The orbitofrontal cortex maps future navigational goals.

Accurate navigation to a desired goal requires consecutive estimates of spatial relationships between the current position and future destination throughout the journey. Although neurons in the hippocampal formation can represent the position of an animal as well as its nearby trajectories1-7, their role in determining the destination of the animal has been questioned8,9. It is, thus, unclear whether the brain can possess a precise estimate of target location during active environmental exploration. Here we describe neurons in the rat orbitofrontal cortex (OFC) that form spatial representations persistently pointing to the subsequent goal destination of an animal throughout navigation. This destination coding emerges before the onset of navigation, without direct sensory access to a distal goal, and even predicts the incorrect destination of an animal at the beginning of an error trial. Goal representations in the OFC are maintained by destination-specific neural ensemble dynamics, and their brief perturbation at the onset of a journey led to a navigational error. These findings suggest that the OFC is part of the internal goal map of the brain, enabling animals to navigate precisely to a chosen destination that is beyond the range of sensory perception.

In vivo extracellular recordings of thalamic and cortical visual responses reveal V1 connectivity rules.

The brain's connectome provides the scaffold for canonical neural computations. However, a comparison of connectivity studies in the mouse primary visual cortex (V1) reveals that the average number and strength of connections between specific neuron types can vary. Can variability in V1 connectivity measurements coexist with canonical neural computations? We developed a theory-driven approach to deduce V1 network connectivity from visual responses in mouse V1 and visual thalamus (dLGN). Our method revealed that the same recorded visual responses were captured by multiple connectivity configurations. Remarkably, the magnitude and selectivity of connectivity weights followed a specific order across most of the inferred connectivity configurations. We argue that this order stems from the specific shapes of the recorded contrast response functions and contrast invariance of orientation tuning. Remarkably, despite variability across connectivity studies, connectivity weights computed from individual published connectivity reports followed the order we identified with our method, suggesting that the relations between the weights, rather than their magnitudes, represent a connectivity motif supporting canonical V1 computations.

Targeting operational regimes of interest in recurrent neural networks.

Neural computations emerge from local recurrent neural circuits or computational units such as cortical columns that comprise hundreds to a few thousand neurons. Continuous progress in connectomics, electrophysiology, and calcium imaging require tractable spiking network models that can consistently incorporate new information about the network structure and reproduce the recorded neural activity features. However, for spiking networks, it is challenging to predict which connectivity configurations and neural properties can generate fundamental operational states and specific experimentally reported nonlinear cortical computations. Theoretical descriptions for the computational state of cortical spiking circuits are diverse, including the balanced state where excitatory and inhibitory inputs balance almost perfectly or the inhibition stabilized state (ISN) where the excitatory part of the circuit is unstable. It remains an open question whether these states can co-exist with experimentally reported nonlinear computations and whether they can be recovered in biologically realistic implementations of spiking networks. Here, we show how to identify spiking network connectivity patterns underlying diverse nonlinear computations such as XOR, bistability, inhibitory stabilization, supersaturation, and persistent activity. We establish a mapping between the stabilized supralinear network (SSN) and spiking activity which allows us to pinpoint the location in parameter space where these activity regimes occur. Notably, we find that biologically-sized spiking networks can have irregular asynchronous activity that does not require strong excitation-inhibition balance or large feedforward input and we show that the dynamic firing rate trajectories in spiking networks can be precisely targeted without error-driven training algorithms.

Computational insights into mRNA and protein dynamics underlying synaptic plasticity rules.

Recent advances in experimental techniques provide an unprecedented peek into the intricate molecular dynamics inside synapses and dendrites. The experimental insights into the molecular turnover revealed that such processes as diffusion, active transport, spine uptake, and local protein synthesis could dynamically modulate the copy numbers of plasticity-related molecules in synapses. Subsequently, theoretical models were designed to understand the interaction of these processes better and to explain how local synaptic plasticity cues can up or down-regulate the molecular copy numbers across synapses. In this review, we discuss the recent advances in experimental techniques and computational models to highlight how these complementary approaches can provide insight into molecular cross-talk across synapses, ultimately allowing us to develop biologically-inspired neural network models to understand brain function.

How to incorporate biological insights into network models and why it matters.

Due to the staggering complexity of the brain and its neural circuitry, neuroscientists rely on the analysis of mathematical models to elucidate its function. From Hodgkin and Huxley's detailed description of the action potential in 1952 to today, new theories and increasing computational power have opened up novel avenues to study how neural circuits implement the computations that underlie behaviour. Computational neuroscientists have developed many models of neural circuits that differ in complexity, biological realism or emergent network properties. With recent advances in experimental techniques for detailed anatomical reconstructions or large-scale activity recordings, rich biological data have become more available. The challenge when building network models is to reflect experimental results, either through a high level of detail or by finding an appropriate level of abstraction. Meanwhile, machine learning has facilitated the development of artificial neural networks, which are trained to perform specific tasks. While they have proven successful at achieving task-oriented behaviour, they are often abstract constructs that differ in many features from the physiology of brain circuits. Thus, it is unclear whether the mechanisms underlying computation in biological circuits can be investigated by analysing artificial networks that accomplish the same function but differ in their mechanisms. Here, we argue that building biologically realistic network models is crucial to establishing causal relationships between neurons, synapses, circuits and behaviour. More specifically, we advocate for network models that consider the connectivity structure and the recorded activity dynamics while evaluating task performance.

Modulation of working memory duration by synaptic and astrocytic mechanisms.

Short-term synaptic plasticity and modulations of the presynaptic vesicle release rate are key components of many working memory models. At the same time, an increasing number of studies suggests a potential role of astrocytes in modulating higher cognitive function such as WM through their influence on synaptic transmission. Which influence astrocytic signaling could have on the stability and duration of WM representations, however, is still unclear. Here, we introduce a slow, activity-dependent astrocytic regulation of the presynaptic release probability in a synaptic attractor model of WM. We compare and analyze simulations of a simple WM protocol in firing rate and spiking networks with and without astrocytic regulation, and underpin our observations with analyses of the phase space dynamics in the rate network. We find that the duration and stability of working memory representations are altered by astrocytic signaling and by noise. We show that astrocytic signaling modulates the mean duration of WM representations. Moreover, if the astrocytic regulation is strong, a slow presynaptic timescale introduces a 'window of vulnerability', during which WM representations are easily disruptable by noise before being stabilized. We identify two mechanisms through which noise from different sources in the network can either stabilize or destabilize WM representations. Our findings suggest that (i) astrocytic regulation can act as a crucial determinant for the duration of WM representations in synaptic attractor models of WM, and (ii) that astrocytic signaling could facilitate different mechanisms for volitional top-down control of WM representations and their duration.

Stabilized supralinear network can give rise to bistable, oscillatory, and persistent activity.

A hallmark of cortical circuits is their versatility. They can perform multiple fundamental computations such as normalization, memory storage, and rhythm generation. Yet it is far from clear how such versatility can be achieved in a single circuit, given that specialized models are often needed to replicate each computation. Here, we show that the stabilized supralinear network (SSN) model, which was originally proposed for sensory integration phenomena such as contrast invariance, normalization, and surround suppression, can give rise to dynamic cortical features of working memory, persistent activity, and rhythm generation. We study the SSN model analytically and uncover regimes where it can provide a substrate for working memory by supporting two stable steady states. Furthermore, we prove that the SSN model can sustain finite firing rates following input withdrawal and present an exact connectivity condition for such persistent activity. In addition, we show that the SSN model can undergo a supercritical Hopf bifurcation and generate global oscillations. Based on the SSN model, we outline the synaptic and neuronal mechanisms underlying computational versatility of cortical circuits. Our work shows that the SSN is an exactly solvable nonlinear recurrent neural network model that could pave the way for a unified theory of cortical function.

Astrocytes enhance plasticity response during reversal learning.

Astrocytes play a key role in the regulation of synaptic strength and are thought to orchestrate synaptic plasticity and memory. Yet, how specifically astrocytes and their neuroactive transmitters control learning and memory is currently an open question. Recent experiments have uncovered an astrocyte-mediated feedback loop in CA1 pyramidal neurons which is started by the release of endocannabinoids by active neurons and closed by astrocytic regulation of the D-serine levels at the dendrites. D-serine is a co-agonist for the NMDA receptor regulating the strength and direction of synaptic plasticity. Activity-dependent D-serine release mediated by astrocytes is therefore a candidate for mediating between long-term synaptic depression (LTD) and potentiation (LTP) during learning. Here, we show that the mathematical description of this mechanism leads to a biophysical model of synaptic plasticity consistent with the phenomenological model known as the BCM model. The resulting mathematical framework can explain the learning deficit observed in mice upon disruption of the D-serine regulatory mechanism. It shows that D-serine enhances plasticity during reversal learning, ensuring fast responses to changes in the external environment. The model provides new testable predictions about the learning process, driving our understanding of the functional role of neuron-glia interaction in learning.

Efficient encoding of aversive location by CA3 long-range projections.

Memorizing locations that are harmful or dangerous is a key capability of all organisms and requires an integration of affective and spatial information. In mammals, the dorsal hippocampus mainly processes spatial information, while the intermediate to ventral hippocampal divisions receive affective information via the amygdala. However, how spatial and aversive information is integrated is currently unknown. To address this question, we recorded the activity of hippocampal long-range CA3 axons at single-axon resolution in mice forming an aversive spatial memory. We show that intermediate CA3 to dorsal CA3 (i-dCA3) projections rapidly overrepresent areas preceding the location of an aversive stimulus due to a spatially selective addition of new place-coding axons followed by spatially non-specific stabilization. This sequence significantly improves the encoding of location by the i-dCA3 axon population. These results suggest that i-dCA3 axons transmit a precise, denoised, and stable signal indicating imminent danger to the dorsal hippocampus.

Energy-efficient encoding by shifting spikes in neocortical neurons.

The speed of computations in neocortical networks critically depends on the ability of populations of spiking neurons to rapidly detect subtle changes in the input and translate them into firing rate changes. However, high sensitivity to perturbations may lead to explosion of noise and increased energy consumption. Can neuronal networks reconcile the requirements for high sensitivity, operation in a low-noise regime, and constrained energy consumption? Using intracellular recordings in slices from the rat visual cortex, we show that layer 2/3 pyramidal neurons are highly sensitive to minor input perturbations. They can change their population firing rate in response to small artificial excitatory postsynaptic currents (aEPSCs) immersed in fluctuating noise very quickly, within 2-2.5 ms. These quick responses were mediated by the generation of new, additional action potentials (APs), but also by shifting spikes into the response peak. In that latter case, the spike count increase during the peak and the decrease after the peak cancelled each other, thus producing quick responses without increases in total spike count and associated energy costs. The contribution of spikes from one or the other source depended on the aEPSCs timing relative to the waves of depolarization produced by ongoing activity. Neurons responded by shifting spikes to aEPSCs arriving at the beginning of a depolarization wave, but generated additional spikes in response to aEPSCs arriving towards the end of a wave. We conclude that neuronal networks can combine high sensitivity to perturbations and operation in a low-noise regime. Moreover, certain patterns of ongoing activity favor this combination and energy-efficient computations.

Linking spontaneous and stimulated spine dynamics.

Our brains continuously acquire and store memories through synaptic plasticity. However, spontaneous synaptic changes can also occur and pose a challenge for maintaining stable memories. Despite fluctuations in synapse size, recent studies have shown that key population-level synaptic properties remain stable over time. This raises the question of how local synaptic plasticity affects the global population-level synaptic size distribution and whether individual synapses undergoing plasticity escape the stable distribution to encode specific memories. To address this question, we (i) studied spontaneously evolving spines and (ii) induced synaptic potentiation at selected sites while observing the spine distribution pre- and post-stimulation. We designed a stochastic model to describe how the current size of a synapse affects its future size under baseline and stimulation conditions and how these local effects give rise to population-level synaptic shifts. Our study offers insights into how seemingly spontaneous synaptic fluctuations and local plasticity both contribute to population-level synaptic dynamics.

Ultrafast population encoding by cortical neurons.

The processing speed of the brain depends on the ability of neurons to rapidly relay input changes. Previous theoretical and experimental studies of the timescale of population firing rate responses arrived at controversial conclusions, some advocating an ultrafast response scale but others arguing for an inherent disadvantage of mean encoded signals for rapid detection of the stimulus onset. Here we assessed the timescale of population firing rate responses of neocortical neurons in experiments performed in the time domain and the frequency domain in vitro and in vivo. We show that populations of neocortical neurons can alter their firing rate within 1 ms in response to somatically delivered weak current signals presented on a fluctuating background. Signals with amplitudes of miniature postsynaptic currents can be robustly and rapidly detected in the population firing. We further show that population firing rate of neurons of rat visual cortex in vitro and cat visual cortex in vivo can reliably encode weak signals varying at frequencies up to ∼200-300 Hz, or ∼50 times faster than the firing rate of individual neurons. These results provide coherent evidence for the ultrafast, millisecond timescale of cortical population responses. Notably, fast responses to weak stimuli are limited to the mean encoding. Rapid detection of current variance changes requires extraordinarily large signal amplitudes. Our study presents conclusive evidence showing that cortical neurons are capable of rapidly relaying subtle mean current signals. This provides a vital mechanism for the propagation of rate-coded information within and across brain areas.

Representation of dynamical stimuli in populations of threshold neurons.

Many sensory or cognitive events are associated with dynamic current modulations in cortical neurons. This raises an urgent demand for tractable model approaches addressing the merits and limits of potential encoding strategies. Yet, current theoretical approaches addressing the response to mean- and variance-encoded stimuli rarely provide complete response functions for both modes of encoding in the presence of correlated noise. Here, we investigate the neuronal population response to dynamical modifications of the mean or variance of the synaptic bombardment using an alternative threshold model framework. In the variance and mean channel, we provide explicit expressions for the linear and non-linear frequency response functions in the presence of correlated noise and use them to derive population rate response to step-like stimuli. For mean-encoded signals, we find that the complete response function depends only on the temporal width of the input correlation function, but not on other functional specifics. Furthermore, we show that both mean- and variance-encoded signals can relay high-frequency inputs, and in both schemes step-like changes can be detected instantaneously. Finally, we obtain the pairwise spike correlation function and the spike triggered average from the linear mean-evoked response function. These results provide a maximally tractable limiting case that complements and extends previous results obtained in the integrate and fire framework.

Dopamine and serotonin interplay for valence-based spatial learning.

Dopamine (DA) and serotonin (5-HT) are important neuromodulators of synaptic plasticity that have been linked to learning from positive or negative outcomes or valence-based learning. In the hippocampus, both affect long-term plasticity but play different roles in encoding uncertainty or predicted reward. DA has been related to positive valence, from reward consumption or avoidance behavior, and 5-HT to aversive encoding. We propose DA produces overall LTP while 5-HT elicits LTD. Here, we compare two reward-modulated spike timing-dependent plasticity (R-STDP) rules to describe the action of these neuromodulators. We examined their role in cognitive performance and flexibility for computational models of the Morris water maze task and reversal learning. Our results show that the interplay of DA and 5-HT improves learning performance and can explain experimental evidence. This study reinforces the importance of neuromodulation in determining the direction of plasticity.

Unbiased choice of global clustering parameters for single-molecule localization microscopy.

Single-molecule localization microscopy resolves objects below the diffraction limit of light via sparse, stochastic detection of target molecules. Single molecules appear as clustered detection events after image reconstruction. However, identification of clusters of localizations is often complicated by the spatial proximity of target molecules and by background noise. Clustering results of existing algorithms often depend on user-generated training data or user-selected parameters, which can lead to unintentional clustering errors. Here we suggest an unbiased algorithm (FINDER) based on adaptive global parameter selection and demonstrate that the algorithm is robust to noise inclusion and target molecule density. We benchmarked FINDER against the most common density based clustering algorithms in test scenarios based on experimental datasets. We show that FINDER can keep the number of false positive inclusions low while also maintaining a low number of false negative detections in densely populated regions.

The prevalence and specificity of local protein synthesis during neuronal synaptic plasticity.

To supply proteins to their vast volume, neurons localize mRNAs and ribosomes in dendrites and axons. While local protein synthesis is required for synaptic plasticity, the abundance and distribution of ribosomes and nascent proteins near synapses remain elusive. Here, we quantified the occurrence of local translation and visualized the range of synapses supplied by nascent proteins during basal and plastic conditions. We detected dendritic ribosomes and nascent proteins at single-molecule resolution using DNA-PAINT and metabolic labeling. Both ribosomes and nascent proteins positively correlated with synapse density. Ribosomes were detected at ~85% of synapses with ~2 translational sites per synapse; ~50% of the nascent protein was detected near synapses. The amount of locally synthesized protein detected at a synapse correlated with its spontaneous Ca2+ activity. A multifold increase in synaptic nascent protein was evident following both local and global plasticity at respective scales, albeit with substantial heterogeneity between neighboring synapses.

Correlations and synchrony in threshold neuron models.

We study how threshold models and neocortical neurons transfer temporal and interneuronal input correlations to correlations of spikes. In both, we find that the low common input regime is governed by firing rate dependent spike correlations which are sensitive to the detailed structure of input correlation functions. In the high common input regime, the spike correlations are largely insensitive to the firing rate and exhibit a universal peak shape. We further show that pairs with different firing rates driven by common inputs in general exhibit asymmetric spike correlations.

Nonlinear response characteristics of neural networks and single neurons undergoing optogenetic excitation.

Optogenetic stimulation has become the method of choice for investigating neural computation in populations of neurons. Optogenetic experiments often aim to elicit a network response by stimulating specific groups of neurons. However, this is complicated by the fact that optogenetic stimulation is nonlinear, more light does not always equal to more spikes, and neurons that are not directly but indirectly stimulated could have a major impact on how networks respond to optogenetic stimulation. To clarify how optogenetic excitation of some neurons alters the network dynamics, we studied the temporal and spatial response of individual neurons and recurrent neural networks. In individual neurons, we find that neurons show a monotonic, saturating rate response to increasing light intensity and a nonmonotonic rate response to increasing pulse frequency. At the network level, we find that Gaussian light beams elicit spatial firing rate responses that are substantially broader than the stimulus profile. In summary, our analysis and our network simulation code allow us to predict the outcome of an optogenetic experiment and to assess whether the observed effects can be attributed to direct or indirect stimulation of neurons.

How Repair-or-Dispose Decisions Under Stress Can Initiate Disease Progression.

Glia, the helper cells of the brain, are essential in maintaining neural resilience across time and varying challenges: By reacting to changes in neuronal health glia carefully balance repair or disposal of injured neurons. Malfunction of these interactions is implicated in many neurodegenerative diseases. We present a reductionist model that mimics repair-or-dispose decisions to generate a hypothesis for the cause of disease onset. The model assumes four tissue states: healthy and challenged tissue, primed tissue at risk of acute damage propagation, and chronic neurodegeneration. We discuss analogies to progression stages observed in the most common neurodegenerative conditions and to experimental observations of cellular signaling pathways of glia-neuron crosstalk. The model suggests that the onset of neurodegeneration can result as a compromise between two conflicting goals: short-term resilience to stressors versus long-term prevention of tissue damage.

Statistical Laws of Protein Motion in Neuronal Dendritic Trees.

Across their dendritic trees, neurons distribute thousands of protein species that are necessary for maintaining synaptic function and plasticity and that need to be produced continuously and trafficked to their final destination. As each dendritic branchpoint splits the protein flow, increasing branchpoints decreases the total protein number downstream. Consequently, a neuron needs to produce more proteins to maintain a minimal protein number at distal synapses. Combining in vitro experiments and a theoretical framework, we show that proteins that diffuse within the cell plasma membrane are, on average, 35% more effective at reaching downstream locations than proteins that diffuse in the cytoplasm. This advantage emerges from a bias for forward motion at branchpoints when proteins diffuse within the plasma membrane. Using 3D electron microscopy (EM) data, we show that pyramidal branching statistics and the diffusion lengths of common proteins fall into a region that minimizes the overall protein need.