Julijana Gjorgjieva

A triplet spike-timing–dependent plasticity model generalizes the Bienenstock–Cooper–Munro rule to higher-order spatiotemporal correlations

Synaptic strength depresses for low and potentiates for high activation of the postsynaptic neuron. This feature is a key property of the Bienenstock–Cooper–Munro (BCM) synaptic learning rule, which has been shown to maximize the selectivity of the postsynaptic neuron, and thereby offers a possible explanation for experience-dependent cortical plasticity such as orientation selectivity. However, the BCM framework is rate-based and a significant amount of recent work has shown that synaptic plasticity also depends on the precise timing of presynaptic and postsynaptic spikes. Here we consider a triplet model of spike-timing–dependent plasticity (STDP) that depends on the interactions of three precisely timed spikes. Triplet STDP has been shown to describe plasticity experiments that the classical STDP rule, based on pairs of spikes, has failed to capture. In the case of rate-based patterns, we show a tight correspondence between the triplet STDP rule and the BCM rule. We analytically demonstrate the selectivity property of the triplet STDP rule for orthogonal inputs and perform numerical simulations for nonorthogonal inputs. Moreover, in contrast to BCM, we show that triplet STDP can also induce selectivity for input patterns consisting of higher-order spatiotemporal correlations, which exist in natural stimuli and have been measured in the brain. We show that this sensitivity to higher-order correlations can be used to develop direction and speed selectivity.

Emergence of Adaptive Computation by Single Neurons in the Developing Cortex

Adaptation is a fundamental computational motif in neural processing. To maintain stable perception in the face of rapidly shifting input, neural systems must extract relevant information from background fluctuations under many different contexts. Many neural systems are able to adjust their input–output properties such that an inputs ability to trigger a response depends on the size of that input relative to its local statistical context. This “gain-scaling” strategy has been shown to be an efficient coding strategy. We report here that this property emerges during early development as an intrinsic property of single neurons in mouse sensorimotor cortex, coinciding with the disappearance of spontaneous waves of network activity, and can be modulated by changing the balance of spike-generating currents. Simultaneously, developing neurons move toward a common intrinsic operating point and a stable ratio of spike-generating currents. This developmental trajectory occurs in the absence of sensory input or spontaneous network activity. Through a combination of electrophysiology and modeling, we demonstrate that developing cortical neurons develop the ability to perform nearly perfect gain scaling by virtue of the maturing spike-generating currents alone. We use reduced single neuron models to identify the conditions for this property to hold.

Neural circuits for peristaltic wave propagation in crawling Drosophila larvae: analysis and modeling

Drosophila larvae crawl by peristaltic waves of muscle contractions, which propagate along the animal body and involve the simultaneous contraction of the left and right side of each segment. Coordinated propagation of contraction does not require sensory input, suggesting that movement is generated by a central pattern generator (CPG). We characterized crawling behavior of newly hatched Drosophila larvae by quantifying timing and duration of segmental boundary contractions. We developed a CPG network model that recapitulates these patterns based on segmentally repeated units of excitatory and inhibitory (EI) neuronal populations coupled with immediate neighboring segments. A single network with symmetric coupling between neighboring segments succeeded in generating both forward and backward propagation of activity. The CPG network was robust to changes in amplitude and variability of connectivity strength. Introducing sensory feedback via “stretch-sensitive” neurons improved wave propagation properties such as speed of propagation and segmental contraction duration as observed experimentally. Sensory feedback also restored propagating activity patterns when an inappropriately tuned CPG network failed to generate waves. Finally, in a two-sided CPG model we demonstrated that two types of connectivity could synchronize the activity of two independent networks: connections from excitatory neurons on one side to excitatory contralateral neurons (E to E), and connections from inhibitory neurons on one side to excitatory contralateral neurons (I to E). To our knowledge, such I to E connectivity has not yet been found in any experimental system; however, it provides the most robust mechanism to synchronize activity between contralateral CPGs in our model. Our model provides a general framework for studying the conditions under which a single locally coupled network generates bilaterally synchronized and longitudinally propagating waves in either direction.

Benefits of Pathway Splitting in Sensory Coding

In many sensory systems, the neural signal splits into multiple parallel pathways. For example, in the mammalian retina, ∼20 types of retinal ganglion cells transmit information about the visual scene to the brain. The purpose of this profuse and early pathway splitting remains unknown. We examine a common instance of splitting into ON and OFF neurons excited by increments and decrements of light intensity in the visual scene, respectively. We test the hypothesis that pathway splitting enables more efficient encoding of sensory stimuli. Specifically, we compare a model system with an ON and an OFF neuron to one with two ON neurons. Surprisingly, the optimal ON–OFF system transmits the same information as the optimal ON–ON system, if one constrains the maximal firing rate of the neurons. However, the ON–OFF system uses fewer spikes on average to transmit this information. This superiority of the ON–OFF system is also observed when the two systems are optimized while constraining their mean firing rate. The efficiency gain for the ON–OFF split is comparable with that derived from decorrelation, a well known processing strategy of early sensory systems. The gain can be orders of magnitude larger when the ecologically important stimuli are rare but large events of either polarity. The ON–OFF system also provides a better code for extracting information by a linear downstream decoder. The results suggest that the evolution of ON–OFF diversification in sensory systems may be driven by the benefits of lowering average metabolic cost, especially in a world in which the relevant stimuli are sparse.

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.

When do microcircuits produce beyond-pairwise correlations?

Describing the collective activity of neural populations is a daunting task. Recent empirical studies in retina, however, suggest a vast simplification in how multi-neuron spiking occurs: the activity patterns of retinal ganglion cell (RGC) populations under some conditions are nearly completely captured by pairwise interactions among neurons. In other circumstances, higher-order statistics are required and appear to be shaped by input statistics and intrinsic circuit mechanisms. Here, we study the emergence of higher-order interactions in a model of the RGC circuit in which correlations are generated by common input. We quantify the impact of higher-order interactions by comparing the responses of mechanistic circuit models vs. “null” descriptions in which all higher-than-pairwise correlations have been accounted for by lower order statistics; these are known as pairwise maximum entropy (PME) models. We find that over a broad range of stimuli, output spiking patterns are surprisingly well captured by the pairwise model. To understand this finding, we study an analytically tractable simplification of the RGC model. We find that in the simplified model, bimodal input signals produce larger deviations from pairwise predictions than unimodal inputs. The characteristic light filtering properties of the upstream RGC circuitry suppress bimodality in light stimuli, thus removing a powerful source of higher-order interactions. This provides a novel explanation for the surprising empirical success of pairwise models.

Self-organization in the developing nervous system: theoretical models

Sensory maps in the nervous system often connect to each other in a topographic fashion. This is most strikingly seen in the visual system, where neighboring neurons in the retina project to neighboring neurons in the target structure, such as the superior colliculus. This article discusses the developmental mechanisms that are involved in the formation of topographic maps, with an emphasis on the role of theoretical models in helping us to understand these mechanisms. Recent experimental advances in studying the roles of guidance molecules and patterns of spontaneous activity mean that there are new challenges to be addressed by theoretical models. Key questions include understanding what instructional cues are present in the patterns of spontaneous activity, and how activity and guidance molecules might interact. Our discussion concludes by comparing development of visual maps with development of maps in the olfactory system, where the influence of neural activity seems to differ.

Modeling developmental patterns of spontaneous activity.

Spontaneous activity is found in many regions of the developing nervous system; such activity is thought to be instructive for guiding developmental processes. In particular, the developing retina generates correlated patterns of activity known as retinal waves. We review the main theoretical models that have been developed to study the mechanisms for generation and propagation of retinal waves. Much of the progress in this field has been due to the close interaction between experimentalists and theorists in analyzing and modeling spontaneous activity. We conclude by describing spontaneous activity models in other systems and suggestions for future modeling work.

Relationship between individual neuron and network spontaneous activity in developing mouse cortex

Spontaneous synchronous activity (SSA) that propagates as electrical waves is found in numerous central nervous system structures and is critical for normal development, but the mechanisms of generation of such activity are not clear. In previous work, we showed that the ventrolateral piriform cortex is uniquely able to initiate SSA in contrast to the dorsal neocortex, which participates in, but does not initiate, SSA (Lischalk JW, Easton CR, Moody WJ. Dev Neurobiol 69: 407-414, 2009). In this study, we used Ca(2+) imaging of cultured embryonic day 18 to postnatal day 2 coronal slices (embryonic day 17 + 1-4 days in culture) of the mouse cortex to investigate the different activity patterns of individual neurons in these regions. In the piriform cortex where SSA is initiated, a higher proportion of neurons was active asynchronously between waves, and a larger number of groups of coactive cells was present compared with the dorsal cortex. When we applied GABA and glutamate synaptic antagonists, asynchronous activity and cellular clusters remained, while synchronous activity was eliminated, indicating that asynchronous activity is a result of cell-intrinsic properties that differ between these regions. To test the hypothesis that higher levels of cell-autonomous activity in the piriform cortex underlie its ability to initiate waves, we constructed a conductance-based network model in which three layers differed only in the proportion of neurons able to intrinsically generate bursting behavior. Simulations using this model demonstrated that a gradient of intrinsic excitability was sufficient to produce directionally propagating waves that replicated key experimental features, indicating that the higher level of cell-intrinsic activity in the piriform cortex may provide a substrate for SSA generation.

Homeostatic Activity-Dependent Tuning of Recurrent Networks for Robust Propagation of Activity

Developing neuronal networks display spontaneous bursts of action potentials that are necessary for circuit organization and tuning. While spontaneous activity has been shown to instruct map formation in sensory circuits, it is unknown whether it plays a role in the organization of motor networks that produce rhythmic output. Using computational modeling, we investigate how recurrent networks of excitatory and inhibitory neuronal populations assemble to produce robust patterns of unidirectional and precisely timed propagating activity during organism locomotion. One example is provided by the motor network in Drosophila larvae, which generates propagating peristaltic waves of muscle contractions during crawling. We examine two activity-dependent models, which tune weak network connectivity based on spontaneous activity patterns: a Hebbian model, where coincident activity in neighboring populations strengthens connections between them; and a homeostatic model, where connections are homeostatically regulated to maintain a constant level of excitatory activity based on spontaneous input. The homeostatic model successfully tunes network connectivity to generate robust activity patterns with appropriate timing relationships between neighboring populations. These timing relationships can be modulated by the properties of spontaneous activity, suggesting its instructive role for generating functional variability in network output. In contrast, the Hebbian model fails to produce the tight timing relationships between neighboring populations required for unidirectional activity propagation, even when additional assumptions are imposed to constrain synaptic growth. These results argue that homeostatic mechanisms are more likely than Hebbian mechanisms to tune weak connectivity based on spontaneous input in a recurrent network for rhythm generation and robust activity propagation. SIGNIFICANCE STATEMENT How are neural circuits organized and tuned to maintain stable function and produce robust output? This task is especially difficult during development, when circuit properties change in response to variable environments and internal states. Many developing circuits exhibit spontaneous activity, but its role in the synaptic organization of motor networks that produce rhythmic output is unknown. We studied a model motor network, that when appropriately tuned, generates propagating activity as during crawling in Drosophila larvae. Based on experimental evidence of activity-dependent tuning of connectivity, we examined plausible mechanisms by which appropriate connectivity emerges. Our results suggest that activity-dependent homeostatic mechanisms are better suited than Hebbian mechanisms for organizing motor network connectivity, and highlight an important difference from sensory areas.