Parallel functional architectures within a single dendritic tree.

The input-output transformation of individual neurons is a key building block of neural circuit dynamics. While previous models of this transformation vary widely in their complexity, they all describe the underlying functional architecture as unitary, such that each synaptic input makes a single contribution to the neuronal response. Here, we show that the input-output transformation of CA1 pyramidal cells is instead best captured by two distinct functional architectures operating in parallel. We used statistically principled methods to fit flexible, yet interpretable, models of the transformation of input spikes into the somatic "output" voltage and to automatically select among alternative functional architectures. With dendritic Na+ channels blocked, responses are accurately captured by a single static and global nonlinearity. In contrast, dendritic Na+-dependent integration requires a functional architecture with multiple dynamic nonlinearities and clustered connectivity. These two architectures incorporate distinct morphological and biophysical properties of the neuron and its synaptic organization.

Sampling motion trajectories during hippocampal theta sequences.

Efficient planning in complex environments requires that uncertainty associated with current inferences and possible consequences of forthcoming actions is represented. Representation of uncertainty has been established in sensory systems during simple perceptual decision making tasks but it remains unclear if complex cognitive computations such as planning and navigation are also supported by probabilistic neural representations. Here, we capitalized on gradually changing uncertainty along planned motion trajectories during hippocampal theta sequences to capture signatures of uncertainty representation in population responses. In contrast with prominent theories, we found no evidence of encoding parameters of probability distributions in the momentary population activity recorded in an open-field navigation task in rats. Instead, uncertainty was encoded sequentially by sampling motion trajectories randomly and efficiently in subsequent theta cycles from the distribution of potential trajectories. Our analysis is the first to demonstrate that the hippocampus is well equipped to contribute to optimal planning by representing uncertainty.

Impact of functional synapse clusters on neuronal response selectivity.

Clustering of functionally similar synapses in dendrites is thought to affect neuronal input-output transformation by triggering local nonlinearities. However, neither the in vivo impact of synaptic clusters on somatic membrane potential (sVm), nor the rules of cluster formation are elucidated. We develop a computational approach to measure the effect of functional synaptic clusters on sVm response of biophysical model CA1 and L2/3 pyramidal neurons to in vivo-like inputs. We demonstrate that small synaptic clusters appearing with random connectivity do not influence sVm. With structured connectivity,  ~10-20 synapses/cluster are optimal for clustering-based tuning via state-dependent mechanisms, but larger selectivity is achieved by 2-fold potentiation of the same synapses. We further show that without nonlinear amplification of the effect of random clusters, action potential-based, global plasticity rules cannot generate functional clustering. Our results suggest that clusters likely form via local synaptic interactions, and have to be moderately large to impact sVm responses.

Synaptic Plasticity Depends on the Fine-Scale Input Pattern in Thin Dendrites of CA1 Pyramidal Neurons.

Coordinated long-term plasticity of nearby excitatory synaptic inputs has been proposed to shape experience-related neuronal information processing. To elucidate the induction rules leading to spatially structured forms of synaptic potentiation in dendrites, we explored plasticity of glutamate uncaging-evoked excitatory input patterns with various spatial distributions in perisomatic dendrites of CA1 pyramidal neurons in slices from adult male rats. We show that (1) the cooperativity rules governing the induction of synaptic LTP depend on dendritic location; (2) LTP of input patterns that are subthreshold or suprathreshold to evoke local dendritic spikes (d-spikes) requires different spatial organization; and (3) input patterns evoking d-spikes can strengthen nearby, nonsynchronous synapses by local heterosynaptic plasticity crosstalk mediated by NMDAR-dependent MEK/ERK signaling. These results suggest that multiple mechanisms can trigger spatially organized synaptic plasticity on various spatial and temporal scales, enriching the ability of neurons to use synaptic clustering for information processing.SIGNIFICANCE STATEMENT A fundamental question in neuroscience is how neuronal feature selectivity is established via the combination of dendritic processing of synaptic input patterns with long-term synaptic plasticity. As these processes have been mostly studied separately, the relationship between the rules of integration and rules of plasticity remained elusive. Here we explore how the fine-grained spatial pattern and the form of voltage integration determine plasticity of different excitatory synaptic input patterns in perisomatic dendrites of CA1 pyramidal cells. We demonstrate that the plasticity rules depend highly on three factors: (1) the location of the input within the dendritic branch (proximal vs distal), (2) the strength of the input pattern (subthreshold or suprathreshold for dendritic spikes), and (3) the stimulation of neighboring synapses.

Global and Multiplexed Dendritic Computations under In Vivo-like Conditions.

Dendrites integrate inputs nonlinearly, but it is unclear how these nonlinearities contribute to the overall input-output transformation of single neurons. We developed statistically principled methods using a hierarchical cascade of linear-nonlinear subunits (hLN) to model the dynamically evolving somatic response of neurons receiving complex, in vivo-like spatiotemporal synaptic input patterns. We used the hLN to predict the somatic membrane potential of an in vivo-validated detailed biophysical model of a L2/3 pyramidal cell. Linear input integration with a single global dendritic nonlinearity achieved above 90% prediction accuracy. A novel hLN motif, input multiplexing into parallel processing channels, could improve predictions as much as conventionally used additional layers of local nonlinearities. We obtained similar results in two other cell types. This approach provides a data-driven characterization of a key component of cortical circuit computations: the input-output transformation of neurons during in vivo-like conditions.

Robust and efficient coding with grid cells.

The neuronal code arising from the coordinated activity of grid cells in the rodent entorhinal cortex can uniquely represent space across a large range of distances, but the precise conditions for optimal coding capacity are known only for environments with finite size. Here we consider a coding scheme that is suitable for unbounded environments, and present a novel, number theoretic approach to derive the grid parameters that maximise the coding range in the presence of noise. We derive an analytic upper bound on the coding range and provide examples for grid scales that achieve this bound and hence are optimal for encoding in unbounded environments. We show that in the absence of neuronal noise, the capacity of the system is extremely sensitive to the choice of the grid periods. However, when the accuracy of the representation is limited by neuronal noise, the capacity quickly becomes more robust against the choice of grid scales as the number of modules increases. Importantly, we found that the capacity of the system is near optimal even for random scale choices already for a realistic number of grid modules. Our study demonstrates that robust and efficient coding can be achieved without parameter tuning in the case of grid cell representation and provides a solid theoretical explanation for the large diversity of the grid scales observed in experimental studies. Moreover, we suggest that having multiple grid modules in the entorhinal cortex is not only required for the exponentially large coding capacity, but is also a prerequisite for the robustness of the system.

Location-dependent synaptic plasticity rules by dendritic spine cooperativity.

Nonlinear interactions between coactive synapses enable neurons to discriminate between spatiotemporal patterns of inputs. Using patterned postsynaptic stimulation by two-photon glutamate uncaging, here we investigate the sensitivity of synaptic Ca(2+) signalling and long-term plasticity in individual spines to coincident activity of nearby synapses. We find a proximodistally increasing gradient of nonlinear NMDA receptor (NMDAR)-mediated amplification of spine Ca(2+) signals by a few neighbouring coactive synapses along individual perisomatic dendrites. This synaptic cooperativity does not require dendritic spikes, but is correlated with dendritic Na(+) spike propagation strength. Furthermore, we show that repetitive synchronous subthreshold activation of small spine clusters produces input specific, NMDAR-dependent cooperative long-term potentiation at distal but not proximal dendritic locations. The sensitive synaptic cooperativity at distal dendritic compartments shown here may promote the formation of functional synaptic clusters, which in turn can facilitate active dendritic processing and storage of information encoded in spatiotemporal synaptic activity patterns.

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits.

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits.