Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

A novel component of cannabis extract potentiates excitatory synaptic transmission in rat olfactory cortex in vitro

Cannabis is a potential treatment for epilepsy, although the few human studies supporting this use have proved inconclusive. Previously, we showed that a standardized cannabis extract (SCE), isolated Delta(9)-tetrahydrocannabinol (Delta(9)-THC), and even Delta(9)-THC-free SCE inhibited muscarinic agonist-induced epileptiform bursting in rat olfactory cortical brain slices, acting via CB1 receptors. The present work demonstrates that although Delta(9)-THC (1microM) significantly depressed evoked depolarizing postsynaptic potentials (PSPs) in rat olfactory cortex neurones, both SCE and Delta(9)-THC-free SCE significantly potentiated evoked PSPs (all results were fully reversed by the CB1 receptor antagonist SR141716A, 1microM); interestingly, the potentiation by Delta(9)-THC-free SCE was greater than that produced by SCE. On comparing the effects of Delta(9)-THC-free SCE upon evoked PSPs and artificial PSPs (aPSPs; evoked electrotonically following brief intracellular current injection), PSPs were enhanced, whereas aPSPs were unaffected, suggesting that the effect was not due to changes in background input resistance. Similar recordings made using CB1 receptor-deficient knockout mice (CB1(-/-)) and wild-type littermate controls revealed cannabinoid or extract-induced changes in membrane resistance, cell excitability and synaptic transmission in wild-type mice that were similar to those seen in rat neurones, but no effect on these properties were seen in CB1(-/-) cells. It appears that the unknown extract constituent(s) effects over-rode the suppressive effects of Delta(9)-THC on excitatory neurotransmitter release, which may explain some patients' preference for herbal cannabis rather than isolated Delta(9)-THC (due to attenuation of some of the central Delta(9)-THC side effects) and possibly account for the rare incidence of seizures in some individuals taking cannabis recreationally

Age-related effects of Ginkgo biloba extract on synaptic plasticity and excitability

EGb 761 is a standardized extract from the Ginkgo biloba leaf and is purported to improve age-related memory impairment. The acute and chronic effect of EGb 761 on synaptic transmission and plasticity in hippocampal slices from young adult (8-12 weeks) and aged (18-24 months) C57B1/6 mice was tested because hippocampal plasticity is believed to be a key component of memory. Acutely applied EGb 761 significantly increased neuronal excitability in slices from aged mice by reducing the population spike threshold and increased the early phase of long-term potentiation, though there was no effect in slices from young adults. In chronically treated mice fed for 30 days with an EGb 761-supplemented diet, EGb 761 significantly increased the population spike threshold and long-term potentiation in slices from aged animals, but had no effect on slices from young adults. The rapid effects of EGb 761 on plasticity indicate a direct interaction with the glutamatergic system and raise interesting implications with respect to a mechanism explaining its effect on cognitive enhancement in human subjects experiencing dementia. (C) 2003 Elsevier Inc. All rights reserved.

The impact of flavonoids on memory: physiological and molecular considerations

Emerging evidence suggests that a group of dietary-derived phytochemicals known as flavonoids are able to induce improvements in memory acquisition, consolidation, storage and retrieval. These low molecular weight polyphenols are widespread in the human diet, are absorbed to only a limited degree and localise in the brain at low concentration. However, they have been found to be highly effective in reversing age-related declines in memory via their ability to interact with the cellular and molecular architecture of the brain responsible for memory. These interactions include an ability to activate signalling pathways, critical in controlling synaptic plasticity, and a potential to induce vascular effects capable of causing new nerve cell growth in the hippocampus. Their ability to activate the extracellular signal-regulated kinase (ERK1/2) and the protein kinase B (PKB/Akt) signalling pathways, leading to the activation of the cAMP response element-binding protein (CREB), a transcription factor responsible for increasing the expression of a number of neurotrophins important in de. ning memory, will be discussed. How these effects lead to improvements in memory through induction of synapse growth and connectivity, increases in dendritic spine density and the functional integration of old and new neurons will be illustrated. The overall goal of this critical review is to emphasize future areas of investigation as well as to highlight these dietary agents as promising candidates for the design of memory-enhancing drugs with relevance to normal and pathological brain ageing (161 references).

Maturation of limbic corticostriatal activation and connectivity associated with developmental changes in temporal discounting

Temporal discounting (TD) matures with age, alongside other markers of increased impulse control, and coherent, self-regulated behaviour. Discounting paradigms quantify the ability to refrain from preference of immediate rewards, in favour of delayed, larger rewards. As such, they measure temporal foresight and the ability to delay gratification, functions that develop slowly into adulthood. We investigated the neural maturation that accompanies the previously observed age-related behavioural changes in discounting, from early adolescence into mid-adulthood. We used functional magnetic resonance imaging of a hypothetical discounting task with monetary rewards delayed in the week to year range. We show that age-related reductions in choice impulsivity were associated with changes in activation in ventromedial prefrontal cortex (vmPFC), anterior cingulate cortex (ACC), ventral striatum (VS), insula, inferior temporal gyrus, and posterior parietal cortex. Limbic frontostriatal activation changes were specifically associated with age-dependent reductions in impulsive choice, as part of a more extensive network of brain areas showing age-related changes in activation, including dorsolateral PFC, inferior parietal cortex, and subcortical areas. The maturational pattern of functional connectivity included strengthening in activation coupling between ventromedial and dorsolateral PFC, parietal and insular cortices during selection of delayed alternatives, and between vmPFC and VS during selection of immediate alternatives. We conclude that maturational mechanisms within limbic frontostriatal circuitry underlie the observed post-pubertal reductions in impulsive choice with increasing age, and that this effect is dependent on increased activation coherence within a network of areas associated with discounting behaviour and inter-temporal decision-making.

Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

Inhibition of synaptic transmission and G protein modulation by synthetic CaV2.2 Ca2+ channel peptides

Abstract: Modulation of presynaptic voltage-dependent Ca+ channels is a major means of controlling neurotransmitter release. The CaV 2.2 Ca2+ channel subunit contains several inhibitory interaction sites for Gβγ subunits, including the amino terminal (NT) and I–II loop. The NT and I–II loop have also been proposed to undergo a G protein-gated inhibitory interaction, whilst the NT itself has also been proposed to suppress CaV 2 channel activity. Here, we investigate the effects of an amino terminal (CaV 2.2[45–55]) ‘NT peptide’ and a I–II loop alpha interaction domain (CaV 2.2[377–393]) ‘AID peptide’ on synaptic transmission, Ca2+ channel activity and G protein modulation in superior cervical ganglion neurones (SCGNs). Presynaptic injection of NT or AID peptide into SCGN synapses inhibited synaptic transmission and also attenuated noradrenaline-induced G protein modulation. In isolated SCGNs, NT and AID peptides reduced whole-cell Ca2+ current amplitude, modified voltage dependence of Ca2+ channel activation and attenuated noradrenaline-induced G protein modulation. Co-application of NT and AID peptide negated inhibitory actions. Together, these data favour direct peptide interaction with presynaptic Ca2+ channels, with effects on current amplitude and gating representing likely mechanisms responsible for inhibition of synaptic transmission. Mutations to residues reported as determinants of Ca2+ channel function within the NT peptide negated inhibitory effects on synaptic transmission, Ca2+ current amplitude and gating and G protein modulation. A mutation within the proposed QXXER motif for G protein modulation did not abolish inhibitory effects of the AID peptide. This study suggests that the CaV 2.2 amino terminal and I–II loop contribute molecular determinants for Ca2+ channel function; the data favour a direct interaction of peptides with Ca2+ channels to inhibit synaptic transmission and attenuate G protein modulation. Non-technical summary: Nerve cells (neurones) in the body communicate with each other by releasing chemicals (neurotransmitters) which act on proteins called receptors. An important group of receptors (called G protein coupled receptors, GPCRs) regulate the release of neurotransmitters by an action on the ion channels that let calcium into the cell. Here, we show for the first time that small peptides based on specific regions of calcium ion channels involved in GPCR signalling can themselves inhibit nerve cell communication. We show that these peptides act directly on calcium channels to make them more difficult to open and thus reduce calcium influx into native neurones. These peptides also reduce GPCR-mediated signalling. This work is important in increasing our knowledge about modulation of the calcium ion channel protein; such knowledge may help in the development of drugs to prevent signalling in pathways such as those involved in pain perception.

Brain computer interface control via functional connectivity dynamics

The dynamics of inter-regional communication within the brain during cognitive processing – referred to as functional connectivity – are investigated as a control feature for a brain computer interface. EMDPL is used to map phase synchronization levels between all channel pair combinations in the EEG. This results in complex networks of channel connectivity at all time–frequency locations. The mean clustering coefficient is then used as a descriptive feature encapsulating information about inter-channel connectivity. Hidden Markov models are applied to characterize and classify dynamics of the resulting complex networks. Highly accurate levels of classification are achieved when this technique is applied to classify EEG recorded during real and imagined single finger taps. These results are compared to traditional features used in the classification of a finger tap BCI demonstrating that functional connectivity dynamics provide additional information and improved BCI control accuracies.