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So in total, the number of observations cells might be in the thousands. The number of individuals contributing the cells might be much smaller, and this raises the question of how to think about statistical power for the test.

It is important that the between-individual variation is not larger than the between-conditions variation. When comparing two assigned cell types against each other it is straightforward to account for between-individual variation.

Since ideally each individual contributes with samples of each cell type, an individual-specific effect can be added to the model. If the goal is to compare gene expression between healthy and diseased mice for a particular cell type, it is no longer possible to separate the individual effect from the disease effect.

There is complete confounding between condition and individual. We would for example never have data from the same individual being both healthy and diseased.

This means that when accounting for individual-specific effects on gene expression, it will never be possible to get low p-values. Not without making the assumption that the individuals are directly comparable, and we do not need to consider individual-level effects.

This might be reasonable for lab mice, but when analyzing cells from human donors, there will be a lot of genetic and lifestyle variation between individuals.

A strategy to deal with this is use multilevel regression rather than linear regression. A simple way to think about these models is as means at different levels, with level-specific variance that observations vary around.

Say there is an overall mean expression level, and a between-mouse variance. Then for each mouse there is a mean expression level, with between-cell variance for that particular mouse.

Such a model can be compared to a model where there is an overall mean, with condition-specific variance.

Then each condition healthy vs diseased has a mean, as well as between-mouse variance for the conditions. And in turn, each mouse, within a condition, has a specific mean with between-cell variance.

If grouping the mice by disease give a better model fit for the gene expression values, then this is evidence of the gene being perturbed by the disease state.

While also accounting for between-individual variation! To test this approach to differential expression, I looked at a dataset published by Hrvatin et al [1].

They perform scRNA-seq on cells from the visual cortex of mice. These are mice that have been living in complete darkness for several days.

Some of the mice are exposed to light for an hour before they are sacrificed and cells are collected. The concept is that now you can identify which cell types in the visual cortex get activated by the exposure to light by investigating the differential expression of no light vs 1 hour light exposure.

In the paper they describe that the most dramatic effect was in the cells annotated as ExcL23, so I sorted these out, and only picked cells with either 0h or 1h light stimulation.

In total this data has 1, cells from 17 mice, where 9 mice were not exposed to light and 8 mice were exposed to light for 1 hour.

I used three different models for testing differential expression. In formula notation, these would be the models:.

To obtain p-values, I performed likelihood ratio tests between the H0 and H1 models. Note that the multilevel model is the only one aware of sample mouse grouping!

In the results I am highlighting genes that Hrvatin et al also point out as particularly differential between no light and 1h light. Ordinary regression clearly identifies the genes discussed by Hrvatin et al.

The model is not acknowledging the fact that cells from the same mouse probably have a lot of internal correlation, and therefore the model fit is overly certain.

The same phenomenon can be observed in the GLM model. The multilevel model has much more reasonable p-values. An alternative proposed strategy is a two-step one.

First, define cell types on the single cell level from scRNA-seq. Now we can apply differential expression tests on the summed level.

I applied the same models, but for such summed pseudobulks, now having only 17 observations rather than 1, The OLS regression now seems much more reasonable, the GLM model still has the same issue of seeming overly confident, and interestingly, the Poisson multilevel model for the pseudobulk gives exactly the same results as for the single cell data.

I like that the multilevel approach ties directly to the hierarchical nature of the experiment. Here I only used basic R functions rather than specialized DE packages.

I just wanted to compare these strategies directly with naive implementation. Finally, I used Poisson models here; there are plenty of reasons to think that negative binomial models would be more appropriate, and I might revisit these questions to test that at some point.

Notebooks, R scripts, and other material for making this post are available on Github. Thanks to Lior Pachter for editorial feedback on this post.

Hrvatin et al. Lun and J. Soneson and M. Methods, Feb. It is always good to compare your measurements with measurements others have done before you.

This way you get a feeling for expected outcomes, expected variation in measurement, etc. Single cell RNA-seq data consists of observed counts of molecules generated from different genes in different cells.

Sometimes however, authors only publish counts that have been scaled. One very popular unit is CPM, counts per million, where the counts in each cell is divided by the sum of counts, then multiplied by a million.

Recently I have also noticed data with similar scaling to 10, or ,, or to a median across the data set. To compare data from different sources, it is easier to interpret differences if you know the per-cell total counts.

It allows you to think of the counts in the data in the context of exposure. I recently wanted to look at some 10X data , but it turned out the expression matrix did not consist of counts.

Looking at the mean-variance relation for all the genes in the data it was clear that they had been log-transformed.

Even after exponentiating the expression levels, they were not integers. However, looking at the sum of expression levels in each cell it could easily be seen that the counts had been scaled to 10, counts per cell.

However, the very problem with scaling of counts means we can recover the value used to scale the cell. Follows by a substantial number of genes with 1 counts, followed by a slightly smaller number of genes with 2 counts, etc.

Since the scaling by division just changes the magnitude of the counts, but not the discrete nature, the most common value will correspond to 0, the second most common value to 1, etc.

This plot of a few random cells make this relation clear. Just looking at the second most common value in the histogram of a cell will give us the factor used to scale the cell!

For the sake of some robustness, I used several ranks in the histogram and the corresponding scaled counts and fitted the scaling factor with least squares, but the difference from the second most common value was all in all negligible.

By simply multiplying the cells by the identified scaling factors, the true counts are recovered. After un-scaling, the typical relation between total count and detected genes is clear, and the negative binomial mean-variance relation for genes is apparent.

I wanted to write about this, because the fact that it is possible to recover the original counts after scaling indicates that just scaling the counts is not sufficient for normalization.

The properties if discrete counts are still present in the data, and will be a factor in every analysis where these scaled counts are used.

It will make interpretation hard, since the relation between magnitude and the probability of generating values magnitude will not be tied to each other as clearly as with counts.

Notebook with this analysis is available here. Malaria is one of the world's deadliest diseases with million cases in a year, leading to half a million deaths.

It is caused by mosquito-borne Plasmodium parasites. During parasitic infections our adaptive immune system responds through a complex series of cellular interactions, precipitated by events at the molecular level.

The dynamic ability to suppress and activate genes allow immune cells to maintain surprising plasticity. Switching the states of the cells in response to infection require a network of gene regulatory events to occur.

At the heart of the adaptive immune system are T helper cells. Under healthy conditions, naive T helper cells are quiescent and roam through the body awaiting signals.

Once T helper cells receive activation signals they differentiate into different roles depending on the type of infection. In malaria, naive cells differentiate into two distinct populations with different roles: Th1 cells, which signal macrophages and killer T cells to attack infected cells.

And Tfh cells, which activate survival programs and promote antibody affinity in B cells. Differentiation into a role is orchestrated by a small number of transcription factors regulating expression of large sets of genes.

Identifying transcription factors that direct the differentiation fate is of key importance to understand the immune system, and to what degree in vivo cell-extrinsic factors bias the cell fate has not been studied in detail.

Immunology tightly links cellular biology and molecular genomics. Recently single cell RNA sequencing has gained massive popularity to investigate cells with this joint perspective 1.

This technology allows researchers to measure expression of all genes in thousands of single cells.

Immune cells however have particularly low amounts of RNA and many important genes, such as transcription factors, are present at low levels.

To ensure scRNA-seq would be useful for us we evaluated many different technologies with ground truth molecular input levels 2.

To our surprise we found that expression could be quantified even from tens of copies of RNA molecules! To chart the immune response to malaria we designed a large scRNA-seq time course experiment using a mouse model.

We collected T helper cells, monocytes, and dendritic cells from mice infected by the malaria parasite Plasmodium chabaudi at five points over seven days 3.

We used Gaussian process methods to identify and investigate genes with expression dynamics over time. These are nonparametric machine learning models that can represent and identify any smooth dynamic function.

Later we extended this method to identify spatially variable genes in spatial tissue gene expression systems 4. Unfortunately five time points are not sufficient to make conclusions about the dynamics of gene expression.

However, we could exploit the fact that the immune cells are not synchronized in their response. This Gaussian process latent variable model simultaneously model many genes as different smooth functions, and correct time values so genes are consistent between each other.

Now we could investigate the temporally dynamic genes and looked at when they started, peaked, and stopped expression. This way we learn the order transcriptional programs like activation or proliferation.

The most crucial aspect of our experiment was that the T helper cells had two different fates. We needed a way to analyse gradual commitment to either fate, without knowing which cells were on which path.

We solved this problem using a mixture of overlapping Gaussian processes. A mixture model is a statistical way to formalize the cell fate assignment problem described above.

Machine learning algorithms can be used to infer the most likely groupings of cells into the components of the mixture. After fitting the mixture model to assign cells to fates, we could investigate how each individual gene related to the fates.

This was the final key to uncovering transcriptional programs for the fate choice. This recapitulated the known Tfh markers Bcl6 and Cxcr5, but in particular let us associate the maintenance of Tcf7 with the Tfh fate.

The mixture model identified the Tcf7 antagonist Id2 as the main transcription factor associated with the Th1 fate, along with many known Th1 genes.

The peak times of dynamic genes could be linked to when cells started committing to fates. This identified receptors which were compatible with signaling molecules expressed by the monocytes we had collected in parallel.

We confirmed that mice with reduced numbers of monocytes produced smaller fractions of Th1 cells. Mice with reduced number of B cells on the other hand produce smaller fractions of Tfh cells.

It was possible that T helper cells driven to either fate by the communicating cells had already been primed to respond to only these cells.

Using the T cell receptor sequence in the T helper cells as a natural clonal barcode, we found that both Th1 and Tfh cells shared sequences, and must have originated from common naive progenitors.

In summary our data indicate that in malaria activated T helper cells start expressing Tcf7. After proliferation rate acceleration the cells express receptors which receive signals from monocytes or B cells.

Cells receiving B cell signals maintain Tcf7 expression and become Tfh cells, while cells receiving monocyte signals replace Tcf7 expression with Id2 expression and become Th1 cells.

Biology is entering a new era with the rich measurements from single cell RNA sequencing. It allows us to use machine learning to ask explicit questions about the data.

The power is particularly clear from the joint cellular and molecular perspective. Going forward I hope for more developments that allow us to ask and answer questions from this perspective, and more opportunities for methods like the overlapping mixture of Gaussian processes that can link the two.

This post was originally an essay I submitted for a competition on work done in the field of genomics during PhD. In the last few months a number of interesting brain single cell datasets have been published.

The new promising STARmap method was pusblished by Wang et al in Science using mouse brain data as example applications. Even more recently, two back to back mouse brain atlases were published in Cell.

Zeisel et al characeterized the nervous system of adolescent mice through sequencing over , cells from 19 different regions using the 10X Genomics Chromium technology.

Saunders et al studied adult mouse brain using almost , cells from 9 regions of the brain using the Drop-seq method.

All three papers contain some data from the frontal cortex region. An interesting exercise is to see how these datasets relate to one another, and if they can be analysed as a single entity.

The Wang et al STARmap data measures a panel of genes in the medial prefrontal cortex mPFC , across 3, cells from three separate biological samples.

The STARmap data does not have any clusters annotated, but they do have spatial locations in the tissue preserved! The data from Saunders et al and Zeisel et al are transcriptome wide, so much larger.

But it would be interesting to see how well the small panel of STARmap genes would work to integrate and analyse these datasets.

The anterior cortex data from Zeisel et al consists of 14, cells with annotations for 53 clusters though some of these seem to be enteric neurons which is a bit odd?

The frontal cortex dataset from Saunders et al has over 70, cells annotated with 62 clusters. For the sake of simplicity, here I randomly sampled 15, cells from the Saunders data.

When the datasets are combined we get an expression matrix with 32, cells with counts in genes. To analyze the data together I use scVI an autoencoder based method that have been working well in my current research work.

Technology specific effects can be accounted for by providing them as batches. Because we are looking at very few genes here, running inference on the scVI model takes about 10 minutes for epochs.

The scVI model then gives you access to a low-dimensional 10 dimensional in this case latent representation space which can be used to generate counts for all genes consistent with the structure in the original data.

The main point with this is that many machine learning and statistical methods that have problems with count data. Once the scVI model is fitted, it is a good idea to create a tSNE of the latent space, and color the cells by various known factors to try to figure out what might contribute to variation in the data.

We see that similar patterns of densities overlap for all the datasets. Of course we need to remind ourselves not to read too much into the tSNE representation; the important part is the dimensional latent representation of the data.

We can note that on the larger annotated scale annotation from the Zeisel and Saunders we can see overlap between related terms in the tSNE!

Immune cells close to immune cells, neurons close to neurons, etc. We can also color the cells by the complete cluster annoation.

But with so many clusters it becomes hard to tell the colors apart! And here I even collapsed some of the Saunders et al cluster names so they would fit in the plot.

To learn about how the different annotations in the different datasets relate to each other we can use Ward linkage on the cell group centers to create a common dendrogram for all the groups.

Because of the design of the latent space, we can simply use Euclidean distances. First we look at the broad cell classes from both the annotated datasets.

From the dendrogram it is clear that the class annotations are consistent between the datasets, as we observed in tSNE above. We turn then to looking at all annotated clusters in the frontal cortex data from the two publications.

This dendrogram is on the larger side, bu the text is stil legible. While it seems pretty consistant within a given dataset, the mixing does not seem completely right.

For example neurons in the Saunders et al data are mixed with oligodendrocytes from the Zeisel et l data. This is not necessarily terrible, we are only working with genes from the STARmap panel, the original studies used thousands of genes to define the cell types.

The STARmap cells do not come with cell type annoations. They do however come with spatial locations for every cell!

We can try to link the spatial locations in the STARmap data with the cell type annotion in the othe data sets.

Here however we will just do something simple to see how it works out. Since Euclidean distances are meaningful in the latent d space, we can use a kNN classifier using clusters or classes as targets.

Now we can plot the spatial locations of the STARmap cells, but annotate the cells with predicted clusters from the scRNA-seq datasets.

This way we can qualitatively evaluate whether the clusters are consistent with spatial structure in the brain.

In these plots above, each "stripe" consists of different biological samples, and it wouldn't make sense to plot the cells from different biological samples in a single plane.

I think they are even from different mice. From this it seems that prediction to the annotation from Saunders et al seem more spatially organized in the STARmap data.

I might have misunderstood how the cell clusters are indexed in the Loom files for cortex. There is also an odd thing where the website says there are 7, anterior cortex cells, but the Loom file contains 15, A notebook with all analysis, including fitting the scVI model, is available here.

A while after the invention of the microscope, scientists started applying various chemical dyes when looking at biological samples in the form of tissues from diseased organs.

This revealed anatomical structures on the microscopic scale in many plant and animal tissues, birthing the field of histology.

Microscopy of stained tissue is still an enormously important field, and histopathologists have devised metrics for diagnosing many types of conditions and diseases based on patterns of cells in stained tissues.

Since the original studies of brain microanatomy in the late 19th century we have figured out that the functions and phenotypes of cells including neurons are determined by regulation of gene expression programs.

Many histological assays are now defined by examining particular gene products examined using immunohistochemical assays. Researchers are now making extremely rich molecular measurements with preserved spatial coordinates in tissues.

At the same time as genome wide measurement are being miniaturized into technologies that preserve spatial location in tissues , technologies for counting individual mRNA molecules in cells using imaging are being increasingly parallelized.

We are reaching a point where these two approaches to spatial gene expression analysis are converging to similarly rich assays, with the ability to look at thousands of gene products in thousands of individual cells in tissues.

The function of regions of tissues will in many cases be determined by sets of co-expressed genes. This means there is a coupling between spatial locality of function and particular sets of genes.

The automatic expression histology AEH model which we published in Nature Methods earlier this year attempts to explicitly model this coupling through a probabilistic model:.

The last two lines though specify that means in the GMM should be generated from smooth spatial functions, thus giving the form of a mixture of Gaussian processes.

Modeling the spatial functions with Gaussian processes means you do not need to know what they look like, we just assume they are somewhat smooth.

In this model the expression levels of genes are governed by underlying shared spatial functions. In our paper we applied it to breast cancer tissue and found a set of immune genes spatially co-expressed in a region of tumor infiltration.

We also applied it to mouse olfactory bulb data and got a clear picture of the layer structure of the organ. As well as spatial organization of cell types in a small region of mouse hippocampus.

As a new example here, we can apply the method to an extremely interesting recent dataset that was produced using the novel STARmap technology.

First we run the SpatialDE significance test , and find that of the genes significantly depend on spatial locations of the cells in the tissue.

To perform AEH , we use these genes and set the characteristic length scale in the tissue. Setting these parameters is not trivial, and here we are a bit helped by domain knowledge.

Approximately annotating the image by matching it with the figure in the STARmap paper, we see that the patterns learned by AEH match up with the classical layers of the cortex.

While we used the number of layers when running AEH, no information about the structure of them were provided to the model.

The layer structure that was originally observed by the morphology of stained cells was now automatically identified by the molecular measurements.

Compared to other spatial data this dataset is on the larger side, measuring locations, but even so AEH converges in a reasonable time.

Of course the data sets will get larger, but seeing these technologies spread to more research labs is going to be very interesting.

The same way many cell types have been discovered by single cell RNA sequencing, many new microanatomical structures will be discovered in many organs using these spatial gene expression methods.

This post will describe what they do and why it is exciting, and demonstrate the results of running them on three recent datasets.

In almost all cases, to do anything useful in scRNA-seq the tens of thousands of genes measured need to be summarised and simplified.

An extremely effective way to summarise many variables through their covariance structure is principal component analysis PCA.

However, scRNA-seq data consists of counts, which have particular behaviours that cause issues with the interpretation and of PCA.

Potential ways of dealing with this is either figuring out how to transform count data to emulate the characteristics of continuous Gaussian data, or to reformulate PCA for the count setting.

Omitting some further features, in this model underlying rates of observations of mRNA molecules from specific genes are modelled by a low-dimensional collection of continuous factors.

Every cell has a particular hidden value for these factors, and to fit the model all cells are investigated and assigned the most likely factor values.

In these equations, red color indicates parameters that need to be inferred. With these ZINB based methods, the data does not need to be scaled, nor normalised, and in principle the common step of selecting highly variable genes is not necessary.

The data just plugs in. The inference will need to be rerun with the entire dataset including this new cell. Two new methods, called scVI single cell variational inference and DCA deep count autoencoder rethinks this model, by moving from factor analysis to an autoencoder framework using the same ZINB count distribution.

Their titles and abstracts phrase them as imputation methods, which is a bit odd and substantially undersell them! The two methods have slightly different parameterizations, but conceptually abusing notation a bit , this represents with they both do:.

This unlocks a lot of benefits. For inference, this setup makes it easier to use stochastic optimization, and is directly compatible with inference on mini-batches: you only need to look at a few cells at a time, so no matter how many cells you have, you will not run out of memory.

Scientifically, this allows you to generalize. To illustrate what the methods do, we will apply them to three recent datasets.

One from Rosenberg et al , where I randomly sampled 3, out of , developing mouse brain cells. The second one is a taxon of Peripheral sensory neurons from mousebrain.

To qualitatively inspect the results I ran tSNE on the representations, and colored the cells based on labels provided from the data sources.

The DCA method is implemented around the anndata Python package , and is very easy to run on any data you have. The scVI implementation requires you to manually wrangle your data into TensorFlow tensors with correct data types, which can be frustrating if you are not used to it.

This does however imply that if you want to scale the inference using out-of-core strategies, scVI directly supports that. The scVI method has the option to account for discrete nuisance variables batch effects , but I did not try this.

And even without it, it seems to align the two mice quite well in the Lukassen data! I am curious if there is a way to also account for continuous nuisance parameters e.

Notebooks where I ran the methods on the different datasets are available here. The other day SpatialDE , our statistical test for spatially variable genes in spatial transcriptomics data was published in Nature Methods.

As a demonstration of how to use SpatialDE I also analysed some recent heart tissue. The underlying principle in SpatialDE can be hard to get to grips with, and the aim of this post is to provide an example that hopefully explains it.

One very practical reason it can be hard to see what is going on is that it is generally difficult to make plots to visualize data in more than 2 dimensions so that noise is easily interpreted.

In terms of spatial gene expression, it is then easiest to make an example with a 1-dimensional tissue, and illustrate things that way. There is actually a spatial transcriptomics dataset which is in fact 1-dimensional!

Without pre-specifying the shapes of gene expression we need a way to express properties of how genes could behave across the coordinates. An effective way to look at this is to consider spatial coordinates as locally informative.

If you know expression in a coordinate, then nearby coordinates should be pretty similar, while coordinates further away are still somewhat similar.

In other words, genes may be expressed in or close to the head while not expressed at all in the tail, or vice versa.

The right side of the plot shows a couple of expression curves drawn from a multivariate normal distribution with this covariance matrix. Models like this where the covariance between points are parameterized are known as Gaussian processes.

The curves above are random draws, but have you ever seen data that looks so clean? More likely there is additional noise which we cannot explain by only considering the spatial covariance between zebrafish slices.

This is a number between 0 and 1 which indicate how much of the variance in data is due to spatial covariance.

To illustrate, we can randomly simulate data with different levels of FSV. The simulated data in the panels have the same variance.

But we can see that the spatial contribution to the variance decreases as the FSV decreases. This way it is possible to distinguish between genes with high variance and genes with high spatial variance.

This dataset had 95 samples of 20, genes, and the SpatialDE test took about 5 minutes to run. As an illustration, let us look at the expression patterns of a number of genes identified with different FSVs in the zebrafish embryo.

We can look at the relation between total variance and spatial variance, and how the FSVs are distributed compared to these.

On the right side the standard plot from SpatialDE illustrates the relation between the FSV and the statistical significance for all genes. I put in references to the genes I used as examples, as well as some genes that were highlighted by Junker et al in the original paper.

If you have spatial gene expression data, I recommend trying SpatialDE to identify genes of interest. The analysis associated with this post is available in a notebook here.

If you want to use SpatialDE for your spatial data, you can install it by pip install spatialde. Thanks to Lynn Yi for editorial feedback on this post.

The general idea is that if there is not differential expression between clusters, they should be merged. This is a good idea, and putting criteria like this highlights expectations of what we mean by clusters, and may in the future direct explicit clustering models that incorporate these.

The workflow Jean presents is similar to how I have been looking at these things recently, and the post inspired me to 1 write down my typical workflow for cell types or clusters, and 2 put my code in Python modules rather than copy-pasting it between Notebooks whenever there's new data to look at.

Of course in this post I'll be making commands and images much more stylized than they would typically be, but the concept is representative.

To assess whether an approach is reasonable, it is good to make some simulations of the ideal case. To simulate cells from different cell types, I make use of 1 a theory that cell types are defined by "pathways" of genes, and 2 observations from interpreting principal component analysis from many datasets.

These indicate that to produce a transcriptional cell type, a small number of genes are upregulated and covary among each other. With this in mind, simulation is done by, for each cell type, creating a multivarate normal distribution for each cell type, which have increased mean and covariance for a defining "module" of genes.

The process is repeated for each cell type, leaving a number of genes as inactive background. In this particular case I simulate 10 cluster spread over 1, cells, with 20 active marker gene per cluster, and finally add "unused" genes.

Here a tSNE plot is used as a handy way to look at all the cells at once. The most unrealistic part of this simulation is probably the uniform distribution of cell numbers per cell type.

In real data this is very uncommon. To cluster cells it is pretty effective to work in the space of a number or principal components. I like to use Bayesian Gaussian mixture models to group cells into clusters in this space.

First I will cluster with an overly large number of clusters. In this tSNE plot each color correspond to a cluster. As Jean points out, for a cluster to be useful in followup experiments we must be able to define it with a small number of genes.

That is, there should be some genes which will allow us to predict whether a particular cell belongs to the cell type or not. For many this is a bit reductionist, and t is not impossible functional cell types are defined by hugely complex nonlinear interactions of hundreds of genes.

But in practice, we wouldn't know what to do with such cell types. The definition of an actionable cell type being one we can predict leads to predictive models.

In particular regularised logistic regression is good for this. By controlling the regularisation so that each cluster has a "marker budget" of only a handful genes, we can ensure that a few markers can predict the types.

ROC curves from the predicted assignment probabilites in logistic regression is a practical way to assess whether we are able to predict the cell types correctly.

The printed numbers in the training command are the number of positive markers for each cell type. I interactively change the sparsity parameter to keep these numbers generally low.

In this regard this is all quite supervised and subjective, and far from automated. The colors of the curves here correspond to clusters.

A number of the clusters are relatively close to the unit line, indicating that we have a hard time predicting these, and they will not end up being actionable.

So we decrease the K and try again. We iterate this procedure until we are happy with the predictability of the clusters. Here I have also plotted cases of "under clustering" the data.

The larger clusters are still pretty predictice, but we would want to maximize the number of clusters which would be experimentally actionable.

To visualise how these weight relate the expression of cells with different cluster annotations, we can plot a "marker map", which sorts cells by cluster, and plots the top marker genes in corresponding order on the Y axis.

This is a very common plot in scRNA-seq cluster studies. We see that structure we simulated is largely recovered! The diagonal blocks indicate genes which predict the cell types.

Now we try this strategy on real data. In particular, we are using one of the batches of bone marrow data from the recently published Mouse Cell Atlas.

This batch has 5, cells and expression values for 16, genes. For the sake of speeding up the analysis a little I randomly sample 3, of the cells.

Now we perform the same procedure of training GMM's and attempting to predict held out data with logistic regression.

At 7 clusters I stop, here the clusters are very easy predict. Again we can create the marker map. Obviosuly this is a lot noisier than the simulated data.

Another thing we notice is that the number of cells per cluster is much less even than for the simulated data. This will cause some issues with interpreting the ROC curves, but in practice we want to try to have some minimal size for clusters in order to keep them reliable.

I find this workflow fairly straightforward and quick to work around. There are some clear drawbacks of course: tt is quite manual, and we are not quantifying the uncertainty of these predictive weights, so we can't do proper statistics.

Notebooks for this post are available here. In a previous post I wrote about the Poisson distribution seeming like a good error model for scRNA-seq counts.

This suggests using GLM with Poisson likelihood to analyse your data, as long as the offset due to count depth variation is taken into consideration.

An alternative strategy could be to transform the counts to roughly normal, and perform analysis in that setting.

This is effectively what the vast majority of studies do for unsupervised analysis: counts are transformed, then PCA is used to find a low-dimensional representation for further analysis such as clustering.

What if we try to adjust for the count depth variation in a supervised setting assuming Gaussian noise? A huge benefit of assuming Gaussian noise is that linear regression has an extremely efficient solution, usually referred to as OLS regression.

I don't recommend anyone use it for final analysis, indeed I called it "Naive DE" because it is a baseline.

Literally every other DE test will be better than it by design, in particular with regards to false positive P-values.

Well maybe not according to a recent study , the test in NaiveDE should be equivalent to the t-test. It is nevertheless convenient during exploratory analysis to iterate through models.

Alternative and null models are specified by Patsy formulas , and significance is calculated with a likelihood ratio test. A Bonferroni corrected version of the P-value is also reported.

For flexibility, intercept is optionally part of the design matrix. In the negative control 10X dataset from Svensson et al , the only variation in observed expression should in theory be due technical effects, in particular the count depth variation.

Here we are using 2, cells with 24, genes. Ideally the weights for the log counts should be found to be 1, and the intercept 0. In this plot np.

Each dot is a gene rather than droplet. The P-value comes from comparing the model with one that does not consider the depth.

The marjority of genes are found to have gene count weights much smaller than 1. It turns out that lowly abundant genes will have delfated total count slopes.

From this, it is clear that increased observations on the low count values, in particular 0, are responsible for decrease in the total count weight.

Now let us investigate how this count depth effect plays in to a differential expression analysis. With all published large scale experiments cataloging cell types, it is getting increasingly easy to simply fetch some data and do quick comparisons.

We will use data from the recent single cell Mouse Cell Atlas To get something easy to compare, we use the samples called "Brain" and focus on the cells annotated as "Microglia" and "Astrocyte".

On average they have about total UMI counts each, so while the entire study is a pretty large scale, the individual cell types and cells are on a relatively small scale.

The final table has cells and 21, genes. In a differential expression test you simply include a covariate in the design matrix that informs the linear model about the different conditions you want to compare.

Here we are comparing microglia and astrocytes. Similar to above, we can look at the relation between count depth and observed counts for a few genes, but we can also make sure to plot the stratifiction into the two cell types and how the regression models are predicting the counts.

Again we can see the overall abundance is related to the slope of the lines. Another thing which seem to pop out in these plots is an interaction between cell type and slope.

For example looking at C1qa the slope for the microglia seem underestimated. Fuck Tube Club Mature Videos Porn Granny Porn Videos Hot Fuck Films Xhamster Fuck Milf Porn Anal Sex Tube Free Wife Porn Indian Porn Videos Japan Xxx Movies Fetish Xxx Tube Xxx Fuck Sex Mommy Porn Videos Erotic Sex Videos Mobile Tube Xxx Bhabhi Porn Free Hd Porn Free Latina Porn Free Xxx Vids Mature Mom Fucker Hard Categories Japan Hd Porn Plumper Porn Movies Lesbian Mature Porn Anal Porn Tube Hot Mom Porn Free Asian Porn Free Anal Porn Bbw Tube Sex Xxx Tube List Sex Tube Videos Free Adult Amateur Porn Free Tube Private Sex Arion Porn Movies Sex Tube Star Sex Traces Sex Only Tube Porn Tasty Xxx Tube Porn Free Porn Videos Porn 4 Real New Sex TV It is Porn Hot Free Tube Hot Big Tube Free Anal Tube Cum Comes Public Porn Videos Hq Sex Free Xxx Cam Best Xxx Porn Public Xxx Videos Xxx Sex Videos Milf Anal Fuck Beeg Porn Tube Beeg Tube Hardsextube Porn

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