Mathematical modelling of neurons and neural networks

The basic concepts and techniques involved in the development and analysis of mathematical models for individual neurons and networks of neurons are reviewed. Some of the interesting results obtained from recent work in this field are described. The current status of research in this field in India is discussed

Fe as Hydrogen/Halogen Bond Acceptor in Square Pyramidal Fe(CO)(5)

Hydrogen bonded complexes formed between the square pyramidal Fe(CO)(5) with HX (X = F, Cl, Br), showing X-H center dot center dot center dot Fe interactions, have been investigated theoretically using density functional theory (DFT) including dispersion correction. Geometry, interaction energy, and large red shift of about 400 cm(-1) in the FIX stretching frequency confirm X-H center dot center dot center dot Fe hydrogen bond formation. In the (CO)(5)Fe center dot center dot center dot HBr complex, following the significant red shift, the HBr stretching mode is coupled with the carbonyl stretching modes. This clearly affects the correlation between frequency shift and binding energy, which is a hallmark of hydrogen bonds. Atoms in Molecule (AIM) theoretical analyses show the presence of a bond critical point between the iron and the hydrogen of FIX and significant mutual penetration. These X-H center dot center dot center dot Fe hydrogen bonds follow most but not all of the eight criteria proposed by Koch and Popelier (J. Phys. Chem. 1995, 99, 9747) based on their investigations on C-H center dot center dot center dot O hydrogen bonds. Natural bond orbital (NBO) analysis indicates charge transfer from the organometallic system to the hydrogen bond donor. However, there is no correlation between the extent of charge transfer and interaction,energy, contrary to what is proposed in the recent IUPAC recommendation (Pure Appl.. Chem. 2011, 83, 1637). The ``hydrogen bond radius'' for iron has been determined to be 1.60 +/- 0.02 angstrom, and not surprisingly it is between the covalent (127 angstrom) and van der Waals (2.0) radii of Fe. DFT and AIM theoretical studies reveal that Fe in square pyramidal Fe(CO)(5) can also form halogen bond with CIF and ClH as ``halogen bond donor''. Both these complexes show mutual penetration as well, though the Fe center dot center dot center dot Cl distance is closer to the sum of van der Waals radii of Fe and Cl in (CO)5Fe center dot center dot center dot ClH, and it is about 1 angstrom less in (CO)(5)Fe center dot center dot center dot ClF.

Corticosterone Treatment Results in Enhanced Release of Peptidergic Vesicles in Astrocytes via Cytoskeletal Rearrangements

While the effect of stress on neuronal physiology is widely studied, its effect on the functionality of astrocytes is not well understood. We studied the effect of high doses of stress hormone corticosterone, on two physiological properties of astrocytes, i.e., gliotransmission and interastrocytic calcium waves. To study the release of peptidergic vesicles from astrocytes, hippocampal astrocyte cultures were transfected with a plasmid to express pro-atrial natriuretic peptide (ANP) fused with the emerald green fluorescent protein (ANP.emd). The rate of decrease in fluorescence of ANP.emd on application of ionomycin, a calcium ionophore was monitored. Significant increase in the rate of calcium-dependent exocytosis of ANP.emd was observed with the 100 nM and 1 M corticosterone treatments for 3 h, which depended on the activation of the glucocorticoid receptor. ANP.emd tagged vesicles exhibited increased mobility in astrocyte culture upon corticosterone treatment. Increasing corticosterone concentrations also resulted in concomitant increase in the calcium wave propagation velocity, initiated by focal ATP application. Corticosterone treatment also resulted in increased GFAP expression and F-actin rearrangements. FITC-Phalloidin immunostaining revealed increased formation of cross linked F-actin networks with the 100 nM and 1 M corticosterone treatment. Alternatively, blockade of actin polymerization and disruption of microtubules prevented the corticosterone-mediated increase in ANP.emd release kinetics. This study reports for the first time the effect of corticosterone on gliotransmission via modulation of cytoskeletal elements. As ANP acts on both neurons and blood vessels, modulation of its release could have functional implications in neurovascular coupling under pathophysiological conditions of stress.

Reach task-associated excitatory overdrive of motor cortical neurons following infusion with ALS-CSF

Converging evidence from transgenic animal models of amyotrophic lateral sclerosis (ALS) and human studies suggest alterations in excitability of the motor neurons in ALS. Specifically, in studies on human subjects with ALS the motor cortex was reported to be hyperexcitable. The present study was designed to test the hypothesis that infusion of cerebrospinal fluid from patients with sporadic ALS (ALS-CSF) into the rat brain ventricle can induce hyperexcitability and structural changes in the motor cortex leading to motor dysfunction. A robust model of sporadic ALS was developed experimentally by infusing ALS-CSF into the rat ventricle. The effects of ALS-CSF at the single neuron level were examined by recording extracellular single unit activity from the motor cortex while rats were performing a reach to grasp task. We observed an increase in the firing rate of the neurons of the motor cortex in rats infused with ALS-CSF compared to control groups. This was associated with impairment in a specific component of reach with alterations in the morphological characteristics of the motor cortex. It is likely that the increased cortical excitability observed in the present study could be the result of changes in the intrinsic properties of motor cortical neurons, a dysfunctional inhibitory mechanism and/or an underlying structural change culminating in a behavioral deficit.

Corticosterone targets distinct steps of synaptic transmission via concentration specific activation of mineralocorticoid and glucocorticoid receptors

Hippocampal neurons are affected by chronic stress and have a high density of cytoplasmic mineralocorticoid and glucocorticoid receptors (MR and GR). Detailed studies on the genomic effects of the stress hormone corticosterone at physiologically relevant concentrations on different steps in synaptic transmission are limited. In this study, we tried to delineate how activation of MR and GR by different concentrations of corticosterone affects synaptic transmission at various levels. The effect of 3-h corticosterone (25, 50, and 100nM) treatment on depolarization-mediated calcium influx, vesicular release and properties of miniature excitatory post-synaptic currents (mEPSCs) were studied in cultured hippocampal neurons. Activation of MR with 25nM corticosterone treatment resulted in enhanced depolarization-mediated calcium influx via a transcription-dependent process and increased frequency of mEPSCs with larger amplitude. On the other hand, activation of GR upon 100nM corticosterone treatment resulted in increase in the rate of vesicular release via the genomic actions of GR. Furthermore, GR activation led to significant increase in the frequency of mEPSCs with larger amplitude and faster decay. Our studies indicate that differential activation of the dual receptor system of MR and GR by corticosterone targets the steps in synaptic transmission differently.

Beadex Function in the Motor Neurons Is Essential for Female Reproduction in Drosophila melanogaster

Drosophila melanogaster has served as an excellent model system for understanding the neuronal circuits and molecular mechanisms regulating complex behaviors. The Drosophila female reproductive circuits, in particular, are well studied and can be used as a tool to understand the role of novel genes in neuronal function in general and female reproduction in particular. In the present study, the role of Beadex, a transcription co-activator, in Drosophila female reproduction was assessed by generation of mutant and knock down studies. Null allele of Beadex was generated by transposase induced excision of P-element present within an intron of Beadex gene. The mutant showed highly compromised reproductive abilities as evaluated by reduced fecundity and fertility, abnormal oviposition and more importantly, the failure of sperm release from storage organs. However, no defect was found in the overall ovariole development. Tissue specific, targeted knock down of Beadex indicated that its function in neurons is important for efficient female reproduction, since its neuronal knock down led to compromised female reproductive abilities, similar to Beadex null females. Further, different neuronal class specific knock down studies revealed that Beadex function is required in motor neurons for normal fecundity and fertility of females. Thus, the present study attributes a novel and essential role for Beadex in female reproduction through neurons.

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.

Can stress-strain relationships be obtained from indentation curves using conical and pyramidal indenters?

Applying the scaling relationships developed recently for conical indentation in elastic-plastic solids with work-hardening, we examine the question of whether stress-strain relationships of such solids can be uniquely determined by matching the calculated loading and unloading curves with that measured experimentally. We show that there can be multiple stress-strain curves for a given set of loading and unloading curves. Consequently, stress-strain relationships may not be uniquely determined from loading and unloading curves alone using a conical or pyramidal indenter.

First human hNT neurons patterned on parylene-C/silicon dioxide substrates: Combining an accessible cell line and robust patterning technology for the study of the pathological adult human brain

In this communication, we describe a new method which has enabled the first patterning of human neurons (derived from the human teratocarcinoma cell line (hNT)) on parylene-C/silicon dioxide substrates. We reveal the details of the nanofabrication processes, cell differentiation and culturing protocols necessary to successfully pattern hNT neurons which are each key aspects of this new method. The benefits in patterning human neurons on silicon chip using an accessible cell line and robust patterning technology are of widespread value. Thus, using a combined technology such as this will facilitate the detailed study of the pathological human brain at both the single cell and network level. © 2010 Elsevier B.V.