How spiking neurons give rise to a temporal-feature map

A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells’ synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit from the nonlinearity

Spikelets in pyramidal neurons: generating mechanisms, distinguishing properties, and functional implications

Spikelets are small spike-like depolarizations that are found in somatic recordings of many neuron types. Spikelets have been assigned important functions, ranging from neuronal synchronization to the regulation of synaptic plasticity, which are specific to the particular mechanism of spikelet generation. As spikelets reflect spiking activity in neuronal compartments that are electrotonically distinct from the soma, four modes of spikelet generation can be envisaged: (1) dendritic spikes or (2) axonal action potentials occurring in a single cell as well as action potentials transmitted via (3) gap junctions or (4) ephaptic coupling in pairs of neurons. In one of the best studied neuron type, cortical pyramidal neurons, the origins and functions of spikelets are still unresolved; all four potential mechanisms have been proposed, but the experimental evidence remains ambiguous. Here we attempt to reconcile the scattered experimental findings in a coherent theoretical framework. We review in detail the various mechanisms that can give rise to spikelets. For each mechanism, we present the biophysical underpinnings as well as the resulting properties of spikelets and compare these predictions to experimental data from pyramidal neurons. We also discuss the functional implications of each mechanism. On the example of pyramidal neurons, we illustrate that several independent spikelet-generating mechanisms fulfilling vastly different functions might be operating in a single cell

Early Cortical Changes in Gamma Oscillations in Alzheimer’s Disease

The entorhinal cortices in the temporal lobe of the brain are key structures relaying memory related information between the neocortex and the hippocampus. The medial entorhinal cortex (MEC) routes spatial information, whereas the lateral entorhinal cortex (LEC) routes predominantly olfactory information to the hippocampus. Gamma oscillations are known to coordinate information transfer between brain regions by precisely timing population activity of neuronal ensembles. Here, we studied the organization of in vitro gamma oscillations in the MEC and LEC of the transgenic (tg) amyloid precursor protein (APP)-presenilin 1 (PS1) mouse model of Alzheimer’s Disease (AD) at 4–5 months of age. In vitro gamma oscillations using the kainate model peaked between 30–50 Hz and therefore we analyzed the oscillatory properties in the 20–60 Hz range. Our results indicate that the LEC shows clear alterations in frequency and power of gamma oscillations at an early stage of AD as compared to the MEC. The gamma-frequency oscillation slows down in the LEC and also the gamma power in dorsal LEC is decreased as early as 4–5 months in the tg APP-PS1 mice. The results of this study suggest that the timing of olfactory inputs from LEC to the hippocampus might be affected at an early stage of AD, resulting in a possible erroneous integration of the information carried by the two input pathways to the hippocampal subfields.Peer Reviewe

Equilibrium Properties of Temporally Asymmetric Hebbian Plasticity

A theory of temporally asymmetric Hebb (TAH) rules which depress or potentiate synapses depending upon whether the postsynaptic cell fires before or after the presynaptic one is presented. Using the Fokker-Planck formalism, we show that the equilibrium synaptic distribution induced by such rules is highly sensitive to the manner in which bounds on the allowed range of synaptic values are imposed. In a biologically plausible multiplicative model, we find that the synapses in asynchronous networks reach a distribution that is invariant to the firing rates of either the pre- or post-synaptic cells. When these cells are temporally correlated, the synaptic strength varies smoothly with the degree and phase of synchrony between the cells.Comment: 3 figures, minor corrections of equations and tex

Double- to Single-Strand Transition Induces Forces and Motion in DNA Origami Nanostructures

The design of dynamic, reconfigurable devices is crucial for the bottom-up construction of artificial biological systems. DNA can be used as an engineering material for the de-novo design of such dynamic devices. A self-assembled DNA origami switch is presented that uses the transition from double- to single-stranded DNA and vice versa to create and annihilate an entropic force that drives a reversible conformational change inside the switch. It is distinctively demonstrated that a DNA single-strand that is extended with 0.34 nm per nucleotide - the extension this very strand has in the double-stranded configuration - exerts a contractive force on its ends leading to large-scale motion. The operation of this type of switch is demonstrated via transmission electron microscopy, DNA-PAINT super-resolution microscopy and darkfield microscopy. The work illustrates the intricate and sometimes counter-intuitive forces that act in nanoscale physical systems that operate in fluids

Intrinsic Stabilization of Output Rates by Spike-Based Hebbian Learning

We study analytically a model of long-term synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time differences between pre- and postsynaptic spikes. We show that plasticity can lead to an intrinsic stabilization of the mean firing rate of the postsynaptic neuron. Subtractive normalization of the synaptic weights (summed over all presynaptic inputs converging on a postsynaptic neuron) follows if, in addition, the mean input rates and the mean input correlations are identical at all synapses. If the integral over the learning window is positive, firing-rate stabilization requires a non-Hebbian component, whereas such a component is not needed, if the integral of the learning window is negative. A negative integral corresponds to `anti-Hebbian' learning in a model with slowly varying firing rates. For spike-based learning, a strict distinction between Hebbian and `anti-Hebbian' rules is questionable since learning is driven by correlations on the time scale of the learning window. The correlations between presynaptic and postsynaptic firing are evaluated for a piecewise-linear Poisson model and for a noisy spiking neuron model with refractoriness. Whereas a negative integral over the learning window leads to intrinsic rate stabilization, the positive part of the learning window picks up spatial and temporal correlations in the input

Hebbian learning and spiking neurons

A correlation-based (``Hebbian'') learning rule at the spike level is formulated, mathematically analyzed, and compared with learning in a firing-rate description. As for spike coding, we take advantage of a ``learning window'' that describes the effect of timing of pre- and postsynaptic spikes on synaptic weights. A differential equation for the learning dynamics is derived under the assumption that the time scales of learning and spiking dynamics can be separated. Formation of structured synapses is analyzed for a Poissonian neuron model which receives time-dependent stochastic input. It is shown that correlations between input and output spikes tend to stabilize structure formation. With an appropriate choice of parameters, learning leads to an intrinsic normalization of the average weight and the output firing rates. Noise generates diffusion-like spreading of synaptic weights