Stability of Negative Image Equilibria in Spike-Timing Dependent Plasticity

We investigate the stability of negative image equilibria in mean synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of external electric fields. We derive a necessary and sufficient condition for stability, for arbitrary postsynaptic potential functions and arbitrary learning rules. We then apply the general result to several examples of biological interest.Comment: 13 pages, revtex4; uses packages: graphicx, subfigure; 9 figures, 16 subfigure

PULSED DOPPLER FROM THE SUPRASTERNAL NOTCH SYSTEMATICALLY UNDERESTIMATES MEAN BLOOD FLOW VELOCITY IN THE ASCENDING AORTA COMPARED TO PHASE CONTRAST MRI

Background Continuous pulsed-wave Doppler readings of flow velocity in the ascending aorta from the suprasternal position (sCD) are widely used in estimating stroke volume, particularly during physiological challenge maneuvers such as head-up tilt testing. Stroke volume is derived from velocity time integrals and vessel area. We compared the sCD against an established gold standard. Methods In 12 healthy women and men, we obtained 2D cross sectional, velocity encoded phase contrast MRI of the ascending aorta (2DMRI) and sCD to measure mean blood flow velocity (Vmean) at the ascending aorta. We compared sCD insonation depth to the distance between Doppler probe and sinotubular junction measured by MRI. Within an aortic 4D-Flow dataset, allowing flow measurements in every anatomical point along the ascending aorta, Vmean was determined at the sCD measurement point for comparison. Results sCD significantly underestimated Vmean compared with 2DMRI at the sinotubular junction (Vmean 2DMRI – Vmean sCD = 24.42 cm/s ± 12.55 cm/s, p = <0.001). Moreover, sCD sampled flow velocities 21.8 mm ± 7mm (p = <0.001) or 26% off the sinotubular junction. Yet, depth and velocity differences between sCD and 2DMRI were not correlated with each other (Pearson r = -0.147; p = 0.648). When we applied 4DMRI to assess flow velocity at the sCD measurement site, the Vmean difference between methodologies was reduced to 9.1 cm/s ± 12.38 cm/s (p = 0.035). Conclusion sCD profoundly underestimates Vmean in the ascending aorta compared to 4DMRI. The methodology has important limitations in accessing the ideal position for aortic flow measurements and precise information regarding the position of data acquisition for vessel area quantification cannot be ascertained. Overall, sCD is of limited utility in measuring absolute stroke volum

Evaluation of a Novel Thiol–Norbornene-Functionalized Gelatin Hydrogel for Bioprinting of Mesenchymal Stem Cells

Introduction: Three-dimensional bioprinting can be considered as an advancement of the classical tissue engineering concept. For bioprinting, cells have to be dispersed in hydrogels. Recently, a novel semi-synthetic thiolene hydrogel system based on norbornene-functionalized gelatin (GelNB) and thiolated gelatin (GelS) was described that resulted in the photoclick hydrogel GelNB/GelS. In this study, we evaluated the printability and biocompatibility of this hydrogel system towards adipose-tissue-derived mesenchymal stem cells (ASCs). Methods: GelNB/GelS was synthesized with three different crosslinking densities (low, medium and high), resulting in different mechanical properties with moduli of elasticity between 206 Pa and 1383 Pa. These hydrogels were tested for their biocompatibility towards ASCs in terms of their viability, proliferation and differentiation. The extrusion-based bioprinting of ASCs in GelNB/GelS-high was performed to manufacture three-dimensional cubic constructs. Results: All three hydrogels supported the viability, proliferation and chondrogenic differentiation of ASCs to a similar extent. The adipogenic differentiation of ASCs was better supported by the softer hydrogel (GelNB/GelS-low), whereas the osteogenic differentiation was more pronounced in the harder hydrogel (GelNB/GelS-high), indicating that the differentiation fate of ASCs can be influenced via the adaption of the mechanical properties of the GelNB/GelS system. After the ex vivo chondrogenic differentiation and subcutaneous implantation of the bioprinted construct into immunocompromised mice, the production of negatively charged sulfated proteoglycans could be observed with only minimal inflammatory signs in the implanted material. Conclusions: Our results indicate that the GelNB/GelS hydrogels are very well suited for the bioprinting of ASCs and may represent attractive hydrogels for subsequent in vivo tissue engineering applications

Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron

We model the dynamics of the leaky integrate-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier work and thus solves the long-standing reset problem. The neuron exhibits stochastic resonance, both with respect to input noise intensity and stimulus frequency. The latter resonance arises by matching the stimulus frequency to the refractory time of the neuron. The Markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism.Comment: 23 pages, 10 figure

An associative memory of Hodgkin-Huxley neuron networks with Willshaw-type synaptic couplings

An associative memory has been discussed of neural networks consisting of spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which memorize P patterns in their synaptic weights. In addition to excitatory synapses whose strengths are modified after the Willshaw-type learning rule with the 0/1 code for quiescent/active states, the network includes uniform inhibitory synapses which are introduced to reduce cross-talk noises. Our simulations of the HH neuron network for the noise-free state have shown to yield a fairly good performance with the storage capacity of $\alpha_c = P_{\rm max}/N \sim 0.4 - 2.4$ for the low neuron activity of $f \sim 0.04-0.10$. This storage capacity of our temporal-code network is comparable to that of the rate-code model with the Willshaw-type synapses. Our HH neuron network is realized not to be vulnerable to the distribution of time delays in couplings. The variability of interspace interval (ISI) of output spike trains in the process of retrieving stored patterns is also discussed.Comment: 15 pages, 3 figures, changed Titl

Burst-Time-Dependent Plasticity Robustly Guides ON/OFF Segregation in the Lateral Geniculate Nucleus

Spontaneous retinal activity (known as “waves”) remodels synaptic connectivity to the lateral geniculate nucleus (LGN) during development. Analysis of retinal waves recorded with multielectrode arrays in mouse suggested that a cue for the segregation of functionally distinct (ON and OFF) retinal ganglion cells (RGCs) in the LGN may be a desynchronization in their firing, where ON cells precede OFF cells by one second. Using the recorded retinal waves as input, with two different modeling approaches we explore timing-based plasticity rules for the evolution of synaptic weights to identify key features underlying ON/OFF segregation. First, we analytically derive a linear model for the evolution of ON and OFF weights, to understand how synaptic plasticity rules extract input firing properties to guide segregation. Second, we simulate postsynaptic activity with a nonlinear integrate-and-fire model to compare findings with the linear model. We find that spike-time-dependent plasticity, which modifies synaptic weights based on millisecond-long timing and order of pre- and postsynaptic spikes, fails to segregate ON and OFF retinal inputs in the absence of normalization. Implementing homeostatic mechanisms results in segregation, but only with carefully-tuned parameters. Furthermore, extending spike integration timescales to match the second-long input correlation timescales always leads to ON segregation because ON cells fire before OFF cells. We show that burst-time-dependent plasticity can robustly guide ON/OFF segregation in the LGN without normalization, by integrating pre- and postsynaptic bursts irrespective of their firing order and over second-long timescales. We predict that an LGN neuron will become ON- or OFF-responsive based on a local competition of the firing patterns of neighboring RGCs connecting to it. Finally, we demonstrate consistency with ON/OFF segregation in ferret, despite differences in the firing properties of retinal waves. Our model suggests that diverse input statistics of retinal waves can be robustly interpreted by a burst-based rule, which underlies retinogeniculate plasticity across different species

Intrinsic Stability of Temporally Shifted Spike-Timing Dependent Plasticity

Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains and it generates competition among synapses. However, STDP has an inherent instability because strong synapses are more likely to be strengthened than weak ones, causing them to grow in strength until some biophysical limit is reached. Through simulations and analytic calculations, we show that a small temporal shift in the STDP window that causes synchronous, or nearly synchronous, pre- and postsynaptic action potentials to induce long-term depression can stabilize synaptic strengths. Shifted STDP also stabilizes the postsynaptic firing rate and can implement both Hebbian and anti-Hebbian forms of competitive synaptic plasticity. Interestingly, the overall level of inhibition determines whether plasticity is Hebbian or anti-Hebbian. Even a random symmetric jitter of a few milliseconds in the STDP window can stabilize synaptic strengths while retaining these features. The same results hold for a shifted version of the more recent “triplet” model of STDP. Our results indicate that the detailed shape of the STDP window function near the transition from depression to potentiation is of the utmost importance in determining the consequences of STDP, suggesting that this region warrants further experimental study

Emergence of Connectivity Motifs in Networks of Model Neurons with Short- and Long-term Plastic Synapses

Recent evidence in rodent cerebral cortex and olfactory bulb suggests that short-term dynamics of excitatory synaptic transmission is correlated to stereotypical connectivity motifs. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form unidirectional pairwise connections. The cause of these structural differences in synaptic microcircuits is unknown. We propose that these connectivity motifs emerge from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. We formulate a computational model by combining SD and STDP, which captures faithfully short- and long-term dependence on both spike times and frequency. As a proof of concept, we simulate recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical background inputs, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. This holds for heterogeneous networks including both facilitating and depressing synapses. Our study highlights the conditions under which SD-STDP might the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs. We further suggest experiments for the validation of the proposed mechanism