On the spectra of certain integro-differential-delay problems with applications in neurodynamics

We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.

Differential brain activity during emotional versus nonemotional reversal learning

The ability to change an established stimulus–behavior association based on feedback is critical for adaptive social behaviors. This ability has been examined in reversal learning tasks, where participants first learn a stimulus–response association (e.g., select a particular object to get a reward) and then need to alter their response when reinforcement contingencies change. Although substantial evidence demonstrates that the OFC is a critical region for reversal learning, previous studies have not distinguished reversal learning for emotional associations from neutral associations. The current study examined whether OFC plays similar roles in emotional versus neutral reversal learning. The OFC showed greater activity during reversals of stimulus–outcome associations for negative outcomes than for neutral outcomes. Similar OFC activity was also observed during reversals involving positive outcomes. Furthermore, OFC activity is more inversely correlated with amygdala activity during negative reversals than during neutral reversals. Overall, our results indicate that the OFC is more activated by emotional than neutral reversal learning and that OFC's interactions with the amygdala are greater for negative than neutral reversal learning.

Differential interaction of estrogen receptor and thyroid hormone receptor isoforms on the rat oxytocin receptor promoter leads to differences in transcriptional regulation

Both the estrogen receptor (ER) and thyroid hormone receptor (TR) are members of the nuclear receptor superfamily. Two isoforms of the ER, alpha and beta, exist. The TRalpha and beta isoforms are products of two distinct genes that are further differentially spliced to give TRalpha1 and alpha2, TRbeta1 and beta2. The TRs have been shown to interfere with ER-mediated transcription from both the consensus estrogen response element (ERE) and the rat preproenkephalin (PPE) promoter, possibly by competing with ER binding to the ERE or by squelching coactivators essential for ER-mediated transcription. The rat oxytocin receptor (OTR) gene is thought to be involved in several facets of reproductive and affiliative behaviors. 17beta-Estradiol-bound ERs upregulate the OTR gene in the ventromedial hypothalamus, a region critical for the induction of lordosis behavior in several species. We investigated the effects of the ligand-binding TR isoforms on the ER-mediated transcription from a physiological promoter of a behaviorally relevant gene such as the OTR. Only ERalpha could induce the OTR gene in two cell lines tested, the CV-1 and the SK-N-BE2C neuroblastoma cell lines. ERbeta was incapable of inducing the gene in either cell line. ERalpha is therefore not equivalent to ERbeta on this physiological promoter. Indeed, in the neural cell line, ERbeta can inhibit ERalpha-mediated induction from the OTR promoter. While the TRalpha1 isoform inhibited ERalpha-mediated induction in the neural cell line, the TRbeta1 isoform stimulated induction, thus demonstrating isoform specificity in the interaction. The use of a DNA-binding mutant, the TR P box mutant, showed that inhibition of ERalpha-mediated induction of the rat OTR gene promoter by the TRalpha1 isoform does not require DNA-binding ability. SRC-1 overexpression relieved TRalpha1-mediated inhibition in both cell lines, suggesting that squelching for coactivators is an important molecular mechanism in TRalpha-mediated inhibition. Such interactions between TR and ER isoforms on the rat OTR promoter provide a mechanism to achieve neuroendocrine integration.

Differential crosstalk between estrogen receptor (ER) alpha and ER beta and the thyroid hormone receptor isoforms results in flexible regulation of the consensus ERE

Crosstalk between nuclear receptors is important for conversion of external and internal stimuli to a physiologically meaningful response by cells. Previous studies from this laboratory have demonstrated crosstalk between the estrogen (ER) and thyroid hormone receptors (TR) on two estrogen responsive physiological promoters, the preproenkephalin and oxytocin receptor gene promoter. Since ERa and ERb are isoforms possessing overlapping and distinct transactivation properties, we hypothesized that the interaction of ERa and b with the various TR isoforms would not be equivalent. To explore this hypothesis, the consensus estrogen response element (ERE)derived from the Xenopus vitellogenin gene is used to investigate the differences in interaction between ERa and b isoforms and the different TR isoforms in fibroblast cells. Both the ER isoforms transactivate from the consensus ERE, though ERa transactivates to a greater extent than ERb. Although neither of the TRb isoforms have an effect on ERa transactivation from the consensus ERE, the liganded TRa1 inhibits the ERa transactivation from the consensus ERE. In contrast, the liganded TRa1 facilitates ERb-mediated transactivation. The crosstalk between the TRb isoforms with the ERa isoform, on the consensus ERE, is different from that with the ERb isoform. The use of a TRa1 mutant, which is unable to bind DNA, abolishes the ability of the TRa1 isoform to interact with either of the ER isoforms. These differences in nuclear receptor crosstalk reveal an important functional difference between isoforms, which provides a novel mechanism for neuroendocrine integration.