Mixed vine copula flows for flexible modeling of neural dependencies

Recordings of complex neural population responses provide a unique opportunity for advancing our understanding of neural information processing at multiple scales and improving performance of brain computer interfaces. However, most existing analytical techniques fall short of capturing the complexity of interactions within the concerted population activity. Vine copula-based approaches have shown to be successful at addressing complex high-order dependencies within the population, disentangled from the single-neuron statistics. However, most applications have focused on parametric copulas which bear the risk of misspecifying dependence structures. In order to avoid this risk, we adopted a fully non-parametric approach for the single-neuron margins and copulas by using Neural Spline Flows (NSF). We validated the NSF framework on simulated data of continuous and discrete types with various forms of dependency structures and with different dimensionality. Overall, NSFs performed similarly to existing non-parametric estimators, while allowing for considerably faster and more flexible sampling which also enables faster Monte Carlo estimation of copula entropy. Moreover, our framework was able to capture low and higher order heavy tail dependencies in neuronal responses recorded in the mouse primary visual cortex during a visual learning task while the animal was navigating a virtual reality environment. These findings highlight an often ignored aspect of complexity in coordinated neuronal activity which can be important for understanding and deciphering collective neural dynamics for neurotechnological applications

CalciumGAN: A Generative Adversarial Network Model for Synthesising Realistic Calcium Imaging Data of Neuronal Populations

Calcium imaging has become a powerful and popular technique to monitor the activity of large populations of neurons in vivo. However, for ethical considerations and despite recent technical developments, recordings are still constrained to a limited number of trials and animals. This limits the amount of data available from individual experiments and hinders the development of analysis techniques and models for more realistic size of neuronal populations. The ability to artificially synthesize realistic neuronal calcium signals could greatly alleviate this problem by scaling up the number of trials. Here we propose a Generative Adversarial Network (GAN) model to generate realistic calcium signals as seen in neuronal somata with calcium imaging. To this end, we adapt the WaveGAN architecture and train it with the Wasserstein distance. We test the model on artificial data with known ground-truth and show that the distribution of the generated signals closely resembles the underlying data distribution. Then, we train the model on real calcium signals recorded from the primary visual cortex of behaving mice and confirm that the deconvolved spike trains match the statistics of the recorded data. Together, these results demonstrate that our model can successfully generate realistic calcium imaging data, thereby providing the means to augment existing datasets of neuronal activity for enhanced data exploration and modeling

Parametric Copula-GP model for analyzing multidimensional neuronal and behavioral relationships

One of the main goals of current systems neuroscience is to understand how neuronal populations integrate sensory information to inform behavior. However, estimating stimulus or behavioral information that is encoded in high-dimensional neuronal populations is challenging. We propose a method based on parametric copulas which allows modeling joint distributions of neuronal and behavioral variables characterized by different statistics and timescales. To account for temporal or spatial changes in dependencies between variables, we model varying copula parameters by means of Gaussian Processes (GP). We validate the resulting Copula-GP framework on synthetic data and on neuronal and behavioral recordings obtained in awake mice. We show that the use of a parametric description of the high-dimensional dependence structure in our method provides better accuracy in mutual information estimation in higher dimensions compared to other non-parametric methods. Moreover, by quantifying the redundancy between neuronal and behavioral variables, our model exposed the location of the reward zone in an unsupervised manner (i.e., without using any explicit cues about the task structure). These results demonstrate that the Copula-GP framework is particularly useful for the analysis of complex multidimensional relationships between neuronal, sensory and behavioral variables

Raptor-Mediated Proteasomal Degradation of Deamidated 4E-BP2 Regulates Postnatal Neuronal Translation and NF-κB Activity

The translation initiation repressor 4E-BP2 is deamidated in the brain on asparagines N99/N102 during early postnatal brain development. This post-translational modification enhances 4E-BP2 association with Raptor, a central component of mTORC1 and alters the kinetics of excitatory synaptic transmission. We show that 4E-BP2 deamidation is neuron specific, occurs in the human brain, and changes 4E-BP2 subcellular localization, but not its disordered structure state. We demonstrate that deamidated 4E-BP2 is ubiquitinated more and degrades faster than the unmodified protein. We find that enhanced deamidated 4E-BP2 degradation is dependent on Raptor binding, concomitant with increased association with a Raptor-CUL4B E3 ubiquitin ligase complex. Deamidated 4E-BP2 stability is promoted by inhibiting mTORC1 or glutamate receptors. We further demonstrate that deamidated 4E-BP2 regulates the translation of a distinct pool of mRNAs linked to cerebral development, mitochondria, and NF-κB activity, and thus may be crucial for postnatal brain development in neurodevelopmental disorders, such as ASD

Representation of perceptual uncertainty in mouse primary visual cortex

Uncertainty in various modalities (perceptual, motor, cognitive) is a fundamental problem that the brain must solve to ensure optimal responses to the demands of the environment. It has been shown theoretically that the optimal solution when faced with uncertainty is to represent and propagate full probability distributions over variables of interest and perform probabilistic inference according to Bayes’ rule. Previous studies in humans and other animals have shown that the brain does indeed implement a version of Bayesian Inference. Several computational theories have proposed different models for the underlying representation of probability distributions that this requires. The most prominent of these are Probabilistic Population Codes (PPC) and Sampling-Based Codes (SBC). However, existing studies have been unable to prove or disprove these theories conclusively, especially due to the lack of neural population-level recordings concurrent with single-trial measures of uncertainty. In the present thesis, I investigated the representation of perceptual uncertainty in the brain, using the mouse primary visual cortex as a model system. I recorded the activity of large neuronal populations in vivo using two-photon calcium-imaging. I employed a variety of both passive (presentation of visual grating stimuli on a monitor) and active (visually-guided goal-directed behaviour) visual stimulation paradigms to manipulate the sensory uncertainty of the animals. Additionally, I derive a trial-by-trial behavioural uncertainty measure based on the licks that the animals make. My results show that: 1) repeated exposure to behaviourally-relevant (but not neutral) stimuli increases the precision of their representation in the cortex. 2) In a passive viewing setting, manipulation of visual contrast modulates neural responses in a manner partially consistent with both PPC and SBC, with higher contrasts evoking, in general, larger mean responses and larger response variance, and leading to more discriminable stimulus representations. 3) During a two-alternative forced choice task, mouse behavioural uncertainty was modulated in an asymmetrical way by stimulus uncertainty (contrast/aperture) and orientation. Behavioural responses were explained by similarity of neural population responses to two stimulus “archetypes”