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Spike timing-dependent plasticity (STDP) is a temporally asymmetric form of Hebbian plasticity in which the sign and magnitude of synaptic strength is determined by the precise timing between pre- and postsynaptic spikes. Postsynaptic NMDA receptors (NMDARs) play an important role in STDP due to their characteristic magnesium ion (Mg2+) gating process [1]. The Mg2+ gate is opened by near coincident presynaptic glutamate release and postsynaptic spiking. Contrary to previous belief, this gating process is not instantaneous but has distinct fast and slow time constants, which might influence the time window over which spike-EPSP coincidence occurs [2,3]. The aim of this study is to investigate how local activity in dendrites alters NMDAR kinetics and in turn controls the time window over which STDP occurs. Using a detailed biophysical model of an NR2A subunit, we find the NMDAR current to be temporally asymmetric with a faster block than unblock process. This is due to the voltage-dependent fast and slow time constants of Mg2+ gating. These time constants were on the order of 0.8 ms and 5 ms respectively and changed nonlinearly with membrane potential. By varying both amplitude and duration of a model action potential (AP), we find that dendritic Ca2+ spikes cause Mg2+ unblock to be dominated by its fast time constant. Conversely, somatic Na+ spikes elicit a slower unblocking. Since backpropagating APs (BAPs) attenuate along the dendritic arbor, our results suggest that NMDAR kinetics vary depending on synapse location. Next, we incorporated this biophysical model into a compartmentalized model of a neocortical pyramidal cell in order to investigate the effect that dendritic inhibition and synapse location has on STDP. NMDAR kinetics is significantly different in the basal and apical compartments, which gives rise to a heterogeneous set of STDP curves along the length of the dendrite. Distal synapses had a broader potentiation window than apical synapses, suggesting that distal branches are less selective to correlated inputs. This synapse-location dependent STDP learning rule agrees with previous findings [4]. Dendritic inhibition plays an important role in shaping the computations performed by pyramidal neurons in the neocortex. However, the role that inhibition plays in controlling synaptic plasticity is less clear. By incorporating inhibitory synapses in our model, we find that varying the timing of inhibition relative to the EPSP shifted the peak of the STDP curve, resulting in a reversal of the temporal order of depression and potentiation. Inhibition altered NMDAR kinetics by increasing its blocking rate. As a result, changing the balance between excitation and inhibition in the dendritic branch results in a sliding threshold between LTP and LTD. In summary, we show that NMDAR kinetics can be altered in an activity-dependent manner resulting in different STDP learning rules. When taken in context of the BCM theory, our finding implies that dendritic inhibition can dynamically alter the threshold between LTP and LTD by altering the time constants of the NMDAR. Our model provides a novel framework for understanding how STDP in different dendritic compartments selects inputs alters information processing in individual neurons.

Natural scenes, although complex in appearance, contain numerous statistical regularities. For instance, owing to surfaces and textures, neighboring pixels in natural images are strongly correlated in both space and time (Figure 1B). These correlations create strong dependencies between neurons that may limit neural coding efficiency. Thus, to produce an efficient representation, it has been proposed that neural circuits in the early visual system function to remove extraneous stimulus correlations. Although extensively studied in the retina and LGN, the mechanisms of efficient coding in primary visual cortex (V1) remain elusive. The goal of this study is to establish a relationship between population coding in V1 and spatial correlations in natural scenes. Mathematically, the Fourier amplitude spectrum describes second-order correlations between pixels. In contrast, the phase spectrum describes higher-order correlations, which arise due to edges and other salient features. To understand how stimulus correlations influence coding in V1, we developed a novel technique that allowed us to systematically perturb the Fourier amplitude spectrum of natural movies, while keeping the edge structure intact. Using this method, we generated movies with four different levels of spatial correlation (Figure 1A). Visually, edges in the most decorrelated movies (K0 spectrum) appear shaper, while edges in the most strongly correlated movies appear occluded (K2 spectrum). To assess how populations of neurons respond to these movies, we performed high-speed 2-photon calcium imaging in layer 2/3 of mouse V1. This method permitted us to monitor the activity of close to 100 neurons with high spatial and temporal resolution.

Networks in the neocortex serve an important purpose of extracting information from sensory inputs. One appealing theory is the efficient coding hypothesis, which postulates that information about a stimulus is maximized when redundancy between neurons is reduced [1]. This gives rise to the notion of a sparse population code where only neurons that are highly selective to certain stimulus features respond. However, sparse codes are highly sensitivity to noise. An alternative strategy is to use a synchronized code, which is robust to noise but reduces the representational capacity of the network [2,3]. Hence, it is only logical to ask what level of redundancy between neurons maximizes the amount of information contained in a population code. In this study, we investigated how the collective dynamics of a population of neurons represent stimulus-specific information. Our aim was to investigate (1) the conditions required for a network to synchronize and (2) the amount of information contained in a synchronized rate code. By applying nonlinear contraction analysis on a recurrent network with time varying inputs, we found that the degree of synchronization depended critically on the gain of the feedforward projection. Our analysis showed that changing the feedforward gain exploits different symmetries in the network, resulting in different patterns of synchrony and different population codes. We hypothesized that the coding strategy can by optimized by altering this synaptic gain. We tested this prediction computationally using a two-layered network. The receiver layer was a balanced recurrent network of 5000 integrate-and-fire neurons. Input to the network was provided by a population of "visually responsive" neurons, which was modeled using a linear-nonlinear Poisson (LNP) cascade. The LNP neurons were tuned to 16 orientations and projected nonspecifically to 20% of the neurons in the receiver layer. We assumed that the stimulus was a sequence of drifting gratings with random orientations. In response to stimuli, the network displayed transiently synchronized responses. Because similarly tuned LNP neurons projected to different subsets of neurons, the pattern of network activity was different for each stimulus sequence. By gradually modifying the feedforward gain, we were able to alter this pattern of stimulus-specific synchronization, confirming the results from our mathematical analysis. In the high gain condition, neurons became redundant and responded to all stimuli. However, when gain was low, only sparse subsets of neurons were activated by different stimuli. Finally, we used an optimal linear decoder to measure of how well the network encoded the stimuli. We found that classification accuracy varied as a function of the degree of synchronization between neurons. Classification accuracy was highest when approximately 15% of the neurons responded concurrently to the stimulus. In both densely synchronized and sparse codes, the decoder performed below chance. Our results show that stimulus-specific information is maximized only when small ensembles of neurons are synchronized. Our finding that stimulus-dependent synchronization is controlled by the gain of feedforward synapses is unique as it suggests that mechanisms which alter synaptic gain such as attention can alter the coding strategy employed by the neocortex.