A framework for studying synaptic plasticity with neural spike train data
Learning and memory in the brain are implemented by complex, time-varying changes in neural circuitry. The computational rules according to which synaptic weights change over time are the subject of much research, and are not precisely understood. Until recently, limitations in experimental methods have made it challenging to test hypotheses about synaptic plasticity on a large scale. However, as such data become available and these barriers are lifted, it becomes necessary to develop analysis techniques to validate plasticity models. Here, we present a highly extensible framework for modeling arbitrary synaptic plasticity rules on spike train data in populations of interconnected neurons. We treat synaptic weights as a (potentially nonlinear) dynamical system embedded in a fullyBayesian generalized linear model (GLM). In addition, we provide an algorithm for inferring synaptic weight trajectories alongside the parameters of the GLM and of the learning rules. Using this method, we perform model comparison of two proposed variants of the well-known spike-timing-dependent plasticity (STDP) rule, where nonlinear effects play a substantial role. On synthetic data generated from the biophysical simulator NEURON, we show that we can recover the weight trajectories, the pattern of connectivity, and the underlying learning rules.
In this paper, the authors present a beefed up GLM model where the matrix which defines interactions between the neurons is time-varying based on some learning rule such as STDP. Also, sparsity is promoted with a spike-and-slab like factorization of the weight matrix. Inference in the model is performed using particle MCMC which is a powerful hybridization of SMC and MCMC (in this case Gibbs sampling).I think this paper presents an important variation in models of neural dynamics in that it attempts to model time-varying dynamics - a problem that computational neuroscientists and the NIPS community are likely interested in. While it doesn't assess its performance on real data, it does assess its performance on data generated from a biophysical model with unobserved neurons - the latter being an important component to consider. Though the results are on toy networks, the method's potential is convincing. Also, it is the first application of pMCMC to computational neuroscience that I'm aware of. That being said, I have one main area of concern in this draft.I think the relationship between this model and the current methods in experimental neuroscience is not always presented correctly. In line 41 the word "optogenetics" may be inappropriate. Optogenetics is not related to recording activity, only stimulating. Maybe use the word optical here instead of optogenetic. I'd also reconsider the usage of reference 2. That is a voltage imaging paper where the analysis requires trial averaging. Also, voltage imaging is not really ready to be used for population imaging. However, a more recent paper from Adam Cohen's group does have a demonstration of this (All-optical electrophysiology in mammalian neurons using engineered microbial rhodopsins). Generally people use Ca++ indicators for population imaging. For recent advances in Ca++ imaging, see "Ultrasensitive fluorescent proteins for imaging neuronal activity" from a collaboration of Janelia Farm labs. There are plenty of other Ca++ imaging papers that would be appropriate as well. The one I listed doesn't demonstrate poulation imaging, but the indicator from that paper is regularly used to image populations of neurons in vitro and in vivo.The authors often cite optical methods as motivation for their model. The idea is that optical methods allow the recording of cells that are near each other and presumably some of them are synaptically connected. There is a major issue that goes unmentioned in this paper: extracting spikes from imaging data is a non-trivial problem (see papers by Josh Vogelstein and Liam Paninski for commonly used algorithms), and the temporal resolution of imaging does not often permit the precise measurements needed to identify STDP type rules. The papers referenced which do infer synaptic connections [5,6] use electrophysiological data which does provide highly accurate and precise spike times. That being said, fast and reliable optical indicators of action potentials are likely on the horizon, and the model is still interesting even if it does not admit a causal, synaptic interpretation. Besides that, there are a few smaller specific points that should be clarified. Because the GLM model does not necessarily admit a true PSP or PSC interpretation, using units of nA here maybe disingenuous. Furthermore, for PSC amplitudes, even 1 nA would be very big. One might expect a max current in the range of 5-100 of pA. In addition, you reference PSPs earlier (post-synaptic potentials) in the paper. These would be measured in millivolts not pico- or nanoamps. A PSC (post-synaptic current) would be measured in amperes. Because the membrane resistance changes over time, the two are not interchangeable.Given that the probability of spiking is voltage-dependent, not current-dependent, you could stick with a PSP interpretation and change the units to millivolts.  That being said, many STDP models vary the max current parameter - they don't explicitly model some max potential change. Perhaps it's worth considering dropping the units here and saying that the unitless GLM weights are modulated in a way that is based on STDP. I think this is reasonable and avoids the slippery-slope of claiming your model captures electrophysiological properties.It's not clear how the noise variable is truncated to ensure that the bounds are maintained. Is it a function of W(t) and dW(t) such that you update the weights without noise and then truncate the Gaussian at (0+W(t)+dW(t),W_max-W(t)+dW(t))? Or is it dependent on A_+ and A_-? In any case, it's not clear how the model results in noise from a truncated Gaussian random variable which will not violate the bounds.The way you've written it, it seems like you are claiming the model in Song et al. is infeasible because the weights are unbounded. But they do in fact bound synaptic weights from below at 0 and from above by some $g_{max}$ (in their notation).It's not clear to me that Eldawlatly et al. model time-varying synaptic parameters - as you claim - as much as causal influences that act at multiple time lags in a discrete-time model. The interpretation - depending on the bin size and length of the delay - could be either indirect (e.g. polysynaptic effects) or direct (e.g. delay due to axon length), but none of the model parameters are time-varying.Finally, I'm concerned about the tractability of the inference algorithm. It is not uncommon for optical recordings to contain 100s of neurons. How long would a network of that size take to fit? How much data would be needed to fit the model?