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Recent advances in multiplexed single-cell transcriptomics experiments facilitate the high-throughput study of drug and genetic perturbations. However, an exhaustive exploration of the combinatorial perturbation space is experimentally unfeasible. Therefore, computational methods are needed to predict, interpret, and prioritize perturbations. Here, we present the compositional perturbation autoencoder (CPA), which combines the interpretability of linear models with the flexibility of deep-learning approaches for single-cell response modeling. CPA learns to in silico predict transcriptional perturbation response at the single-cell level for unseen dosages, cell types, time points, and species. Using newly generated single-cell drug combination data, we validate that CPA can predict unseen drug combinations while outperforming baseline models. Additionally, the architecture's modularity enables incorporating the chemical representation of the drugs, allowing the prediction of cellular response to completely unseen drugs. Furthermore, CPA is also applicable to genetic combinatorial screens. We demonstrate this by imputing in silico 5,329 missing combinations (97.6% of all possibilities) in a single-cell Perturb-seq experiment with diverse genetic interactions. We envision CPA will facilitate efficient experimental design and hypothesis generation by enabling in silico response prediction at the single-cell level and thus accelerate therapeutic applications using single-cell technologies.

Motivation While generative models have shown great success in sampling high-dimensional samples conditional on low-dimensional descriptors (stroke thickness in MNIST, hair color in CelebA, speaker identity in WaveNet), their generation out-of-distribution poses fundamental problems due to the difficulty of learning compact joint distribution across conditions. The canonical example of the conditional variational autoencoder (CVAE), for instance, does not explicitly relate conditions during training and, hence, has no explicit incentive of learning such a compact representation. Results We overcome the limitation of the CVAE by matching distributions across conditions using maximum mean discrepancy in the decoder layer that follows the bottleneck. This introduces a strong regularization both for reconstructing samples within the same condition and for transforming samples across conditions, resulting in much improved generalization. As this amount to solving a style-transfer problem, we refer to the model as transfer VAE (trVAE). Benchmarking trVAE on high-dimensional image and single-cell RNA-seq, we demonstrate higher robustness and higher accuracy than existing approaches. We also show qualitatively improved predictions by tackling previously problematic minority classes and multiple conditions in the context of cellular perturbation response to treatment and disease based on high-dimensional single-cell gene expression data. For generic tasks, we improve Pearson correlations of high-dimensional estimated means and variances with their ground truths from 0.89 to 0.97 and 0.75 to 0.87, respectively. We further demonstrate that trVAE learns cell-type-specific responses after perturbation and improves the prediction of most cell-type-specific genes by 65%. Availability and implementation The trVAE implementation is available via github.com/theislab/trvae. The results of this article can be reproduced via github.com/theislab/trvae_reproducibility. [ABSTRACT FROM AUTHOR]

Motivation: The identification of heterogeneities in cell populations by utilizing single-cell technologies such as single-cell RNA-Seq, enables inference of cellular development and lineage trees. Several methods have been proposed for such inference from high-dimensional single-cell data. They typically assign each cell to a branch in a differentiation trajectory. However, they commonly assume specific geometries such as tree-like developmental hierarchies and lack statistically sound methods to decide on the number of branching events. Results: We present K-Branches, a solution to the above problem by locally fitting half-lines to single-cell data, introducing a clustering algorithm similar to K-Means. These halflines are proxies for branches in the differentiation trajectory of cells. We propose a modified version of the GAP statistic for model selection, in order to decide on the number of lines that best describe the data locally. In this manner, we identify the location and number of subgroups of cells that are associated with branching events and full differentiation, respectively. We evaluate the performance of our method on single-cell RNA-Seq data describing the differentiation of myeloid progenitors during hematopoiesis, single-cell qPCR data of mouse blastocyst development, single-cell qPCR data of human myeloid monocytic leukemia and artificial data. [ABSTRACT FROM AUTHOR]

We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of T = 0 many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor ~1/6. We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time-evolution algorithm that instead of the group operator e-iHt only involves the action of the generator H. For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within the dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from H than time evolution algorithms when fixing a given amount of created entanglement. [ABSTRACT FROM AUTHOR]

We solve nonequilibrium dynamical mean-field theory (DMFT) using matrix product states (MPS). This allows us to treat much larger bath sizes and by that reach substantially longer times (factor ∼2–3) than with exact diagonalization. We show that the star geometry of the underlying impurity problem can have substantially better entanglement properties than the previously favored chain geometry. This has immense consequences for the efficiency of an MPS-based description of general impurity problems: in the case of equilibrium DMFT, it leads to an orders-of-magnitude speedup. We introduce an approximation for the two-time hybridization function that uses time-translational invariance, which can be observed after a certain relaxation time after a quench to a time-independent Hamiltonian. [ABSTRACT FROM AUTHOR]

We compute the spectral functions for the two-site dynamical cluster theory and for the two-orbital dynamical mean-field theory in the density-matrix renormalization group (DMRG) framework using Chebyshev expansions represented with matrix product states (MPS). We obtain quantitatively precise results at modest computational effort through technical improvements regarding the truncation scheme and the Chebyshev rescaling procedure. We furthermore establish the relation of the Chebyshev iteration to real-time evolution and discuss technical aspects as computation time and implementation in detail. [ABSTRACT FROM AUTHOR]

A quantum many-body system that is prepared in the ground state of an integrable Hamiltonian does not directly thermalize after a sudden small parameter quench away from integrability. Rather, it will be trapped in a prethermalized state and can thermalize only at a later stage. We discuss several examples for which this prethermalized state shares some properties with the nonthermal steady state that emerges in the corresponding integrable system. These examples support the notion that nonthermal steady states in integrable systems may be viewed as prethermalized states that never decay further. Furthermore, we show that prethermalization plateaus are under certain conditions correctly predicted by generalized Gibbs ensembles, which are the appropriate extension of standard statistical mechanics in the presence of many constants of motion. This establishes that the relaxation behaviors of integrable and nearly integrable systems are continuously connected and described by the same statistical theory. [ABSTRACT FROM AUTHOR]

Many numerical techniques for the description of quantum systems that are coupled to a continuous bath require the discretization of the latter. To this end, a wealth of methods has been developed in the literature, which we classify as (i) direct discretization, (ii) orthogonal polynomial, and (iii) numerical optimization strategies. We recapitulate strategies (i) and (ii) to clarify their relation. For quadratic Hamiltonians, we show that (ii) is the best strategy in the sense that it gives the numerically exact time evolution up to a maximum time tmax, for which we give a simple expression. For nonquadratic Hamiltonians, we show that no such best strategy exists. We present numerical examples relevant to open quantum systems and strongly correlated systems, as treated by dynamical mean-field theory (DMFT). [ABSTRACT FROM AUTHOR]

The temporal order of differentiating cells is intrinsically encoded in their single-cell expression profiles. We describe an efficient way to robustly estimate this order according to diffusion pseudotime (DPT), which measures transitions between cells using diffusion-like random walks. Our DPT software implementations make it possible to reconstruct the developmental progression of cells and identify transient or metastable states, branching decisions and differentiation endpoints.