Soma-Axon Coupling Configurations That Enhance Neuronal Coincidence Detection

Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the input region (soma and dendrite) and the spike-generating output region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on the interaction between coupling configuration and two currents that provide dynamic, voltage-gated, negative feedback in subthreshold voltage range: sodium current with rapid inactivation and low-threshold potassium current, IKLT. These currents reduce synaptic summation and can prevent spike generation unless inputs arrive with near simultaneity. We show that strong soma-to-axon coupling promotes the negative feedback effects of sodium inactivation and is, therefore, advantageous for coincidence detection. Furthermore, the feedforward combination of strong soma-to-axon coupling and weak axon-to-soma coupling enables spikes to be generated efficiently (few sodium channels needed) and with rapid recovery that enhances high-frequency coincidence detection. These observations detail the functional benefit of the strongly feedforward configuration that has been observed in physiological studies of MSO neurons. We find that IKLT further enhances coincidence detection sensitivity, but with effects that depend on coupling configuration. For instance, in models with weak soma-to-axon and weak axon-to-soma coupling, IKLT in the axon enhances coincidence detection more effectively than IKLT in the soma. By using a minimal model of soma-to-axon coupling, we connect structure, dynamics, and computation. Although we consider the particular case of MSO coincidence detectors, our method for creating and exploring a parameter space of two-compartment models can be applied to other neurons

Factoring Higher-Dimensional Shifts Of Finite Type Onto The Full Shift

A one-dimensional shift of finite type with entropy at least log factors onto the full -shift. The factor map is constructed by exploiting the fact that , or a subshift of , is conjugate to a shift of finite type in which every symbol can be followed by at least symbols. We will investigate analogous statements for higher-dimensional shifts of finite type. We will also show that for a certain class of mixing higher-dimensional shifts of finite type, sufficient entropy implies that is finitely equivalent to a shift of finite type that maps onto the full -shift

Configuration Spaces Of Convex And Embedded Polygons In The Plane

This paper concerns the topology of configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that, modulo translations and rotations, each component of the space of convex configurations is homeomorphic to a closed Euclidean ball and each component of the space of embedded configurations is homeomorphic to a Euclidean space. This represents an elaboration on the topological information that follows from the convexification theorem of Connelly, Demaine, and Rote

Combined analysis of the K+K−K^{+}K^{-} interaction using near threshold pp→ppK+K−pp \to ppK^+K^- data

The $K^{+}K^{-}$ final state interaction was investigated based on both the $K^{+}K^{-}$ invariant mass distributions measured at excess energies of Q = 10 and 28 MeV and the near threshold excitation function for the $pp \to ppK^{+}K^{-}$ reaction. The $K^+K^-$ final state enhancement factor was parametrized using the effective range expansion. The effective range of the $K^+K^-$ interaction was estimated to be: $\mathrm{Re}(b_{K^{+}K^{-}}) = -0.1 \pm 0.4_{stat} \pm 0.3_{sys} \mathrm{fm}$ and $\mathrm{Im}(b_{K^{+}K^{-}}) = 1.2^{+0.1_{stat}+0.2_{sys}}_{-0.2_{stat}-0.0_{sys}} \mathrm{fm}$, and the determined real and imaginary parts of the $K^+K^-$ scattering length amount to: $|\mathrm{Re}(a_{K^{+}K^{-}})| = 8.0^{+6.0_{stat}}_{-4.0_{stat}} \mathrm{fm}$ and $\mathrm{Im}(a_{K^{+}K^{-}}) = 0.0^{+20.0_{stat}}_{-5.0_{stat}} \mathrm{fm}$.Comment: 5 pages, 3 figures, article accepted for publication in Phys. Rev.

Strong Bounded Solutions For Nonlinear Parabolic Systems

In this article we study the existence of strong bounded solutions for nonlinear parabolic systems on a domain which is bounded in space and unbounded in time (namely the entire real line). We use nonlinear iteration arguments combined with some a priori estimates to derive the existence results. We also provide conditions under which we have a positive solution. Some examples are given to illustrate the results

The Role Of The Receptive Field Structure In Neuronal Compressive Sensing Signal Processing

The receptive field structure ubiquitous in the visual system is believed to play a crucial role in encoding stimulus characteristics, such as contrast and spectral composition. However, receptive field architecture may also result in unforeseen difficulties in processing particular classes of images. We explore the potential functional benefits and shortcomings of localization and center-surround paradigms in the context of an integrate-and-fire neuronal network model. Utilizing the sparsity of natural scenes, we derive a compressive-sensing based theoretical framework for network input reconstructions based on neuronal firing rate dynamics [1, 2]. This formalism underlines a potential mechanism for efficiently transmitting sparse stimulus information, and further suggests sensory pathways may have evolved to take advantage of the sparsity of visual stimuli [3, 4]. Using this methodology, we investigate how the accuracy of image encoding depends on the network architecture. We demonstrate that the receptive field structure does indeed facilitate marked improvements in natural stimulus encoding at the price of yielding erroneous information about specific classes of stimuli. Relative to uniformly random sampling, we show that localized random sampling yields robust improvements in image reconstructions, which are most pronounced for natural stimuli containing a relatively large spread of dominant low frequency components. This suggests a novel direction for compressive sensing theory and sampling methodology in engineered devices. However, for images with specific gray-scale patterning, such as the Hermann grid depicted in Fig. 1, we show that localization in sampling produces systematic errors in image encoding that may underlie several optical illusions. We expect that these connections between input characteristics, network topology, and neuronal dynamics will give new insights into the structure-function relationship of the visual system

The Symbolic Dynamics Of Multidimensional Tiling Systems

We prove a multidimensional version of the theorem that every shift of finite type has a power that can be realized as the same power of a tiling system. We also show that the set of entropies of tiling systems equals the set of entropies of shifts of finite type

Auslander Systems

The authors generalize the dynamical system constructed by J. Auslander in 1959, resulting in perhaps the simplest family of examples of minimal but not strictly ergodic systems. A characterization of unique ergodicity and mean-L-stability is given. The new systems are also shown to have zero topological entropy and fail to be weakly rigid. Some results on the set of idempotents in the enveloping semigroup are also achieved

An Interview With Albert W. Tucker

The mathematical career of Albert W. Tucker, Professor Emeritus at Princeton University, spans more than 50 years. Best known today for his work in mathematical programming and the theory of games (e.g., the Kuhn-Tucker theorem, Tucker tableaux, and the Prisoner\u27s Dilemma), he was also in his earlier years prominent in topology. Outstanding teacher, administrator and leader, he has been President of the MAA, Chairman of the Princeton Mathematics Department, and course instructor, thesis advisor or general mentor to scores of active mathematicians. He is also known for his views on mathematics education and the proper interplay between teaching and research. Tucker took an active interest in this interview, helping with both the planning and the editing. The interviewer, Professor Maurer, received his Ph.D. under Tucker in 1972 and teaches at Swarthmore College