Fixed points in a Hopfield model with random asymmetric interactions

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

On the problem of spurious patterns in neural associative memory models

The problem of spurious patterns in neural associative memory models is discussed, Some suggestions to solve this problem from the literature are reviewed and their inadequacies are pointed out, A solution based on the notion of neural self-interaction with a suitably chosen magnitude is presented for the Hebb learning rule. For an optimal learning rule based on linear programming, asymmetric dilution of synaptic connections is presented as another solution to the problem of spurious patterns, With varying percentages of asymmetric dilution it is demonstrated numerically that this optimal learning rule leads to near total suppression of spurious patterns. For practical usage of neural associative memory networks a combination of the two solutions with the optimal learning rule is recommended to be the best proposition.

Glassy behavior in neural network models of associative memory

Neural network models of associative memory exhibit a large number of spurious attractors of the network dynamics which are not correlated with any memory state. These spurious attractors, analogous to "glassy" local minima of the energy or free energy of a system of particles, degrade the performance of the network by trapping trajectories starting from states that are not close to one of the memory states. Different methods for reducing the adverse effects of spurious attractors are examined with emphasis on the role of synaptic asymmetry. (C) 2002 Elsevier Science B.V. All rights reserved.

A Real-time clustering system for spatio-temporal signals from network of neurons

Over past few years, the studies of cultured neuronal networks have opened up avenues for understanding the ion channels, receptor molecules, and synaptic plasticity that may form the basis of learning and memory. The hippocampal neurons from rats are dissociated and cultured on a surface containing a grid of 64 electrodes. The signals from these 64 electrodes are acquired using a fast data acquisition system MED64 (Alpha MED Sciences, Japan) at a sampling rate of 20 K samples with a precision of 16-bits per sample. A few minutes of acquired data runs in to a few hundreds of Mega Bytes. The data processing for the neural analysis is highly compute-intensive because the volume of data is huge. The major processing requirements are noise removal, pattern recovery, pattern matching, clustering and so on. In order to interface a neuronal colony to a physical world, these computations need to be performed in real-time. A single processor such as a desk top computer may not be adequate to meet this computational requirements. Parallel computing is a method used to satisfy the real-time computational requirements of a neuronal system that interacts with an external world while increasing the flexibility and scalability of the application. In this work, we developed a parallel neuronal system using a multi-node Digital Signal processing system. With 8 processors, the system is able to compute and map incoming signals segmented over a period of 200 ms in to an action in a trained cluster system in real time.

Tractable theories for the synthesis of neural networks

The Radius of Direct attraction of a discrete neural network is a measure of stability of the network. it is known that Hopfield networks designed using Hebb's Rule have a radius of direct attraction of Omega(n/p) where n is the size of the input patterns and p is the number of them. This lower bound is tight if p is no larger than 4. We construct a family of such networks with radius of direct attraction Omega(n/root plog p), for any p greater than or equal to 5. The techniques used to prove the result led us to the first polynomial-time algorithm for designing a neural network with maximum radius of direct attraction around arbitrary input patterns. The optimal synaptic matrix is computed using the ellipsoid method of linear programming in conjunction with an efficient separation oracle. Restrictions of symmetry and non-negative diagonal entries in the synaptic matrix can be accommodated within this scheme.

Ca2+ Binding to the ExDxD Motif Regulates the DNA Cleavage Specificity of a Promiscuous Endonuclease

Most of the restriction endonucleases (REases) are dependent on Mg2+ for DNA cleavage, and in general, Ca2+ inhibits their activity. RKpnI, an HNH active site containing beta beta alpha-Me finger nuclease, is an exception. In presence of Ca2+, the enzyme exhibits high-fidelity DNA cleavage and complete suppression of Mg2+-induced promiscuous activity. To elucidate the mechanism of unusual Ca2+-mediated activity, we generated alanine variants in the putative Ca-2+ binding motif, E(132)xD(134)xD(136), of the enzyme. Mutants showed decreased levels of DNA cleavage in the presence of Ca2+. We demonstrate that ExDxD residues are involved in Ca2+ coordination; however, the invariant His of the catalytic HNH motif acts as a general base for nucleophile activation, and the other two active site residues, D148 and Q175, also participate in Ca2+-mediated cleavage. Insertion of a 10-amino acid linker to disrupt the spatial organization of the ExDxD and HNH motifs impairs Ca2+ binding and affects DNA cleavage by the enzyme. Although ExDxD mutant enzymes retained efficient cleavage at the canonical sites in the presence of Mg2+, the promiscuous activity was greatly reduced, indicating that the carboxyl residues of the acidic triad play an important role in sequence recognition by the enzyme. Thus, the distinct Ca2+ binding motif that confers site specific cleavage upon Ca2+ binding is also critical for the promiscuous activity of the Mg2+-bound enzyme, revealing its role in metal ion-mediated modulation of DNA cleavage.

Transition in subicular burst firing neurons from epileptiform activity to suppressed state by feedforward inhibition

The subiculum, a para-hippocampal structure positioned between the cornu ammonis 1 subfield and the entorhinal cortex, has been implicated in temporal lobe epilepsy in human patients and in animal models of epilepsy. The structure is characterized by the presence of a significant population of burst firing neurons that has been shown previously to lead epileptiform activity locally. Phase transitions in epileptiform activity in neurons following a prolonged challenge with an epileptogenic stimulus has been shown in other brain structures, but not in the subiculum. Considering the importance of the subicular burst firing neurons in the propagation of epileptiform activity to the entorhinal cortex, we have explored the phenomenon of phase transitions in the burst firing neurons of the subiculum in an in vitro rat brain slice model of epileptogenesis. Whole-cell patch-clamp and extracellular field recordings revealed a distinct phenomenon in the subiculum wherein an early hyperexcitable state was followed by a late suppressed state upon continuous perfusion with epileptogenic 4-aminopyridine and magnesium-free medium. The suppressed state was characterized by inhibitory post-synaptic potentials in pyramidal excitatory neurons and bursting activity in local fast-spiking interneurons at a frequency of 0.1-0.8Hz. The inhibitory post-synaptic potentials were mediated by GABA(A) receptors that coincided with excitatory synaptic inputs to attenuate action potential discharge. These inhibitory post-synaptic potentials ceased following a cut between the cornu ammonis 1 and subiculum. The suppression of epileptiform activity in the subiculum thus represents a homeostatic response towards the induced hyperexcitability. Our results suggest the importance of feedforward inhibition in exerting this homeostatic control.

Information and Efficiency in the Nervous System-A Synthesis

In systems biology, questions concerning the molecular and cellular makeup of an organism are of utmost importance, especially when trying to understand how unreliable components-like genetic circuits, biochemical cascades, and ion channels, among others-enable reliable and adaptive behaviour. The repertoire and speed of biological computations are limited by thermodynamic or metabolic constraints: an example can be found in neurons, where fluctuations in biophysical states limit the information they can encode-with almost 20-60% of the total energy allocated for the brain used for signalling purposes, either via action potentials or by synaptic transmission. Here, we consider the imperatives for neurons to optimise computational and metabolic efficiency, wherein benefits and costs trade-off against each other in the context of self-organised and adaptive behaviour. In particular, we try to link information theoretic (variational) and thermodynamic (Helmholtz) free-energy formulations of neuronal processing and show how they are related in a fundamental way through a complexity minimisation lemma.

The effect of cell size and channel density on neuronal information encoding and energy efficiency

Identifying the determinants of neuronal energy consumption and their relationship to information coding is critical to understanding neuronal function and evolution. Three of the main determinants are cell size, ion channel density, and stimulus statistics. Here we investigate their impact on neuronal energy consumption and information coding by comparing single-compartment spiking neuron models of different sizes with different densities of stochastic voltage-gated Na+ and K+ channels and different statistics of synaptic inputs. The largest compartments have the highest information rates but the lowest energy efficiency for a given voltage-gated ion channel density, and the highest signaling efficiency (bits spike(-1)) for a given firing rate. For a given cell size, our models revealed that the ion channel density that maximizes energy efficiency is lower than that maximizing information rate. Low rates of small synaptic inputs improve energy efficiency but the highest information rates occur with higher rates and larger inputs. These relationships produce a Law of Diminishing Returns that penalizes costly excess information coding capacity, promoting the reduction of cell size, channel density, and input stimuli to the minimum possible, suggesting that the trade-off between energy and information has influenced all aspects of neuronal anatomy and physiology.

Optical microscopy methods for understanding learning and memory

Structural dynamics of dendritic spines is one of the key correlative measures of synaptic plasticity for encoding short-term and long-term memory. Optical studies of structural changes in brain tissue using confocal microscopy face difficulties of scattering. This results in low signal-to-noise ratio and thus limiting the imaging depth to few tens of microns. Multiphoton microscopy (MpM) overcomes this limitation by using low-energy photons to cause localized excitation and achieve high resolution in all three dimensions. Multiple low-energy photons with longer wavelengths minimize scattering and allow access to deeper brain regions at several hundred microns. In this article, we provide a basic understanding of the physical phenomena that give MpM an edge over conventional microscopy. Further, we highlight a few of the key studies in the field of learning and memory which would not have been possible without the advent of MpM.

High-conductance states and A-type K+ channels are potential regulators of the conductance-current balance triggered by HCN channels

An increase in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel conductance reduces input resistance, whereas the consequent increase in the inward h current depolarizes the membrane. This results in a delicate and unique conductance-current balance triggered by the expression of HCN channels. In this study, we employ experimentally constrained, morphologically realistic, conductance-based models of hippocampal neurons to explore certain aspects of this conductance-current balance. First, we found that the inclusion of an experimentally determined gradient in A-type K+ conductance, but not in M-type K+ conductance, tilts the HCN conductance-current balance heavily in favor of conductance, thereby exerting an overall restorative influence on neural excitability. Next, motivated by the well-established modulation of neuronal excitability by synaptically driven high-conductance states observed under in vivo conditions, we inserted thousands of excitatory and inhibitory synapses with different somatodendritic distributions. We measured the efficacy of HCN channels, independently and in conjunction with other channels, in altering resting membrane potential (RMP) and input resistance (R-in) when the neuron received randomized or rhythmic synaptic bombardments through variable numbers of synaptic inputs. We found that the impact of HCN channels on average RMP, R in, firing frequency, and peak-to-peak voltage response was severely weakened under high-conductance states, with the impinging synaptic drive playing a dominant role in regulating these measurements. Our results suggest that the debate on the role of HCN channels in altering excitability should encompass physiological and pathophysiological neuronal states under in vivo conditions and the spatiotemporal interactions of HCN channels with other channels.

Calcium Permeable AMPA Receptor-Dependent Long Lasting Plasticity of Intrinsic Excitability in Fast Spiking Interneurons of the Dentate Gyrus Decreases Inhibition in the Granule Cell Layer

The local fast-spiking interneurons (FSINs) are considered to be crucial for the generation, maintenance, and modulation of neuronal network oscillations especially in the gamma frequency band. Gamma frequency oscillations have been associated with different aspects of behavior. But the prolonged effects of gamma frequency synaptic activity on the FSINs remain elusive. Using whole cell current clamp patch recordings, we observed a sustained decrease of intrinsic excitability in the FSINs of the dentate gyrus (DG) following repetitive stimulations of the mossy fibers at 30 Hz (gamma bursts). Surprisingly, the granule cells (GCs) did not express intrinsic plastic changes upon similar synaptic excitation of their apical dendritic inputs. Interestingly, pairing the gamma bursts with membrane hyperpolarization accentuated the plasticity in FSINs following the induction protocol, while the plasticity attenuated following gamma bursts paired with membrane depolarization. Paired pulse ratio measurement of the synaptic responses did not show significant changes during the experiments. However, the induction protocols were accompanied with postsynaptic calcium rise in FSINs. Interestingly, the maximum and the minimum increase occurred during gamma bursts with membrane hyperpolarization and depolarization respectively. Including a selective blocker of calcium-permeable AMPA receptors (CP-AMPARs) in the bath; significantly attenuated the calcium rise and blocked the membrane potential dependence of the calcium rise in the FSINs, suggesting their involvement in the observed phenomenon. Chelation of intracellular calcium, blocking HCN channel conductance or blocking CP-AMPARs during the experiment forbade the long lasting expression of the plasticity. Simultaneous dual patch recordings from FSINs and synaptically connected putative GCs confirmed the decreased inhibition in the GCs accompanying the decreased intrinsic excitability in the FSINs. Experimentally constrained network simulations using NEURON predicted increased spiking in the GC owing to decreased input resistance in the FSIN. We hypothesize that the selective plasticity in the FSINs induced by local network activity may serve to increase information throughput into the downstream hippocampal subfields besides providing neuroprotection to the FSINs. (c) 2014 Wiley Periodicals, Inc.

Challenges in the quantification and interpretation of spike-LFP relationships

Brain signals often show fluctuations in particular frequency bands, which are highly conserved across species and are associated with specific behavioural states. Such rhythmic patterns can be captured in the local field potential (LFP), which is obtained by low-pass filtering the extracellular signal recorded from microelectrodes. However, LFP also captures other neural processes that are associated with spikes, such as synaptic events preceding a spike, low-frequency component of the action potential (spike bleed-through'') and spike afterhyperpolarization, which pose difficulties in the estimation of the amplitude and phase of the rhythm with respect to spikes. Here we discuss these issues and different techniques that have been used to dissociate the rhythm from other neural events in the LFP.

HCN channels enhance spike phase coherence and regulate the phase of spikes and LFPs in the theta-frequency range

What are the implications for the existence of subthreshold ion channels, their localization profiles, and plasticity on local field potentials (LFPs)? Here, we assessed the role of hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels in altering hippocampal theta-frequency LFPs and the associated spike phase. We presented spatiotemporally randomized, balanced theta-modulated excitatory and inhibitory inputs to somatically aligned, morphologically realistic pyramidal neuron models spread across a cylindrical neuropil. We computed LFPs from seven electrode sites and found that the insertion of an experimentally constrained HCN-conductance gradient into these neurons introduced a location- dependent lead in the LFP phase without significantly altering its amplitude. Further, neurons fired action potentials at a specific theta phase of the LFP, and the insertion of HCN channels introduced large lags in this spike phase and a striking enhancement in neuronal spike-phase coherence. Importantly, graded changes in either HCN conductance or its half-maximal activation voltage resulted in graded changes in LFP and spike phases. Our conclusions on the impact of HCN channels on LFPs and spike phase were invariant to changes in neuropil size, to morphological heterogeneity, to excitatory or inhibitory synaptic scaling, and to shifts in the onset phase of inhibitory inputs. Finally, we selectively abolished the inductive lead in the impedance phase introduced by HCN channels without altering neuronal excitability and found that this inductive phase lead contributed significantly to changes in LFP and spike phase. Our results uncover specific roles for HCN channels and their plasticity in phase-coding schemas and in the formation and dynamic reconfiguration of neuronal cell assemblies.

Early postnatal exposure to lithium in vitro induces changes in AMPAR mEPSCs and vesicular recycling at hippocampal glutamatergic synapses

Lithium is an effective mood stabilizer but its use is associated with many side effects. Electrophysiological recordings of miniature excitatory postsynaptic currents (mEPSCs) mediated by glutamate receptor AMPA-subtype (AMPARs) in hippocampal pyramidal neurons revealed that CLi (therapeutic concentration of 1 mM lithium, from days in vitro 4-10) decreased the mean amplitude and mean rectification index (RI) of AMPAR mEPSCs. Lowered mean RI indicate that contribution of Ca2+-permeable AMPARs in synaptic events is higher in CLi neurons (supported by experiments sensitive to Ca2+-permeable AMPAR modulation). Co-inhibiting PKA, GSK-3 beta and glutamate reuptake was necessary to bring about changes in AMPAR mEPSCs similar to that seen in CLi neurons. FM1-43 experiments revealed that recycling pool size was affected in CLi cultures. Results from minimum loading, chlorpromazine treatment and hyperosmotic treatment experiments indicate that endocytosis in CLi is affected while not much difference is seen in modes of exocytosis. CLi cultures did not show the high KCl associated presynaptic potentiation observed in control cultures. This study, by calling attention to long-term lithium-exposure-induced synaptic changes, might have implications in understanding the side effects such as CNS complications occurring in perinatally exposed babies and cognitive dulling seen in patients on lithium treatment.