Function of the Shaw potassium channel within the Drosophila circadian clock

Background

In addition to the molecular feedback loops, electrical activity has been shown to be important for the function of networks of clock neurons in generating rhythmic behavior. Most studies have used over-expression of foreign channels or pharmacological manipulations that alter membrane excitability. In order to determine the cellular mechanisms that regulate resting membrane potential (RMP) in the native clock of Drosophila we modulated the function of Shaw, a widely expressed neuronal potassium (K⁺) channel known to regulate RMP in Drosophila central neurons.

Methodology/Principal Findings

We show that Shaw is endogenously expressed in clock neurons. Differential use of clock gene promoters was employed to express a range of transgenes that either increase or decrease Shaw function in different clusters of clock neurons. Under LD conditions, increasing Shaw levels in all clock neurons (LNv, LNd, DN₁, DN₂ and DN₃), or in subsets of clock neurons (LNd and DNs or DNs alone) increases locomotor activity at night. In free-running conditions these manipulations result in arrhythmic locomotor activity without disruption of the molecular clock. Reducing Shaw in the DN alone caused a dramatic lengthening of the behavioral period. Changing Shaw levels in all clock neurons also disrupts the rhythmic accumulation and levels of Pigment Dispersing Factor (PDF) in the dorsal projections of LNv neurons. However, changing Shaw levels solely in LNv neurons had little effect on locomotor activity or rhythmic accumulation of PDF.

Conclusions/Significance

Based on our results it is likely that Shaw modulates pacemaker and output neuronal electrical activity that controls circadian locomotor behavior by affecting rhythmic release of PDF. The results support an important role of the DN clock neurons in Shaw-mediated control of circadian behavior. In conclusion, we have demonstrated a central role of Shaw for coordinated and rhythmic output from clock neurons.     

Anti-Hebbian learning in a non-linear neural network

The Hebbian rule (Hebb 1949), coupled with an appropriate mechanism to limit the growth of synaptic weights, allows a neuron to learn to respond to the first principal component of the distribution of its input signals (Oja 1982). Rubner and Schulten (1990) have recently suggested the use of an anti-Hebbian rule in a network with hierarchical lateral connections. When applied to neurons with linear response functions, this model allows additional neurons to learn to respond to additional principal components (Rubner and Tavan 1989). Here we apply the model to neurons with non-linear response functions characterized by a threshold and a transition width. We propose local, unsupervised learning rules for the threshold and the transition width, and illustrate the operation of these rules with some simple examples. A network using these rules sorts the input patterns into classes, which it identifies by a binary code, with the coarser structure coded by the earlier neurons in the hierarchy.     

6-Dimethyl amino purine and 2-amino purine inhibit the induction of expresion of milk protein genes by prolactin

Two protein kinase-inhibitors, 6-dimethyl amino purine and 2-amino purine inhibited induction of -casein synthesis by prolactin when added to the culture medium of rabbit mammary explant and cells. The accumulation of the mRNA for _s1- and -caseins and for whey acidic protein did not take place in the presence of the inhibitors whereas -actin mRNA concentration was not altered. In the same experimental conditions, H7, an inhibitor of protein kinase C and, to a lower extent, of protein kinase A did not prevent prolactin from acting. These data suggest for the first time that specific protein kinases are involved in the transduction of the prolactin signal to milk protein genes.Abbreviations 6-DMAP 6-dimethyl amino purine - 2-AP 2-amino purine - H7 1-(5 isoquinoline sulfonyl)-2-methyl-piperazine dihydrochloride - WAP whey acidic protein - PRL prolactin     

Study of synaptic plasticity via random graphs

The dynamical random graphs associated with a certain class of biological neural networks are introduced and studied. We describe the phase diagram revealing the parameters of a single neuron and of the synaptic strengths which allow formation of the stable strongly connected large groups of neurons. It is shown that the cycles are the most stable structures when the Hebb rule is implemented into the dynamics of the network of excitatory neurons. We discuss the role of cycles for the synchronization of the neuronal activity.     

Effects of noradrenaline on neuronal response induced in the motor cortex by conditioned stimuli

In chronic experiments on cats, the effects were investigated of iontophoretic application of the adrenomimetic ephedrine and the -blocker obsidan (propranolol) on neuronal response induced in the motor cortex by conditioned stimulus presentation during performances of instrumental lever-pressing response. Inhibition of background firing activity and response in most neurons induced by conditioned stimuli was produced by ephedrine, whereas obsidan application enhanced this activity. It was concluded that steady, tonic inhibitory action of the noradrenergic system on background and induced firing activity in cortical neurons takes place during free-ranging behavior. Temporary reinforcement of noradrenergic influences could be an important element in mechanisms of external inhibition during stressful situations, aversive effects, and distractive stimuli.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 22, No. 5, pp. 680–688, September–October, 1990.     

Incorporating phenotype-dependent growth rates into the color-shift model for preneoplastic hepatocellular lesions

Multi-stage models occupy a central position in modeling the carcinogenesis process. These models formalize the hypothesis that cells have to undergo several transformations on their way to malignancy. This hypothesis assumes that a preneoplastic cell of a later stage arises through a mutational event of a single cell of a previous stage and that preneoplastic cells proliferate clonally. However, there is some evidence that multi-stage models cannot adequately describe the formation and the progression of preneoplastic lesions at least in certain organs [Math. Biosci. 168 (2000) 167]. An alternative model assuming that all cells in a colony of altered hepatocytes change their phenotype more or less simultaneously rather than by mutation of single cells has already been introduced [Math. Biosci. 148 (1998) 181] and is called color-shift model (CSM). This model assumed deterministic phenotype-independent growth for the foci once they are generated. An expansion of the CSM allowing for variability between deterministic growth behaviour of phenotypically different colonies is presented (modCSM) and the model is applied to focal lesion data from a rat hepatocarcinogenesis experiment. The fit of the originally proposed and the modCSM are compared with respect to their ability to predict numbers and radii of preneoplastic cell foci.     

Functional conservation of atonal and Math1 in the CNS and PNS

To determine the extent to which atonal and its mouse homolog Math1 exhibit functional conservation, we inserted (beta)-galactosidase (lacZ) into the Math1 locus and analyzed its expression, evaluated consequences of loss of Math1 function, and expressed Math1 in atonal mutant flies. lacZ under the control of Math1 regulatory elements duplicated the previously known expression pattern of Math1 in the CNS (i.e., the neural tube, dorsal spinal cord, brainstem, and cerebellar external granule neurons) but also revealed new sites of expression: PNS mechanoreceptors (inner ear hair cells and Merkel cells) and articular chondrocytes. Expressing Math1 induced ectopic chordotonal organs (CHOs) in wild-type flies and partially rescued CHO loss in atonal mutant embryos. These data demonstrate that both the mouse and fly homologs encode lineage identity information and, more interestingly, that some of the cells dependent on this information serve similar mechanoreceptor functions.     

Affinity purification of the tobacco plastid RNA polymerase and in vitro reconstitution of the holoenzyme

We affinity-purified the tobacco plastid-encoded plastid RNA polymerase (PEP) complex by the alpha subunit containing a C-terminal 12 x histidine tag using heparin and Ni(2+) chromatography. The composition of the complex was determined by mass spectrometry after separating the proteins of the >900 kDa complex in blue native and SDS polyacrylamide gels. The purified PEP contained the core alpha, beta, beta', beta" subunits and five major associated proteins of unknown function, but lacked sigma factors required for promoter recognition. The holoenzyme efficiently recognized a plastid psbA promoter when it was reconstituted from the purified PEP and recombinant plastid sigma factors. Reconstitution of a plastid holoenzyme with individual sigma factors will facilitate identification of sigma factor-specific promoter elements.     

Calculation of the cumulative distribution function of the time to a small observable tumor

Multistage mathematical models of carcinogenesis (when applied to tumor incidence data) have historically assumed that the growth kinetics of cells in the malignant state are disregarded and the formation of a single malignant cell is equated with the emergence of a detectable tumor. The justification of this simplification is, from a mathematical point of view, to make the estimation of tumor incidence rates tractable. However, analytical forms are not mandatory in the estimation of tumor incidence rates. Portier et al. (1996b, Math. Biosci. 135, 129–146) have demonstrated the utility of the Kolmogorov backward equations in numerically calculating tumor incidence. By extending their results, the cumulative distribution function of the time to a small observable tumor may be numerically obtained.     

A stochastic modeling of early HIV-1 population dynamics

In a recent paper, Tuckwell and Le Corfec [J. Theor. Biol. 195 (1998) 450-463] applied the multi-dimensional diffusion process to model early human immunodeficiency virus type-1 (HIV-1) population dynamics. The purpose of this paper is to assess certain features and consequences of their model in the context of Tan and Wu's stochastic approach [Math. Biosci. 147 (1998) 173-205].     

Prion dynamics with size dependency-strain phenomena

Models for the polymerization process involved in prion self-replication are well-established and studied [H. Engler, J. Pruss, and G.F. Webb, Analysis of a model for the dynamics of prions II, J. Math. Anal. Appl. 324 (2006), pp. 98-117; M.L. Greer, L. Pujo-Menjouet, and G.F. Webb, A mathematical analysis of the dynamics of prion proliferation, J. Theoret. Biol. 242 (2006), pp. 598-606; J. Pruss, L. Pujo-Menjouet, G.F. Webb, and R. Zacher, Analysis of a model for the dynamics of prions, Discrete Cont. Dyn. Sys. Ser. B 6(1) (2006), pp. 215-225] in the case where the dynamics coefficients do not depend on the size of polymers. However, several experimental studies indicate that the structure and size of the prion aggregates are determinant for their pathological effect. This motivated the analysis in Calvez et al. [Size distribution dependence of prion aggregates infectivity, Math Biosci. 217 (2009), pp. 88-99] where the authors take into account size-dependent replicative properties of prion aggregates. We first improve a result concerning the dynamics of prion aggregates when a pathological state exists (high production of the normal protein). Then we study the strain phenomena and more specifically we wonder what specific replicative properties are determinant in strain propagation. We propose to interpret it also as a dynamical property of size repartitions.     

Self-organization of neurons described by the maximum-entropy principle

In the article the maximum-entropy principle and Parzen windows are applied to derive an optimal mapping of a continuous into a descrete random variable. The mapping can be performed by a network of self-organizing information processing units similar to biological neurons. Each neuron is selectively sensitized to one prototype from the sample space of the discrete random variable. The continuous random variable is applied as the input signal exciting the neurons. The response of the network is described by the excitation vector which represents the encoded input signal. Due to the interaction between neurons adaptive changes of prototypes are caused by the excitations. The derived mathematical model explains this interaction in detail; a simplified self-organization rule derived from it corresponds to that of Kohonen. One and two-dimensional examples of self-organization simulated on a computer are shown in the article.     

A phylogenomic study of the general stress response sigma factor sigmaB of Bacillus subtilis and its regulatory proteins

Regulation of expression of the general stress regulon of Bacillus subtilis is mediated by the activation of the alternative sigma factor sigmaB. Activation of sigmaB is accomplished by a complex regulatory network involving protein-protein interactions and reversible protein phosphorylation. PSI-BLAST searches were performed and phylogenetic trees for sigmaB and its regulatory proteins were constructed. Occurrence of sigmaB is restricted to a small group of gram-positive bacteria (Bacillus, Staphylococcus, Listeria). Related sigma factors also involved in stress responses are present in Mycobacterium tuberculosis, Streptomyces species and even in cyanobacteria (Synechocystis species). Putative regulatory proteins found in several other bacterial species can be broadly catagorized into three categories: Anti sigma factors, anti-anti sigma factors and phosphatases. Anti sigma factors are able to bind to sigma factors and are also kinases of anti sigma factor antagonists. Only in their nonphosphorylated state, these antagonists are able to bind to the anti sigma factor. Phosphorylated antagonists can be dephosphorylated by PP2C phosphatases. These phosphatases are of pivotal importance for activation of the sigma factor. Different phosphatases identified in this search contain a wide variety of domains found in signal transducing proteins (PAS/PAC, GAF, REC, HATase_c, HAMP). The HATPase_c domain found in several phosphatases most probably constitutes a serine/threonine kinase domain of anti sigma factors. Such proteins are most probably bifunctional anti-anti sigma factor kinases and phosphatases. The regulatory network of anti-anti sigma factors anti sigma factors and phosphatases is probably ancient and most likely evolved from a structurally similar network found in the Deinococcus radiodurans genome. In completely sequenced genomes of several bacterial species, some elements of the network are missing. The N-terminus of RsbU, a phosphatase activated in response to environmental stress exhibits similarities to a region in the beta chain of phenylalanyl-tRNA synthetases.     

Distinctive topologies of partner-switching signaling networks correlate with their physiological roles

Regulatory networks controlling bacterial gene expression often evolve from common origins and share homologous proteins and similar network motifs. However, when functioning in different physiological contexts, these motifs may be re-arranged with different topologies that significantly affect network performance. Here we analyze two related signaling networks in the bacterium Bacillus subtilis in order to assess the consequences of their different topologies, with the aim of formulating design principles applicable to other systems. These two networks control the activities of the general stress response factor sigma(B) and the first sporulation-specific factor sigma(F). Both networks have at their core a "partner-switching" mechanism, in which an anti-sigma factor forms alternate complexes either with the sigma factor, holding it inactive, or with an anti-anti-sigma factor, thereby freeing sigma. However, clear differences in network structure are apparent: the anti-sigma factor for sigma(F) forms a long-lived, "dead-end" complex with its anti-anti-sigma factor and ADP, whereas the genes encoding sigma(B) and its network partners lie in a sigma(B)-controlled operon, resulting in positive and negative feedback loops. We constructed mathematical models of both networks and examined which features were critical for the performance of each design. The sigma(F) model predicts that the self-enhancing formation of the dead-end complex transforms the network into a largely irreversible hysteretic switch; the simulations reported here also demonstrate that hysteresis and slow turn off kinetics are the only two system properties associated with this complex formation. By contrast, the sigma(B) model predicts that the positive and negative feedback loops produce graded, reversible behavior with high regulatory capacity and fast response time. Our models demonstrate how alterations in network design result in different system properties that correlate with regulatory demands. These design principles agree with the known or suspected roles of similar networks in diverse bacteria.     

Dynamics of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells

Stilianakis and Seydel (Bull. Math. Biol., 1999) proposed an ODE model that describes the T-cell dynamics of human T-cell lymphotropic virus I (HTLV-I) infection and the development of adult T-cell leukemia (ATL). Their model consists of four components: uninfected healthy CD4+ T-cells, latently infected CD4+ T-cells, actively infected CD4+ T-cells, and ATL cells. Mathematical analysis that completely determines the global dynamics of this model has been done by Wang et al. (Math. Biosci., 2002). In this note, we first modify the parameters of the model to distinguish between contact and infectivity rates. Then we introduce a discrete time delay to the model to describe the time between emission of contagious particles by active CD4+ T-cells and infection of pure cells. Using the results in Culshaw and Ruan (Math. Biosci., 2000) in the analysis of time delay with respect to cell-free viral spread of HIV, we study the effect of time delay on the stability of the endemically infected equilibrium. Numerical simulations are presented to illustrate the results.     

A stochastic carcinogenesis model incorporating multiple types of genomic instability fitted to colon cancer data

A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little [Little, M.P. (1995). Are two mutations sufficient to cause cancer? Some generalizations of the two-mutation model of carcinogenesis of Moolgavkar, Venzon, and Knudson, and of the multistage model of Armitage and Doll. Biometrics 51, 1278-1291] and Little and Wright [Little, M.P., Wright, E.G. (2003). A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math. Biosci. 183, 111-134] is developed; the model incorporates multiple types of progressive genomic instability and an arbitrary number of mutational stages. The model is fitted to US Caucasian colon cancer incidence data. On the basis of the comparison of fits to the population-based data, there is little evidence to support the hypothesis that the model with more than one type of genomic instability fits better than models with a single type of genomic instability. Given the good fit of the model to this large dataset, it is unlikely that further information on presence of genomic instability or of types of genomic instability can be extracted from age-incidence data by extensions of this model.     

Math1 expression redefines the rhombic lip derivatives and reveals novel lineages within the brainstem and cerebellum

The rhombic lip (RL) is an embryonic proliferative neuroepithelium that generates several groups of hindbrain neurons. However, the precise boundaries and derivatives of the RL have never been genetically identified. We use beta-galactosidase expressed from the Math1 locus in Math1-heterozygous and Math1-null mice to track RL-derived cells and to evaluate their developmental requirements for Math1. We uncover a Math1-dependent rostral rhombic-lip migratory stream (RLS) that generates some neurons of the parabrachial, lateral lemniscal, and deep cerebellar nuclei, in addition to cerebellar granule neurons. A more caudal Math1-dependent cochlear extramural stream (CES) generates the ventral cochlear nucleus and cochlear granule neurons. Similarly, mossy-fiber precerebellar nuclei require Math1, whereas the inferior olive and locus coeruleus do not. We propose that Math1 expression delimits the extent of the rhombic lip and is required for the generation of the hindbrain superficial migratory streams, all of which contribute neurons to the proprioceptive/vestibular/auditory sensory network.     

Enhancement of a sigma(B)-dependent stress response in Bacillus subtilis by light via YtvA photoreceptor

YtvA of Bacillus subtilis consists of light, oxygen or voltage (LOV) domain and sulfate transporter and anti-sigma antagonist (STAS) domain, and was reported to act as a photoreceptor, sensing light signals through the LOV domain, like a plant blue light receptor, phototropin. At the same time, YtvA was reported to act as a positive regulator for stress responsive-gene expression regulated by sigma(B) factor. Here we indicate that, like phototropins, the conserved Cys residue among the LOV domains is required for light-sensing in YtvA in vitro, possibly by the photoadduct formation, and YtvA forms a homodimer via its LOV domain, independently to light signal. We also indicate that, when ytvA expression is in normal level, light itself does not trigger sigma(B) activation, but a photo-enhancement of sigma(B) activity, activated by salt stress, occurs only in the presence of ytvA. The conserved Cys residue in the LOV domain and the STAS domain seem to be responsible for light-sensing and signal-transmission to the sigma(B) regulatory network, respectively.     

Origins of the Human Brain

Origins of the Human Brain. J. P. Changeux and J. Chavaillon. eds. Oxford, England: Oxford University Press, 1995. 321 pp.