Analysis of temporal structure in spike trains of visual cortical area MT

The temporal structure of neuronal spike trains in the visual cortex can provide detailed information about the stimulus and about the neuronal implementation of visual processing. Spike trains recorded from the macaque motion area MT in previous studies (Newsome et al., 1989a; Britten et al., 1992; Zohary et al., 1994) are analyzed here in the context of the dynamic random dot stimulus which was used to evoke them. If the stimulus is incoherent, the spike trains can be highly modulated and precisely locked in time to the stimulus. In contrast, the coherent motion stimulus creates little or no temporal modulation and allows us to study patterns in the spike train that may be intrinsic to the cortical circuitry in area MT. Long gaps in the spike train evoked by the preferred direction motion stimulus are found, and they appear to be symmetrical to bursts in the response to the anti-preferred direction of motion. A novel cross-correlation technique is used to establish that the gaps are correlated between pairs of neurons. Temporal modulation is also found in psychophysical experiments using a modified stimulus. A model is made that can account for the temporal modulation in terms of the computational theory of biological image motion processing. A frequency domain analysis of the stimulus reveals that it contains a repeated power spectrum that may account for psychophysical and electrophysiological observations.

Some neurons tend to fire bursts of action potentials while others avoid burst firing. Using numerical and analytical models of spike trains as Poisson processes with the addition of refractory periods and bursting, we are able to account for peaks in the power spectrum near 40 Hz without assuming the existence of an underlying oscillatory signal. A preliminary examination of the local field potential reveals that stimulus-locked oscillation appears briefly at the beginning of the trial.

Characterization and developmental regulation of a gene expressed specifically in the skeletogenic lineage of the sea urchin embryo

The sea urchin embryonic skeleton, or spicule, is deposited by mesenchymal progeny of four precursor cells, the micromeres, which are determined to the skeletogenic pathway by a process known as cytoplasmic localization. A gene encoding one of the major products of the skeletogenic mesenchyme, a prominent 50 kD protein of the spicule matrix, has been characterized in detail. cDNA clones were first isolated by antibody screening of a phage expression library, followed by isolation of homologous genomic clones. The gene, known as SM50, is single copy in the sea urchin genome, is divided into two exons of 213 and 1682 bp, and is expressed only in skeletogenic cells. Transcripts are first detectable at the 120 cell stage, shortly after the segregation of the skeletogenic precursors from the rest of the embryo. The SM50 open reading frame begins within the first exon, is 450 amino acids in length, and contains a loosely repeated 13 amino acid motif rich in acidic residues which accounts for 45% of the protein and which is possibly involved in interaction with the mineral phase of the spicule.

The important cis-acting regions of the SM50 gene necessary for proper regulation of expression were identified by gene transfer experiments. A 562 bp promoter fragment, containing 438 bp of 5' promoter sequence and 124 bp of the SM50 first exon (including the SM50 initiation codon), was both necessary and sufficient to direct high levels of expression of the bacterial chloramphenicol acetyltransferase (CAT) reporter gene specifically in the skeletogenic cells. Removal of promoter sequences between positions -2200 and -438, and of transcribed regions downstream of +124 (including the SM50 intron), had no effect on the spatial or transcriptional activity of the transgenes.

Regulatory proteins that interact with the SM50 promoter were identified by the gel retardation assay, using bulk embryo mesenchyme blastula stage nuclear proteins. Five protein binding sites were identified and mapped to various degrees of resolution. Two sites are homologous, may be enhancer elements, and at least one is required for expression. Two additional sites are also present in the promoter of the aboral ectoderm specific cytoskeletal actin gene CyIIIa; one of these is a CCAA T element, the other a putative repressor element. The fifth site overlaps the binding site of the putative repressor and may function as a positive regulator by interfering with binding of the repressor. All of the proteins are detectable in nuclear extracts prepared from 64 cell stage embryos, a stage just before expression of SM50 is initiated, as well as from blastula and gastrula stage; the putative enhancer binding protein may be maternal as well.

Continuous stochastic processes

A general review of stochastic processes is given in the introduction; definitions, properties and a rough classification are presented together with the position and scope of the author's work as it fits into the general scheme.

The first section presents a brief summary of the pertinent analytical properties of continuous stochastic processes and their probability-theoretic foundations which are used in the sequel.

The remaining two sections (II and III), comprising the body of the work, are the author's contribution to the theory. It turns out that a very inclusive class of continuous stochastic processes are characterized by a fundamental partial differential equation and its adjoint (the Fokker-Planck equations). The coefficients appearing in those equations assimilate, in a most concise way, all the salient properties of the process, freed from boundary value considerations. The writer’s work consists in characterizing the processes through these coefficients without recourse to solving the partial differential equations.

First, a class of coefficients leading to a unique, continuous process is presented, and several facts are proven to show why this class is restricted. Then, in terms of the coefficients, the unconditional statistics are deduced, these being the mean, variance and covariance. The most general class of coefficients leading to the Gaussian distribution is deduced, and a complete characterization of these processes is presented. By specializing the coefficients, all the known stochastic processes may be readily studied, and some examples of these are presented; viz. the Einstein process, Bachelier process, Ornstein-Uhlenbeck process, etc. The calculations are effectively reduced down to ordinary first order differential equations, and in addition to giving a comprehensive characterization, the derivations are materially simplified over the solution to the original partial differential equations.

In the last section the properties of the integral process are presented. After an expository section on the definition, meaning, and importance of the integral process, a particular example is carried through starting from basic definition. This illustrates the fundamental properties, and an inherent paradox. Next the basic coefficients of the integral process are studied in terms of the original coefficients, and the integral process is uniquely characterized. It is shown that the integral process, with a slight modification, is a continuous Markoff process.

The elementary statistics of the integral process are deduced: means, variances, and covariances, in terms of the original coefficients. It is shown that an integral process is never temporally homogeneous in a non-degenerate process.

Finally, in terms of the original class of admissible coefficients, the statistics of the integral process are explicitly presented, and the integral process of all known continuous processes are specified.