Single-valued harmonic polylogarithms and the multi-Regge limit

We argue that the natural functions for describing the multi-Regge limit of six-gluon scattering in planar N=4 super Yang-Mills theory are the single-valued harmonic polylogarithmic functions introduced by Brown. These functions depend on a single complex variable and its conjugate, (w,w*). Using these functions, and formulas due to Fadin, Lipatov and Prygarin, we determine the six-gluon MHV remainder function in the leading-logarithmic approximation (LLA) in this limit through ten loops, and the next-to-LLA (NLLA) terms through nine loops. In separate work, we have determined the symbol of the four-loop remainder function for general kinematics, up to 113 constants. Taking its multi-Regge limit and matching to our four-loop LLA and NLLA results, we fix all but one of the constants that survive in this limit. The multi-Regge limit factorizes in the variables (\nu,n) which are related to (w,w*) by a Fourier-Mellin transform. We can transform the single-valued harmonic polylogarithms to functions of (\nu,n) that incorporate harmonic sums, systematically through transcendental weight six. Combining this information with the four-loop results, we determine the eigenvalues of the BFKL kernel in the adjoint representation to NNLLA accuracy, and the MHV product of impact factors to NNNLLA accuracy, up to constants representing beyond-the-symbol terms and the one symbol-level constant. Remarkably, only derivatives of the polygamma function enter these results. Finally, the LLA approximation to the six-gluon NMHV amplitude is evaluated through ten loops.Comment: 71 pages, 2 figures, plus 10 ancillary files containing analytic expressions in Mathematica format. V2: Typos corrected and references added. V3: Typos corrected; assumption about single-Reggeon exchange made explici

A model of direction selectivity in the starburst amacrine cell network

Displaced starburst amacrine cells (SACs) are retinal interneurons that exhibit GABAA receptor-mediated and Cl− cotransporter-mediated, directionally selective (DS) light responses in the rabbit retina. They depolarize to stimuli that move centrifugally through the receptive field surround and hyperpolarize to stimuli that move centripetally through the surround (Gavrikov et al, PNAS 100(26):16047–16052, 2003, PNAS 103(49):18793–18798, 2006). They also play a key role in the activity of DS ganglion cells (DS GC; Amthor et al, Vis Neurosci 19:495–509 2002; Euler et al, Nature 418:845–852, 2002; Fried et al, Nature 420:411– 414, 2002; Gavrikov et al, PNAS 100(26):16047–16052, 2003, PNAS 103(49):18793–18798, 2006; Lee and Zhou, Neuron 51:787–799 2006; Yoshida et al, Neuron 30:771–780, 2001). In this paper we present a model of strong DS behavior of SACs which relies on the GABA-mediated communication within a tightly interconnected network of these cells and on the glutamate signal that the SACs receive from bipolar cells (a presynaptic cell that receives input from cones). We describe how a moving light stimulus can produce a large, sustained depolarization of the SAC dendritic tips that point in the direction that the stimulus moves (i.e., centrifugal motion), but produce a minimal depolarization of the dendritic tips that point in the opposite direction (i.e., centripetal motion). This DS behavior, which is quantified based on the relative size and duration of the depolarizations evoked by stimulus motion at dendritic tips pointing in opposite directions, is robust to changes of many different parameter values and consistent with experimental data. In addition, the DS behavior is strengthened under the assumptions that the Cl− cotransporters Na + -K + -Cl − and K + -Cl − are located in different regions of the SAC dendritic tree (Gavrikov et al, PNAS 103(49):18793–18798, 2006) and that GABA evokes a long-lasting response (Gavrikov et al, PNAS 100(26):16047–16052, 2003, PNAS 103(49):18793–18798, 2006; Lee and Zhou, Neuron 51:787–799, 2006). A possible mechanism is discussed based on the generation of waves of local glutamate and GABA secretion, and their postsynaptic interplay as the waves travel between cell compartments

Direction-Selective Circuitry in Rat Retina Develops Independently of GABAergic, Cholinergic and Action Potential Activity

The ON-OFF direction selective ganglion cells (DSGCs) in the mammalian retina code image motion by responding much more strongly to movement in one direction. They do so by receiving inhibitory inputs selectively from a particular sector of processes of the overlapping starburst amacrine cells, a type of retinal interneuron. The mechanisms of establishment and regulation of this selective connection are unknown. Here, we report that in the rat retina, the morphology, physiology of the ON-OFF DSGCs and the circuitry for coding motion directions develop normally with pharmacological blockade of GABAergic, cholinergic activity and/or action potentials for over two weeks from birth. With recent results demonstrating light independent formation of the retinal DS circuitry, our results strongly suggest the formation of the circuitry, i.e., the connections between the second and third order neurons in the visual system, can be genetically programmed, although emergence of direction selectivity in the visual cortex appears to require visual experience

Dendritic Spikes Amplify the Synaptic Signal to Enhance Detection of Motion in a Simulation of the Direction-Selective Ganglion Cell

The On-Off direction-selective ganglion cell (DSGC) in mammalian retinas responds most strongly to a stimulus moving in a specific direction. The DSGC initiates spikes in its dendritic tree, which are thought to propagate to the soma with high probability. Both dendritic and somatic spikes in the DSGC display strong directional tuning, whereas somatic PSPs (postsynaptic potentials) are only weakly directional, indicating that spike generation includes marked enhancement of the directional signal. We used a realistic computational model based on anatomical and physiological measurements to determine the source of the enhancement. Our results indicate that the DSGC dendritic tree is partitioned into separate electrotonic regions, each summing its local excitatory and inhibitory synaptic inputs to initiate spikes. Within each local region the local spike threshold nonlinearly amplifies the preferred response over the null response on the basis of PSP amplitude. Using inhibitory conductances previously measured in DSGCs, the simulation results showed that inhibition is only sufficient to prevent spike initiation and cannot affect spike propagation. Therefore, inhibition will only act locally within the dendritic arbor. We identified the role of three mechanisms that generate directional selectivity (DS) in the local dendritic regions. First, a mechanism for DS intrinsic to the dendritic structure of the DSGC enhances DS on the null side of the cell's dendritic tree and weakens it on the preferred side. Second, spatially offset postsynaptic inhibition generates robust DS in the isolated dendritic tips but weak DS near the soma. Third, presynaptic DS is apparently necessary because it is more robust across the dendritic tree. The pre- and postsynaptic mechanisms together can overcome the local intrinsic DS. These local dendritic mechanisms can perform independent nonlinear computations to make a decision, and there could be analogous mechanisms within cortical circuitry

Targeted Curing of All Lysogenic Bacteriophage from Streptococcus pyogenes Using a Novel Counter-selection Technique

We thank the members of the Laboratory of Microbial Pathogenesis and Immunology, especially Annette Nelkenbaum and Ben Winer for their technical assistance. We also thank Estee Colleen Cervantes and Sutapa Banerjee from Hunter College for their technical contribution to this project. We are grateful to Joseph Ferretti for S. pyogenes strain SF370.Streptococcus pyogenes is a human commensal and a bacterial pathogen responsible for a wide variety of human diseases differing in symptoms, severity, and tissue tropism. The completed genome sequences of >37 strains of S. pyogenes, representing diverse disease-causing serotypes, have been published. The greatest genetic variation among these strains is attributed to numerous integrated prophage and prophage-like elements, encoding several virulence factors. A comparison of isogenic strains, differing in prophage content, would reveal the effects of these elements on streptococcal pathogenesis. However, curing strains of prophage is often difficult and sometimes unattainable. We have applied a novel counter-selection approach to identify rare S. pyogenes mutants spontaneously cured of select prophage. To accomplish this, we first inserted a two-gene cassette containing a gene for kanamycin resistance (KanR) and the rpsL wild-type gene, responsible for dominant streptomycin sensitivity (SmS), into a targeted prophage on the chromosome of a streptomycin resistant (SmR) mutant of S. pyogenes strain SF370. We then applied antibiotic counter-selection for the re-establishment of the KanS/SmR phenotype to select for isolates cured of targeted prophage. This methodology allowed for the precise selection of spontaneous phage loss and restoration of the natural phage attB attachment sites for all four prophage-like elements in this S. pyogenes chromosome. Overall, 15 mutants were constructed that encompassed every permutation of phage knockout as well as a mutant strain, named CEM1ΔΦ, completely cured of all bacteriophage elements (a ~10% loss of the genome); the only reported S. pyogenes strain free of prophage-like elements. We compared CEM1ΔΦ to the WT strain by analyzing differences in secreted DNase activity, as well as lytic and lysogenic potential. These mutant strains should allow for the direct examination of bacteriophage relationships within S. pyogenes and further elucidate how the presence of prophage may affect overall streptococcal survival, pathogenicity, and evolution.Yeshttp://www.plosone.org/static/editorial#pee