Scientist Stories: Mu Qiao, Deciphering the Genetic Code of Neuronal Type Connectivity

First, thanks to the organizers for this wonderful conference, and it's exciting to learn all this excellent research. So my name is Nqiao, and I was trained as a computational neuroscientist, but now I'm a machine learning practitioner at LinkedIn. So today I want to share the research about applying algorithms stemmed from recommendation systems to this problem of neuronal type connectivity. I want to start by asking the question, why is neuroscience research challenging? Well, there are many reasons. A clear observation is that there are many different types of neurons and there are complex synaptic connections between them. The complexity is evident even in this small piece of tissue within the central nervous system called retina, which is at the back of our eyes. The retina is an excellent model for neuroscience. Because of this regular arrangement of retinal neurons and their synapses. There are 5 type classes of neurons in the retina, photoreceptors that detect light and the interneurons including horizontal cells, bipolar cells, and amacrine cells that relay and transform the signals from photoreceptors. And finally, we have retinal ganglion cells that send the axons to the retinal recipient areas. There are over 70 different types of interneurons and over 40 different types of retinal ganglion cells. And each specific type of retinal ganglion cells form specific connections with certain types of interneurons in this synaptic layer called the inner platform layer. And the consequence of this connectivity is that each type of retinal ganglion cell is tuned to a specific feature such as local motion, approaching motion, lateral motion, or color contrast. This knowledge is abstracted in this wiring diagram of what we call neural circuits, which we use to model and explain specialized encoding of, for example, visual features. However, despite this wiring diagram, the genetic underlying of the specific connectivity, especially that in many other parts of the brain, is still largely unknown. Part of the challenge here is the limitation in traditional approaches, which involve genetically manipulating the expression of candidate molecules in specific cell types and then evaluating the effects on their connectivity. They are inefficient and inadequate for the following two reasons. First, neurons often have complicated connections, with one neuron potentially linking to different types of other neurons. And the second, the genetics behind these connections can be intricate. Instead of having one single molecule mediating the connections between two neurons, it's possible that gradients of molecules or a combination of different molecules that mediate specific neural links. These challenges ask for a systematic approach to decode neuronal type connectivity. Fortunately, we now have emerging data from single-cell transcriptomics and connectomics that pave the way for this decoding effort. The single-cell transcriptomics provides us detailed gene expression profiles of individual neurons, which are then clustered and classified into neuronal types. On the other hand, we have connectome. Or anatomic reconstruction with electron microscopy. From this anatomical reconstruction, we not only can reconstruct the morphology of individual cells, but can also visualize individual synapses between neurons. This provides us detailed connectivity matrix between neuronal types, such as the one between presynaptic bipolar cells and the postsynaptic retinal ganglion cells in the retina. With this data, an intriguing question arises. Can we predict neuronal connectivity based on gene expression? If so, then we can look into the gene expression data and identify which genes are critical contributors to this prediction. So this question parallels one addressed by the recommendation systems in digital platform, particularly in this product People You May Know, which you probably have encountered on LinkedIn or Facebook, where connections between users are predicted based on their profiles. So let's see how this is solved. In general, a recommendation system suggests an item, such as a movie characterized by a feature vector y, to a user whose feature vector is x. It does so by projecting the user and item features into a shared latent space, where similarity in the space predicts user-item interactions. A common algorithm for this is called collaborative filtering. Let's illustrate this with this simplified example. Suppose we assign to each movie a scalar from -1 to +1 that describes whether the movie is for children or adults, and we also assign a scalar to each user from -1 to +1 reflecting the user's interest in children's movie or adult movie. Then the dot product of the movie's embedding and the user's embedding should yield higher value for movies that align with the user's preferences. On the right side, each checkmark identifies a movie that a particular user watched. You can see that the third and fourth users have preferences that are well predicted by this model. However, using only one dimension embedding, we cannot predict the user-item interaction of the first two users. However, when we add the second latent feature, the degree to which the movie is a blockbuster or an arthouse movie, we can now represent each movie with the following two-dimensional embedding. Now the user-movie interactions are well explained by the similarity of the latent features, and we can even predict that the last user is unlikely to watch the movie Shrek. Although here these embeddings are hand-engineered for illustration purposes, in a real-world application, these embeddings can be learned automatically, which is the power of collaborative filtering. So formally, assuming that we have access to the ground truth interaction VIG between a user I and item J, then the learning task is to minimize discrepancy of the predicted interaction and the ground truth expressed in the matrix form, we are minimizing the Frobenius norm of the residual matrix. Now the question is how to adapt the bilinear model to neuronal type connectivity. By considering presynaptic neurons as users and the postsynaptic neurons as items, we can now predict synaptic connections similar to predicting user-item interactions. In an ideal scenario, if we know gene expression and the connectivity of each cell simultaneously, this translation becomes straightforward. The only difference here is the inclusion of this weight matrix adjusted based on the cell counts in each presynaptic and the postsynaptic neuronal type. This is essential, particularly in unbalanced datasets. Where a few cell types could dominate the entire cell population. The weight matrix helps avoid model bias towards overrepresented cell types. In practice, the gene expression and the connectivity data are often from different sources. In this case, while we can align cell types based on established biological knowledge, associating individual cells is not feasible. To address this, we make a simplifying assumption, which is the connectivity and latent gene expressions of individual cells are represented by the average of their respective cell types. We then focus on minimizing the difference between the average connectivity and the gene expression of corresponding cell types while imposing this constraint to minimize the variance of latent gene expression within each neuronal type. Essentially, the goal here is to minimize the discrepancy between these two sources of information while maintaining consistency of the gene expression within neuronal types. To find the optimal transformation, we constructed the Laplacian and used alternating gradient descent method. Here is how it works. In each iteration, we keep matrix B fixed and adjust matrix A by moving in the direction of its gradient. Then we hold A steady and update B according to its gradient. This process repeats until they both stabilize at a solution. For this optimization, we select hyperparameters like lambda and the dimensions of the latent space through a process of cross-validation. We tested our bilinear model with the retinal dataset of bipolar cells and retinal ganglion cells. Using 5-fold cross-validation, we found that the best dimensionality of the latent space is 2. Then with these selected hyperparameters, the model successfully constructed the connectivity matrix between bipolar cell types and retinal ganglion cell types from the transcriptomic data. As I mentioned, the Bayesian model of collaborative filtering is powerful because it can automatically decipher the latent embeddings. Therefore, we deep dive into each of the embedding dimensions and see which attributes they encode. Interestingly, we find that each of the latent dimensions contributes to a unique connectivity pattern or motif. To illustrate, when we group the bipolar cells or retinal ganglion cells based on whether they fall onto the positive half or negative half along each latent dimension and then plot their stratifications using the red color or blue color, we found a clear distinction. For example, the first latent dimension separates bipolar cells and retinal ganglion cells that synapse in the central versus the marginal region of the synaptic layer. In contrast, the second latent dimension focuses on the connections over the outer versus inner parts of the synaptic layer for both bipolar cells and retinal ganglion cells. Remarkably, these motifs align well with recognized properties of retinal neurons. Kinetics means whether the neurons have transient versus sustained responses, or polarity, meaning whether the neurons respond to light onset or light offset. Significantly, these motifs are not predefined or explicitly encoded into the model. Instead, they emerge naturally from the model, attesting the model's power to capture key aspects of retinal circuits. The inherent linearity of the bilinear model allows us to directly quantify the impact of each gene on connectivity through their respective weights. We can then identify critical genes based on the weight magnitude. The gene ontology analysis of these critical genes showed significant terms related to neural development and synaptic organization. But here I want to emphasize two sets of molecules. First, plexins A4 and A2. So these are receptors for semaphorin signaling pathways. And they are predicted to be important for synapses in the OFF layer. And indeed, knockout of the genes shows a disruption of the OFF lamina and its misplacement within the ON lamina. And this happens for both plexin A4 and PlexinA2. Another set of genes, Contactin-5 or Cadherin-8, known as cell-cell adhesion molecules, are predicted to be important for bipolar cells and retinal ganglion cells synapsing in the on and off layers respectively. Indeed, previous studies provide evidence for their crucial involvement in shaping the on and off pathways. For instance, Contactin-5 was shown to be important for the formation of the on pathway of this direction-selective circuit. And the catecholamine 8 expressed in this retinal ganglion cell type called GRGCs is important for its dendritic lamination in the off lamina. What's more important, it makes predictions on promising candidate genes that remain to be tested. Here, I want to pinpoint a set of genes called protocadherin. Protocadherin 7, 9, and 11X, they belong to the delta protocadherin family. Although their roles in the retina are not thoroughly explored, they show adherence in a combinatory manner and are important for neural circuits assembly in other parts of the brain. Therefore, they are promising candidates to be tested in the retina. So here I want to give a brief summary of this talk. So we show that a bilinear model stemmed from recommendation systems was able to integrate transcriptomic and connectomic data to elucidate genetic underlying behind neuronotypes. And we also show that the model's capability to capture recognized connectivity motifs of the retina circuits and provide interpretable insights into gene signatures associated with this motif. This makes this model a valuable tool for investigating gene regulatory mechanisms involved in neural circuit wiring. Looking forward, I'm excited about the future possibilities of developing a recommendation system AI for neuronal connectivity. Contemporary recommendation systems have the scalability potential to model the neuronal connectivity of the entire mouse neuron. As a comparison, there are about 2 billion daily active users on Facebook, while the total number of neurons in the mouse brain is about 70 million. What's more, the recommendation systems have advanced from linear models to deep models such as the two-tower models that project the input features into the latent embedding through a deep neural network that can capture intricate nonlinear interactions of the input features. And to this deep and wide architecture, that is a hybrid of the deep model and the linear model. And the purpose here is to balance the prediction accuracy, interpretability, and inference latency. And to recent practice of augmentation with large language models, I believe following a similar path, we will achieve a system that helps us understand the mechanisms behind the neuronal type synaptic specificity. Thank you very much. I'm here to take any questions.

Very interesting stuff. So the protocadherins have really interesting, like, alternative splicing and also alternative promoter choice that is known to control some amount of neuronal connectivity. So do you have any data where you can look at those aspects? It's obviously tough with 10X data. It's really hard to look at, but I don't know if there's other data sources you could try and look at.

Yeah, that's a very good question. Yes. So basically, in this research, we were using available data, which is from 10X. But yes, I think also, yeah, someone also mentioned this, that this alternative slicing of protocadherins is important for these synaptic connections. So yeah. Looking forward to integrating that data to explore this. Okay, we have a 20-minute break until 2:00, and then we'll have a panel here. So we'll set up some chairs for the live panel members will be here, and there'll be some online, and we'll do the panel.