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Abstract Sodium ions (Na⁺) are major charge carriers mediating neuronal excitation and play a fundamental role in brain physiology. Glutamatergic synaptic activity is accompanied by large transient Na⁺increases, but the spatio-temporal dynamics of Na⁺signals and properties of Na⁺diffusion within dendrites are largely unknown. To address these questions, we employed multi-photon Na⁺imaging combined with whole-cell patch-clamp in dendrites of CA1 pyramidal neurons in tissue slices from mice of both sexes. Fluorescence lifetime microscopy revealed a dendritic baseline Na⁺concentration of ~10 mM. Using intensity-based line-scan imaging we found that local, glutamate-evoked Na⁺signals spread rapidly within dendrites, with peak amplitudes decreasing and latencies increasing with increasing distance from the site of stimulation. Spread of Na⁺along dendrites was independent of dendrite diameter, order or overall spine density in the ranges measured. Our experiments also show that dendritic Na⁺readily invades spines and suggest that spine necks may represent a partial diffusion barrier. Experimental data were well reproduced by mathematical simulations assuming normal diffusion with a diffusion coefficient of. Modeling moreover revealed that lateral diffusion is key for the clearance of local Na⁺increases at early time points, whereas when diffusional gradients are diminished, Na⁺/K⁺-ATPase becomes more relevant. Taken together, our study thus demonstrates that Na⁺influx causes rapid lateral diffusion of Na⁺within spiny dendrites. This results in an efficient redistribution and fast recovery from local Na⁺transients which is mainly governed by concentration differences. Significance statementActivity of excitatory glutamatergic synapses generates large Na⁺transients in postsynaptic cells. Na⁺influx is a main driver of energy consumption and modulates cellular properties by modulating Na⁺-dependent transporters. Knowing the spatio-temporal dynamics of dendritic Na⁺signals is thus critical for understanding neuronal function. To study propagation of Na⁺signals within spiny dendrites, we performed fast Na⁺imaging combined with mathematical simulations. Our data shows that normal diffusion, based on a diffusion coefficient of 600 µm²/s, is crucial for fast clearance of local Na⁺transients in dendrites, whereas Na⁺export by the Na⁺/K⁺-ATPase becomes more relevant at later time points. This fast diffusive spread of Na⁺will reduce the local metabolic burden imposed by synaptic Na⁺influx. 

This theoretical study investigates strategies for minimizing Joule losses in resistive random access memory (ReRAM) cells, which are also referred to as memristive devices. Typically, the structure of ReRAM cells involves a nanoscale layer of resistance-switching material sandwiched between two metal electrodes. The basic question that we ask is what is the optimal driving protocol to switch a memristive device from one state to another. In the case of ideal memristors, in the most basic scenario, the optimal protocol is determined by solving a variational problem without constraints with the help of the Euler-Lagrange equation. In the case of memristive systems, for the same situation, the optimal protocol is found using the method of Lagrange multipliers. We demonstrate the advantages of our approaches through specific examples and compare our results with those of switching with constant voltage or current. Our findings suggest that voltage or current control can be used to reduce Joule losses in emerging memory devices. 

There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin–Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin–Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices. 

Traditional computing is based on an engineering approach that imposes logical states and a computational model upon a physical substrate. Physical or material computing, on the other hand, harnesses and exploits the inherent, naturally-occurring proper- ties of a physical substrate to perform a computation. To do so, reservoir computing is often used as a computing paradigm. In this review and position paper, we take stock of where the field currently stands, delineate opportunities and challenges for future research, and outline steps on how to get material reservoir to the next level. The findings are relevant for beyond CMOS and beyond von Neumann architectures, ML, AI, neuromorphic systems, and computing with novel devices and circuits.