neurons are crucial for understanding of actions by others. We offer the hand-state hypothesis as a new explanation of the evolution of this capability: the basic functionality of the F5 mirror system is to elaborate the appropriate feedback – what we call the hand state– for opposition-space based control of manual grasping of an object. Given this functionality, the social role of the F5 mirror system in understanding the actions of others may be seen as an exaptation gained by generalizing from one's own hand to an other's hand. In other words, mirror neurons first evolved to augment the “canonical” F5 neurons (active during self-movement based on observation of an object) by providing visual feedback on “hand state,” relating the shape of the hand to the shape of the object. We then introduce the MNS1 (mirror neuron system 1) model of F5 and related brain regions. The existing Fagg–Arbib–Rizzolatti–Sakata model represents circuitry for visually guided grasping of objects, linking the anterior intraparietal area (AIP) with F5 canonical neurons. The MNS1 model extends the AIP visual pathway by also modeling pathways, directed toward F5 mirror neurons, which match arm–hand trajectories to the affordances and location of a potential target object. We present the basic schemas for the MNS1 model, then aggregate them into three “grand schemas”– visual analysis of hand state, reach and grasp, and the core mirror circuit – for each of which we present a useful implementation (a non-neural visual processing system, a multijoint 3-D kinematics simulator, and a learning neural network, respectively). With this implementation we show how the mirror system may learnto recognize actions already in the repertoire of the F5 canonical neurons. We show that the connectivity pattern of mirror neuron circuitry can be established through training, and that the resultant network can exhibit a range of novel, physiologically interesting behaviors during the process of action recognition. We train the system on the basis of final grasp but then observe the whole time course of mirror neuron activity, yielding predictions for neurophysiological experiments under conditions of spatial perturbation, altered kinematics, and ambiguous grasp execution which highlight the importance of the timingof mirror neuron activity. Received: 6 August 2001 / Accepted in revised form: 5 February 2002     

Synaptically released zinc: Physiological functions and pathological effects

In addition to its familiar role as a component of metalloproteins, zinc is also sequestered in the presynaptic vesicles of a specialized type of neurons called `zinc-containing' neurons. Here we review the physiological and pathological effects of the release of zinc from these zinc-containing synaptic terminals. The best-established physiological role of synaptically released zinc is the tonic modulation of brain excitability through modulation of amino acid receptors; prominent pathological effects include acceleration of plaque deposition in Alzheimer's disease and exacerbation of excitotoxic neuron injury. Synaptically released zinc functions as a conventional synaptic neurotransmitter or neuromodulator, being released into the cleft, then recycled into the presynaptic terminal. Beyond this, zinc also has the highly unconventional property that it passes into postsynaptic neurons during synaptic events, functioning analogously to calcium in this regard, as a transmembrane neural signal. To stimulate comparisons of zinc signals with calcium signals, we have compiled a list of the important parameters of calcium signals and zinc signals. More speculatively, we hypothesize that zinc signals may loosely mimic phosphate `signals' in the sense that signal zinc ions may commonly bind to proteins in a lasting manner (i.e., `zincylating' the proteins) with consequential changes in protein structure and function.     

Application of information networks to a theory of vision

Some principles of information theory are utilized in the design of neural nets of the McCulloch-Pitts type. In particular, problems are considered where signals from several neurons must pass through a single one, thus resulting in a “bottleneck” in the flow of information, an abstract model of the corresponding bottleneck from the retina to the optic nerve. The first part of the paper deals with a construction of a McCulloch-Pitts net in which the redundancy in the messages originating in two neurons is utilized so that the messages can be sent over a single neuron with little loss of information. In the second part, messages from a set of neurons are “pumped” into two channel neurons. The optimum connection scheme is computed for this case, i.e, one resulting in a minimum loss of information. Possible biological implications of this approach are indicated.     

Statistical independence and neural computation in the leech ganglion

 In this report, the input/output relations in an isolated ganglion of the leech Hirudo medicinalis were studied by simultaneously using six or eight suction pipettes and two intracellular electrodes. Sensory input was mimicked by eliciting action potentials in mechanosensory neurons with intracellular electrodes. The integrated neural output was measured by recording extracellular voltage signals with pipettes sucking the roots and the connectives. A single evoked action potential activated electrical activity in at least a dozen different neurons, some of which were identified. This electrical activity was characterized by a high degree of temporal and spatial variability. The action potentials of coactivated neurons, i.e. activated by the same mechanosensory neuron, did not show any significant pairwise correlation. Indeed, the analysis of evoked action potentials indicates clear statistical independence among coactivated neurons, presumably originating from the independence of synaptic transmission at distinct synapses. This statistical independence may be used to increase reliability when neuronal activity is averaged or pooled. It is suggested that statistical independence among coactivated neurons may be a usual property of distributed processing of neuronal networks and a basic feature of neural computation. Received: 20 September 1999 / Accepted in revised form: 3 March 2000     

美洲大蠊中枢DUM神经元的分离和电压门控Na+电流的记录

【目的】建立美洲大蠊Periplaneta americana中枢神经系统背侧不成对中间神经元（dorsal unpaired median neurons, DUM neurons）的分离方法和DUM神经元电生理实验模型。【方法】IA型胶原酶法消化美洲大蠊末端腹神经节, 机械吹打得到DUM神经元细胞, 运用膜片钳技术记录DUM神经元细胞电压门控Na+电流。【结果】分离得到的DUM神经元细胞状态良好, 具有DUN神经元典型的梨状形态和表面特征。以膜片钳全细胞方式记录到的Na+电流符合钠通道电流特征。【结论】IA型胶原酶消化得到美洲大蠊DUM神经元细胞的方法可靠, 能稳定地记录到Na+电流。本文描述的方法为昆虫神经细胞的电生理机制研究提供一个可用的实验模型。     

A novel key–lock mechanism for inactivating amino acid neurotransmitters during transit across extracellular space

There are two kinds of neurotransmissions that occur in brain. One is neuron to neuron at synapses, and the other is neuron to glia via extracellular fluid (ECF), both of which are important for maintenance of proper neuronal functioning. For neuron to neuron communications, several potent amino acid neurotransmitters are used within the confines of synaptic space. However, their presence at elevated concentrations in extra-synaptic space could be detrimental to well organized neuronal functioning. The significance of the synthesis and release of N-acetylaspartylglutamate (NAAG) by neurons has long been a puzzle since glutamate (Glu) itself is the “key” that can interact with all Glu receptors on membranes of all cells. Nonetheless, neurons synthesize this acetylated dipeptide, which cannot be catabolized by neurons, and release it to ECF where its specific physiological target is the Glu metabotropic receptor 3 on the surface of astrocytes. Since Glu is excitotoxic at elevated concentrations, it is proposed that formation and release of NAAG by neurons allows large quantities of Glu to be transported in ECF without the risk of injurious excitotoxic effects. The metabolic mechanism used by neurons is a key–lock system to detoxify Glu during its intercellular transit. This is accomplished by first synthesizing N-acetylaspartate (NAA), and then joining this molecule via a peptide bond to Glu. In this paper, a hypothesis is presented that neurons synthesize a variety of relatively nontoxic peptides and peptide derivatives, including NAA, NAAG, homocarnosine (γ-aminobutyrylhistidine) and carnosine (β-alanylhistidine) from potent excitatory and inhibitory amino acids for the purpose of releasing them to ECF to function as cell-specific neuron-to-glia neurotransmitters.     

Effect of intracellular injection of cyclic amp on electrical characteristics of identified neurons in Helix pomatia

The effect of intracellular iontophoretic injection of cyclic AMP on electrical activity of neurons RPa1, RPa3, LPa2, LPa3, and LPl1 in the corresponding ganglia ofHelix pomatia was investigated. Injection of cyclic AMP into neuron LPl1 was found to cause the appearance of rhythmic activity (if the neuron was originally "silent"), an increase in the frequency of spike generation (if the neuron had rhythmic activity), and a decrease in amplitude of waves of membrane potential, in the duration of the interval between bursts, and in the number of action potentials in the burst (if the neuron demonstrated bursting activity). In the remaining "silent" neurons injection of cyclic AMP led to membrane depolarization. Injection of cyclic AMP into neurons whose membrane potential was clamped at the resting potential level evoked the development of an inward transmembrane current (cyclic AMP current), the rate of rise and duration of which increased proportionally to the size and duration of the injection. Theophylline in a concentration of 1 mM led to an increase in the amplitude and duration of the cyclic AMP current by about 50%. It is concluded that a change in the cyclic AMP concentration within the nerve cell may modify the ionic permeability of its membrane and, correspondingly, its electrical activity.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 12, No. 5, pp. 517–525, September–October, 1980.     

Zebrafish Rohon-Beard Neuron Development: Cdk5 in the Midst

Cyclin-dependent kinase 5 (cdk5) is a proline-directed serine/threonine kinase that is activated mostly by association with its activators, p35 and p39. Initially projected as a neuron-specific kinase, cdk5 is expressed ubiquitously and its kinase activity solely depends on the presence of its activators, which are also found in some non-neuronal tissues. As a multifunctional protein, cdk5 has been linked to axonogenesis, cell migration, exocytosis, neuronal differentiation and apoptosis. Cdk5 plays a critical role in functions other than normal physiology, especially in neurodegeneration. Its contribution to both normal physiological as well as pathological processes is mediated by its specific substrates. Cdk5-null mice are embryonically lethal, therefore making it difficult to study precisely what cdk5 does to the nervous system at early stages of development, be it neuron development or programmed cell death. Zebrafish model system bypasses the impediment, as it is amenable to reverse genetics studies. One of the functions that we have followed for the cdk5 ortholog in zebrafish in vivo is its effect on the Rohon-Beard (RB) neurons. RB neurons are the primary sensory spinal neurons that die during the first two days of zebrafish development eventually to be replaced by the dorsal root ganglia (DRG). Based on ours studies and others’, here we discuss possible mechanisms that may be involved in cdk5’s role in RB neuron development and survival.     

Visual channels, Hebbian assemblies and the effect of Hebb's rule

 A model of sensory learning is proposed that is based upon Hebb's rule, where Hebb's rule has been generalised by introducing a stabilising function representing some feedback process within or at the adapting (cortical) neuron, preventing synaptic weights from increasing without limit. It will be shown that neurons adapting according to this stabilised Hebb rule will turn into a matched filter for that part of the stimulus pattern that covers the receptive field of a neuron. It follows that the presentation of a stimulus pattern may imply the formation of a set of neurons with overlapping receptive fields, where each neuron has adapted to a certain part of the stimulus. Making simplifying assumptions about the detection process, the model will be illustrated, fitting it to data from Meinhardt and Mortensen [Meinhardt G, Mortensen U (1998) Biol Cybern 79:413–425] which are not compatible with the classical matched filter model introduced by Hauske et al. [Hauske G, Wolf W, Lupp U (1976) Biol Cybern 22:181–188]. Received: 10 May 1999 / Accepted in revised form: 22 October 1999     

Tuning bat LSO neurons to interaural intensity differences through spike-timing dependent plasticity

Bats, like other mammals, are known to use interaural intensity differences (IID) to determine azimuthal position. In the lateral superior olive (LSO) neurons have firing behaviors which vary systematically with IID. Those neurons receive excitatory inputs from the ipsilateral ear and inhibitory inputs from the contralateral one. The IID sensitivity of a LSO neuron is thought to be due to delay differences between the signals coming from both ears, differences due to different synaptic delays and to intensity-dependent delays. In this paper we model the auditory pathway until the LSO. We propose a learning scheme where inputs to LSO neurons start out numerous with different relative delays. Spike timing-dependent plasticity (STDP) is then used to prune those connections. We compare the pruned neuron responses with physiological data and analyse the relationship between IID’s of teacher stimuli and IID sensitivities of trained LSO neurons.     

Frequency sensitivity in Hodgkin–Huxley systems

 The frequency sensitivity of weak periodic signal detection has been studied via numerical simulations for both a single neuron and a neuronal network. The dependence of the critical amplitude of the signal upon its frequency and a resonance between the intrinsic oscillations of a neuron and the signal could account for the frequency sensitivity. In the presence of both a subthreshold periodic signal and noise, the signal-to-noise ratio (SNR) of the output of either a single neuron or a neuronal network present the typical characteristics of stochastic resonance. In particular, there exists a frequency-sensitive range of 30–100 Hz, and for signals with frequencies within this range the SNRs have large values. This implies that the system under consideration (a single neuron or a neuronal network) is more sensitive to the detection of periodic signals, and the frequency sensitivity may be of a functional significance to signal processing. Received: 26 October 1999 / Accepted in revised form: 25 July 2000     

Synaptically released zinc: neuromodulator and toxin

In addition to its familiar role as a component of metalloproteins, zinc is also sequestered in the presynaptic vesicles in ‘zinc‐containing’ neurons. The best‐established physiological role of synaptically released zinc is the tonic modulation of brain excitability through modulation of amino acid receptors; prominent pathological effects include acceleration of plaque deposition in Alzheimer's disease and exacerbation of excitotoxic neuron injury. Synaptically released zinc functions as a conventional synaptic neurotransmitter or neuromodulator being released into the cleft then recycled into the postsynaptic neurons during synaptic events, functioning analogously to calcium in this regard, as a transmembrane neural signal. To stimulate comparisons of zinc signals with calcium signals, we have compiled a list of the important parameters of calcium signals and zinc signals. More speculatively, we hypothesize that zinc signals may loosely mimic phosphate signals in the sense that signal zinc ions may commonly bind to proteins in a lasting manner, as a result changing their structure and function.     

Spatial firing patterns of auditory neuron network modelling by computer simulation

This communication examines, in digital computer simulated network, input signals and response patterns established at excitatory neurons' level i.e. the membrane potential of neuron soma. It is restricted to spatial patterns of the auditory neuron networks and time factor for nervous conduction and transmission is neglected compared with long maintained membrane potentials of neuron somas. The model analyzes the change in the spatial patterns of the membrane potential in the two dimensional networks of the auditory system. In order to evaluate the contribution of the various parameters, it is started that the simplest model has only one parameter, lateral inhibition. The other parameters are then added, one at a time, to successive models. The lateral inhibition is a necessary condition in the auditory nervous system if any sharpening of the response areas in the single neurons is to occur. A necessary condition for the validity of the model is that it should be applicable to the other senses such as vision and chemical patterns, taste. The threshold feature of auditory neurons aids in producing a sharpening in the neuron of the auditory relay nuclei. It does this clipping the spatial response patterns in one dimensional arrays of excitatory neurons. Recurrent inhibition seems a necessary condition in the sensory nervous system that any kinds of input signals are to be preserved over a wide range of stimulus intensity. In other words, this network has a wide dynamic range against any kinds of input signals. A simple self-recurrent negative feedback does not contribute to the sharpening, but more complex socalled averaged type does. A neuron network is capable of responding stably to stimuli with a wide range of intensity and with any kind of spatial patterns if there is a simple negative feedback mechanism. When there is no negative feedback, input signals soon disappear or saturate in the neuron network. Therefore, recurrent inhibition is the most important mechanism. Spontaneous activity appears to aid in the sharpening by providing a kind of contrast, that is by reducting the amount of activity in neurons adjacent to the excitatory area. Moreover, the effect of spontaneous activity in the model seems to make repples around the excitatory area and suggests that an introduction of activity at any stage of the networks, from whatever source for example reticulum formation and thalamus, might appreciably alter the response patterns at subsequent neuron network. This suggests that the mechanism of the consciousness that might be controlled by the thalamus and or reticular formation. These two dimensional neuron networks may be expanded to three dimensional neuron networks. The former might simulate the auditory nervous system while the latter might simulate the visual system.     

Zn2+, mitochondria and neuronal injury

In addition to its familiar role as a component of metalloproteins, zinc is also sequestered in the presynaptic vesicles in 'zinc-containing' neurons. The best-established physiological role of synaptically released zinc is the tonic modulation of brain excitability through modulation of amino acid receptors; prominent pathological effects include acceleration of plaque deposition in Alzheimer's disease and exacerbation of excitotoxic neuron injury. Synaptically released zinc functions as a conventional synaptic neurotransmitter or neuromodulator being released into the cleft then recycled into the postsynaptic neurons during synaptic events, functioning analogously to calcium in this regard, as a transmembrane neural signal. To stimulate comparisons of zinc signals with calcium signals, we have compiled a list of the important parameters of calcium signals and zinc signals. More speculatively, we hypothesize that zinc signals may loosely mimic phosphate signals in the sense that signal zinc ions may commonly bind to proteins in a lasting manner, as a result changing their structure and function.