Peter J. Thomas

Discovering Spike Patterns in Neuronal Responses

When a cortical neuron is repeatedly injected with the same fluctuating current stimulus (frozen noise) the timing of the spikes is highly precise from trial to trial and the spike pattern appears to be unique. We show here that the same repeated stimulus can produce more than one reliable temporal pattern of spikes. A new method is introduced to find these patterns in raw multitrial data and is tested on surrogate data sets. Using it, multiple coexisting spike patterns were discovered in pyramidal cells recorded from rat prefrontal cortex in vitro, in data obtained in vivo from the middle temporal area of the monkey (Buracas et al., 1998) and from the cat lateral geniculate nucleus (Reinagel and Reid, 2002). The spike patterns lasted from a few tens of milliseconds in vitro to several seconds in vivo. We conclude that the prestimulus history of a neuron may influence the precise timing of the spikes in response to a stimulus over a wide range of time scales.

What geometric visual hallucinations tell us about the visual cortex

Many observers see geometric visual hallucinations after taking hallucinogens such as LSD, cannabis, mescaline or psilocybin; on viewing bright flickering lights; on waking up or falling asleep; in near-death experiences; and in many other syndromes. Klver organized the images into four groups called form constants: (I) tunnels and funnels, (II) spirals, (III) lattices, including honeycombs and triangles, and (IV) cobwebs. In most cases, the images are seen in both eyes and move with them. We interpret this to mean that they are generated in the brain. Here, we summarize a theory of their origin in visual cortex (area V1), based on the assumption that the form of the retinocortical map and the architecture of V1 determine their geometry. (A much longer and more detailed mathematical version has been published in Philosophical Transactions of the Royal Society B, 356 [2001].) We model V1 as the continuum limit of a lattice of interconnected hypercolumns, each comprising a number of interconnected iso-orientation columns. Based on anatomical evidence, we assume that the lateral connectivity between hypercolumns exhibits symmetries, rendering it invariant under the action of the Euclidean group E(2), composed of reflections and translations in the plane, and a (novel) shift-twist action. Using this symmetry, we show that the various patterns of activity that spontaneously emerge when V1s spatially uniform resting state becomes unstable correspond to the form constants when transformed to the visual field using the retino-cortical map. The results are sensitive to the detailed specification of the lateral connectivity and suggest that the cortical mechanisms that generate geometric visual hallucinations are closely related to those used to process edges, contours, surfaces, and textures.

Establishing Direction during Chemotaxis in Eukaryotic Cells

Several recent studies have demonstrated that eukaryotic cells, including amoeboid cells of Dictyostelium discoideum and neutrophils, respond to chemoattractants by translocation of PH-domain proteins to the cell membrane, where these proteins participate in the modulation of the cytoskeleton and relay of the signal. When the chemoattractant is released from a pipette, the localization is found predominantly on the proximal side of the cell. The recruitment of PH-domain proteins, particularly for Dictyostelium cells, occurs very rapidly (<2 s). Thus, the mechanism responsible for the first step in the directional sensing process of a cell must be able to establish an asymmetry on the same time scale. Here, we propose a simple mechanism in which a second messenger, generated by local activation of the membrane, diffuses through the interior of the cell, suppresses the activation of the back of the cell, and converts the temporal gradient into an initial cellular asymmetry. Numerical simulations show that such a mechanism is plausible. Available evidence suggests that the internal inhibitor may be cGMP, which accumulates within less than a second following treatment of cells with external cAMP.

Allosteric Models for Cooperative Polymerization of Linear Polymers

In the cytoskeleton, unfavorable nucleation steps allow cells to regulate where, when, and how many polymers assemble. Nucleated polymerization is traditionally explained by a model in which multistranded polymers assemble cooperatively, whereas linear, single-stranded polymers do not. Recent data on the assembly of FtsZ, the bacterial homolog of tubulin, do not fit either category. FtsZ can polymerize into single-stranded protofilaments that are stable in the absence of lateral interactions, but that assemble cooperatively. We developed a model for cooperative polymerization that does not require polymers to be multistranded. Instead, a conformational change allows subunits in oligomers to associate with high affinity, whereas a lower-affinity conformation is favored in monomers. We derive equations for calculating polymer concentrations, subunit conformations, and the apparent affinity of subunits for polymer ends. Certain combinations of equilibrium constants produce the sharp critical concentrations characteristic of cooperative polymerization. In these cases, the low-affinity conformation predominates in monomers, whereas virtually all polymers are composed of high-affinity subunits. Our model predicts that the three routes to forming HH dimers all involve unstable intermediates, limiting nucleation. The mathematical framework developed here can represent allosteric assembly systems with a variety of biochemical interpretations, some of which can show cooperativity, and others of which cannot.

Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex

Bosch Vivancos, Chossat and Melbourne showed that two types of steadystate bifurcations are possible from trivial states when Euclidean equivariant systems are restricted to a planar lattice—scalar and pseudoscalar—and began the study of pseudoscalar bifurcations. The scalar bifurcations have been well studied since they appear in planar reaction–diffusion systems and in plane layer convection problems. Bressloff, Cowan, Golubitsky, Thomas and Wiener showed that bifurcations in models of the visual cortex naturally contain both scalar and pseudoscalar bifurcations, due to a different action of the Euclidean group in that application. In this paper, we review the symmetry discussion in Bressloff et al and we continue the study of pseudoscalar bifurcations. Our analysis furthers the study of pseudoscalar bifurcations in three ways. (a) We complete the classification of axial subgroups on the hexagonal lattice in the shortest wavevector case proving the existence of one new planform—a solution with triangular D3 symmetry. (b) We derive bifurcation diagrams for generic bifurcations giving, in particular, the stability of solutions to perturbations in the hexagonal lattice. For the simplest (codimension zero) bifurcations, these bifurcation diagrams are identical to those derived by Golubitsky, Swift and Knobloch � = � � � � .

Dynamics and sensitivity analysis of high-frequency conduction block

The local delivery of extracellular high-frequency stimulation (HFS) has been shown to be a fast acting and quickly reversible method of blocking neural conduction and is currently being pursued for several clinical indications. However, the mechanism for this type of nerve block remains unclear. In this study, we investigate two hypotheses: (1) depolarizing currents promote conduction block via inactivation of sodium channels and (2) the gating dynamics of the fast sodium channel are the primary determinate of minimal blocking frequency. Hypothesis 1 was investigated using a combined modeling and experimental study to investigate the effect of depolarizing and hyperpolarizing currents on high-frequency block. The results of the modeling study show that both depolarizing and hyperpolarizing currents play an important role in conduction block and that the conductance to each of three ionic currents increases relative to resting values during HFS. However, depolarizing currents were found to promote the blocking effect, and hyperpolarizing currents were found to diminish the blocking effect. Inward sodium currents were larger than the sum of the outward currents, resulting in a net depolarization of the nodal membrane. Our experimental results support these findings and closely match results from the equivalent modeling scenario: intra-peritoneal administration of the persistent sodium channel blocker ranolazine resulted in an increase in the amplitude of HFS required to produce conduction block in rats, confirming that depolarizing currents promote the conduction block phenomenon. Hypothesis 2 was investigated using a spectral analysis of the channel gating variables in a single-fiber axon model. The results of this study suggested a relationship between the dynamical properties of specific ion channel gating elements and the contributions of corresponding conductances to block onset. Specifically, we show that the dynamics of the fast sodium inactivation gate are too slow to track the high-frequency changes in membrane potential during HFS, and that the behavior of the fast sodium current was dominated by the low-frequency depolarization of the membrane. As a result, in the blocked state, only 5.4% of nodal sodium channels were found to be in the activatable state in the node closest to the blocking electrode, resulting in conduction block. Moreover, we find that the corner frequency for the persistent sodium channel activation gate corresponds to the frequency below which high-frequency stimuli of arbitrary amplitude are incapable of inducing conduction block.

Network graph analysis of category fluency testing.

BackgroundCategory fluency is impaired early in Alzheimer disease (AD). Graph theory is a technique to analyze complex relationships in networks. Features of interest in network analysis include the number of nodes and edges, and variables related to their interconnectedness. Other properties important in network analysis are “small world properties” and “scale-free” properties. The small world property (popularized as the so-called “6 degrees of separation”) arises when the majority of connections are local, but a number of connections are to distant nodes. Scale-free networks are characterized by the presence of a few nodes with many connections, and many more nodes with fewer connections. ObjectiveTo determine if category fluency data can be analyzed using graph theory. To compare normal elderly, mild cognitive impairment (MCI) and AD network graphs, and characterize changes seen with increasing cognitive impairment. MethodsCategory fluency results (“animals” recorded over 60 s) from normals (n=38), MCI (n=33), and AD (n=40) completing uniform data set evaluations were converted to network graphs of all unique cooccurring neighbors, and compared for network variables. ResultsFor Normal, MCI and AD, mean clustering coefficients were 0.21, 0.22, 0.30; characteristic path lengths were 3.27, 3.17, and 2.65; small world properties decreased with increasing cognitive impairment, and all graphs showed scale-free properties. Rank correlations of the 25 commonest items ranged from 0.75 to 0.83. Filtering of low-degree nodes in normal and MCI graphs resulted in properties similar to the AD network graph. ConclusionsNetwork graph analysis is a promising technique for analyzing changes in category fluency. Our technique results in nonrandom graphs consistent with well-characterized properties for these types of graphs.

A new high-throughput method for simultaneous detection of drug resistance associated mutations in Plasmodium vivax dhfr, dhps and mdr1 genes.

BackgroundReports of severe cases and increasing levels of drug resistance highlight the importance of improved Plasmodium vivax case management. Whereas monitoring P. vivax resistance to anti-malarial drug by in vivo and in vitro tests remain challenging, molecular markers of resistance represent a valuable tool for high-scale analysis and surveillance studies. A new high-throughput assay for detecting the most relevant markers related to P. vivax drug resistance was developed and assessed on Papua New Guinea (PNG) patient isolates.MethodsPvdhfr, pvdhps and pvmdr1 fragments were amplified by multiplex nested PCR. Then, PCR products were processed through an LDR-FMA (ligase detection reaction - fluorescent microsphere assay). 23 SNPs, including pvdhfr 57-58-61 and 173, pvdhps 382-383, 553, 647 and pvmdr1 976, were simultaneously screened in 366 PNG P. vivax samples.ResultsGenotyping was successful in 95.4% of the samples for at least one gene. The coexistence of multiple distinct haplotypes in the parasite population necessitated the introduction of a computer-assisted approach to data analysis. Whereas 73.1% of patients were infected with at least one wild-type genotype at codons 57, 58 and 61 of pvdhfr, a triple mutant genotype was detected in 65.6% of the patients, often associated with the 117T mutation. Only one patient carried the 173L mutation. The mutant 647P pvdhps genotype allele was approaching genetic fixation (99.3%), whereas 35.1% of patients were infected with parasites carrying the pvmdr1 976F mutant allele.ConclusionsThe LDR-FMA described here allows a discriminant genotyping of resistance alleles in the pvdhfr, pvdhps, and pvmdr1 genes and can be used in large-scale surveillance studies.

Capacity of a simple intercellular signal transduction channel

We model the ligand-receptor molecular communication channel with a discrete-time Markov model, and show how to obtain the capacity of this channel. We show that the capacity-achieving input distribution is iid; further, unusually for a channel with memory, we show that feedback does not increase the capacity of this channel.

Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit ∗

Rhythmic behaviors in neural systems often combine features of limit-cycle dynamics (stability and periodicity) with features of near heteroclinic or near homoclinic cycle dynamics (extended dwell times in localized regions of phase space). Proximity of a limit cycle to one or more saddle equilibria can have a profound effect on the timing of trajectory components and response to both fast and slow perturbations, providing a possible mechanism for adaptive control of rhythmic motions. Reyn [“Generation of limit cycles from separatrix polygons in the phase plane” in Geometrical Approaches to Differential Equations, Lecture Notes in Math. 810, Springer, New York, 1980, pp. 264–289] showed that for a planar dynamical system with a stable heteroclinic cycle (or separatrix polygon), small perturbations satisfying a net inflow condition will generically give rise to a stable limit cycle (see also [J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed...