We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with $d$ smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a parametrization exists, we provide an algorithm for finding it based on sparse non-linear regression in the manifold tangent bundle, bypassing more standard manifold learning algorithms. We also discuss conditions for the existence of such parameterizations in function space and for successful recovery from finite samples. We demonstrate our method with experimental results from a real scientific domain.

Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices. It consists of a novel normalization method followed by multitask basis pursuit. Applied to Jacobians of putative coordinate functions, it helps identity isometric embeddings from within interpretable dictionaries. We provide theoretical and experimental results justifying this method. For problems involving coordinate selection and diversification, it offers a synergistic alternative to greedy and brute force search.

The Allen Mouse Brain Connectivity Atlas consists of anterograde tracing experiments targeting diverse structures and classes of projecting neurons. Beyond regional anterograde tracing done in C57BL/6 wild-type mice, a large fraction of experiments are performed using transgenic Cre-lines. This allows access to cell-class-specific whole-brain connectivity information, with class defined by the transgenic lines. However, even though the number of experiments is large, it does not come close to covering all existing cell classes in every area where they exist. Here, we study how much we can fill in these gaps and estimate the cell-class-specific connectivity function given the simplifying assumptions that nearby voxels have smoothly varying projections, but that these projection tensors can change sharply depending on the region and class of the projecting cells. This paper describes the conversion of Cre-line tracer experiments into class-specific connectivity matrices representing the connection strengths between source and target structures. We introduce and validate a novel statistical model for creation of connectivity matrices. We extend the Nadaraya-Watson kernel learning method that we previously used to fill in spatial gaps to also fill in gaps in cell-class connectivity information. To do this, we construct a "cell-class space" based on class-specific averaged regionalized projections and combine smoothing in 3D space as well as in this abstract space to share information between similar neuron classes. Using this method, we construct a set of connectivity matrices using multiple levels of resolution at which discontinuities in connectivity are assumed. We show that the connectivities obtained from this model display expected cell-type- and structure-specific connectivities. We also show that the wild-type connectivity matrix can be factored using a sparse set of factors, and analyze the informativeness of this latent variable model.

Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned by the embedding algorithm are abstract, and finding their physical or domain-related meaning is not formalized and often left to domain experts. This paper studies the problem of recovering the meaning of the new low-dimensional representation in an automatic, principled fashion. We propose a method to explain embedding coordinates of a manifold as non-linear compositions of functions from a user-defined dictionary. We show that this problem can be set up as a sparse linear Group Lasso recovery problem, find sufficient recovery conditions, and demonstrate its effectiveness on data.

The biasing of dynamical simulations along collective variables uncovered by unsupervised learning has become a standard approach in analysis of molecular systems. However, despite parallels with reinforcement learning (RL), state of the art RL methods have yet to reach the molecular dynamics community. The interaction between un-supervised learning, dynamical simulations, and RL is therefore a promising area of research. We introduce a method for enhanced sampling that uses non-linear geometry estimated by an unsupervised learning algorithm in a reinforcement-learning enhanced sampler. We give theoretical background justifying this method, and show re-sults on data.

Abstract Ex vivo hematopoietic stem and progenitor cell (HSPC) expansion platforms are under active development, designed to increase HSPC numbers and thus engraftment ability of allogeneic cord blood grafts or autologous HSPCs for gene therapies. Murine and in vitro models have not correlated well with clinical outcomes of HSPC expansion, emphasizing the need for relevant pre-clinical models. Our rhesus macaque HSPC competitive autologous transplantation model utilizing genetically-barcoded HSPC allows direct analysis of the relative short and long-term engraftment ability of lentivirally-transduced HSPC, along with additional critical characteristics such as HSPC clonal diversity and lineage bias. We investigated the impact of ex-vivo expansion of macaque HSPCs on the engineered endothelial cell line (E-HUVEC) platform regarding safety, engraftment of transduced and E-HUVEC-expanded HSPC over time compared to non-expanded HSPC for up to 51 months post-transplantation, and both clonal diversity and lineage distribution of output from each engrafted cell source. Short and long-term engraftment were comparable for E-HUVEC expanded and the non-expanded HSPCs in both animals, despite extensive proliferation of CD34+ cells during 8 days of ex vivo culture for the E-HUVEC HSPCs, and optimization of harvesting and infusion of HSPCs co-cultured on E-HUVEC in the second animal. Long-term hematopoietic output from both E-HUVEC expanded and unexpanded HSPCs was highly polyclonal and multilineage. Overall, the comparable HSPC kinetics of macaques to humans, the ability to study post-transplant clonal patterns, and simultaneous multi-arm comparisons of grafts without the complication of interpreting allogeneic effects makes our model ideal to test ex vivo HSPC expansion platforms, particularly for gene therapy applications.

Clonal tracking methods provide quantitative insights into the cellular output of genetically labeled progenitor cells across time and cellular compartments. In the context of gene and cell therapies, clonal tracking methods have enabled the tracking of progenitor cell output both in humans receiving therapies and in corresponding animal models, providing valuable insight into lineage reconstitution, clonal dynamics and vector genotoxicity. However, the absence of a toolbox for analysis of clonal tracking data has precluded the development of standardized analytical frameworks within the field. Thus, we developed barcodetrackR, an R package and accompanying Shiny app containing diverse tools for the analysis and visualization of clonal tracking data. We demonstrate the utility of barcodetrackR in exploring longitudinal clonal patterns and lineage relationships in a number of clonal tracking studies of hematopoietic stem and progenitor cells (HSPCs) in humans receiving HSPC gene therapy and in animals receiving lentivirally transduced HSPC transplants or tumor cells.

Ex vivo hematopoietic stem and progenitor cell (HSPC) expansion platforms are under active development, designed to increase HSPC numbers and thus engraftment ability of allogeneic cord blood grafts or autologous HSPCs for gene therapies. Murine and in vitro models have not correlated well with clinical outcomes of HSPC expansion, emphasizing the need for relevant pre-clinical models. Our rhesus macaque HSPC competitive autologous transplantation model utilizing genetically barcoded HSPC allows direct analysis of the relative short and long-term engraftment ability of lentivirally transduced HSPCs, along with additional critical characteristics such as HSPC clonal diversity and lineage bias. We investigated the impact of ex vivo expansion of macaque HSPCs on the engineered endothelial cell line (E-HUVECs) platform regarding safety, engraftment of transduced and E-HUVEC-expanded HSPC over time compared to non-expanded HSPC for up to 51 months post-transplantation, and both clonal diversity and lineage distribution of output from each engrafted cell source. Short and long-term engraftment were comparable for E-HUVEC expanded and the non-expanded HSPCs in both animals, despite extensive proliferation of CD34(+) cells during 8 days of ex vivo culture for the E-HUVEC HSPCs, and optimization of harvesting and infusion of HSPCs cocultured on E-HUVEC in the second animal. Long-term hematopoietic output from both E-HUVEC expanded and unexpanded HSPCs was highly polyclonal and multilineage. Overall, the comparable HSPC kinetics of macaques to humans, the ability to study post-transplant clonal patterns, and simultaneous multi-arm comparisons of grafts without the complication of interpreting allogeneic effects makes our model ideal to test ex vivo HSPC expansion platforms, particularly for gene therapy applications.

ABSTRACT Clonal tracking methods provide quantitative insights into the cellular output of genetically labelled progenitor cells across time and cellular compartments. In the context of gene and cell therapies, clonal tracking methods have enabled the tracking of progenitor cell output both in humans receiving cellular therapies and in corresponding animal models, providing valuable insight into lineage reconstitution, clonal dynamics, and vector genotoxicity. However, the absence of a toolbox by which to interrogate these data has precluded the development of standardized analytical frameworks within the field. Thus, we developed barcodetrackR , an R package that provides users with tools for the analysis and visualization of clonal dynamics across time and cellular compartments in clonal tracking experiments. Here, we demonstrate the utility of barcodetrackR in exploring longitudinal clonal patterns and lineage relationships in the context of a number of clonal tracking studies of hematopoietic stem and progenitor cells (HSPCs) in humans receiving HSPC gene therapy and in animals receiving lentivirally transduced HSPC transplants.

Single-cell lineage tracking strategies enabled by recent experimental technologies have produced significant insights into cell fate decisions, but lack the quantitative framework necessary for rigorous statistical analysis of mechanistic models describing cell division and differentiation. In this paper, we develop such a framework with corresponding moment-based parameter estimation techniques for continuous-time, multi-type branching processes. Such processes provide a probabilistic model of how cells divide and differentiate, and we apply our method to study hematopoiesis, the mechanism of blood cell production. We derive closed-form expressions for higher moments in a general class of such models. These analytical results allow us to efficiently estimate parameters of much richer statistical models of hematopoiesis than those used in previous statistical studies. After validating the methodology in simulation studies, we apply our estimator to hematopoietic lineage tracking data from rhesus macaques. Our analysis provides a more complete understanding of cell fate decisions during hematopoiesis in non-human primates, which may be more relevant to human biology and clinical strategies than previous findings from murine studies. For example, in addition to previously estimated hematopoietic stem cell self-renewal rate, we are able to estimate fate decision probabilities and to compare structurally distinct models of hematopoiesis using cross validation. These estimates of fate decision probabilities and our model selection results should help biologists compare competing hypotheses about how progenitor cells differentiate. The methodology is transferrable to a large class of stochastic compartmental models and multi-type branching models, commonly used in studies of cancer progression, epidemiology, and many other fields.

Gene therapies using integrating retrovirus vectors to modify hematopoietic stem and progenitor cells have shown great promise for the treatment of immune system and hematologic diseases. However, activation of proto-oncogenes via insertional mutagenesis has resulted in the development of leukemia. We have utilized cellular bar coding to investigate the impact of different vector designs on the clonal behavior of hematopoietic stem and progenitor cells (HSPCs) during in vivo expansion, as a quantitative surrogate assay for genotoxicity in a non-human primate model with high relevance for human biology. We transplanted two rhesus macaques with autologous CD34+ HSPCs transduced with three lentiviral vectors containing different promoters and/or enhancers of a predicted range of genotoxicities, each containing a high-diversity barcode library that uniquely tags each individual transduced HSPC. Analysis of clonal output from thousands of individual HSPCs transduced with these barcoded vectors revealed sustained clonal diversity, with no progressive dominance of clones containing any of the three vectors for up to almost 3 years post-transplantation. Our data support a low genotoxic risk for lentivirus vectors in HSPCs, even those containing strong promoters and/or enhancers. Additionally, this flexible system can be used for the testing of future vector designs.

Understanding mechanisms of late/acquired cancer immunotherapy resistance is critical to improve outcomes; cellular immunotherapy trials offer a means to probe complex tumor–immune interfaces through defined T cell/antigen interactions. We treated two patients with metastatic Merkel cell carcinoma with autologous Merkel cell polyomavirus specific CD8+ T cells and immune-checkpoint inhibitors. In both cases, dramatic remissions were associated with dense infiltration of activated CD8+s into the regressing tumors. However, late relapses developed at 22 and 18 months, respectively. Here we report single cell RNA sequencing identified dynamic transcriptional suppression of the specific HLA genes presenting the targeted viral epitope in the resistant tumor as a consequence of intense CD8-mediated immunologic pressure; this is distinguished from genetic HLA-loss by its reversibility with drugs. Transcriptional suppression of Class I loci may underlie resistance to other immunotherapies, including checkpoint inhibitors, and have implications for the design of improved immunotherapy treatments.

Natural killer (NK) cells recognize and eliminate infected and malignant cells. Their life histories are poorly understood, particularly in humans, due to lack of informative models and endogenous clonal markers. Here, we apply transplantation of barcoded rhesus macaque hematopoietic cells to interrogate the landscape of NK cell production, expansion, and life histories at a clonal level long term and after proliferative challenge. We identify oligoclonal populations of rhesus CD56(-)CD16(+) NK cells that are characterized by marked expansions and contractions over time yet remained long-term clonally uncoupled from other hematopoietic lineages, including CD56(+)CD16(-) NK cells. Individual or groups of CD56(-)CD16(+) expanded clones segregated with surface expression of specific killer immunoglobulin-like receptors. These clonally distinct NK cell subpopulation patterns persisted for more than 4 years, including after transient in vivo anti-CD16-mediated depletion and subsequent regeneration. Profound and sustained interleukin-15-mediated depletion was required to generate new oligoclonal CD56(-)CD16(+) NK cells. Together, our results indicate that linear NK cell production from multipotent hematopoietic progenitors or less mature CD56(+)CD16(-) cells is negligible during homeostasis and moderate proliferative stress. In such settings, peripheral compartmentalized self-renewal can maintain the composition of distinct, differentiated NK cell subpopulations.

Manifold embedding algorithms map high dimensional data, down to coordinates in a much lower dimensional space. One of the aims of the dimension reduction is to find the {\em intrinsic coordinates} that describe the data manifold. However, the coordinates returned by the embedding algorithm are abstract coordinates. Finding their physical, domain related meaning is not formalized and left to the domain experts. This paper studies the problem of recovering the domain-specific meaning of the new low dimensional representation in a semi-automatic, principled fashion. We propose a method to explain embedding coordinates on a manifold as {\em non-linear} compositions of functions from a user-defined dictionary. We show that this problem can be set up as a sparse {\em linear Group Lasso} recovery problem, find sufficient recovery conditions, and demonstrate its effectiveness on data.

The geographic distribution of hematopoiesis at a clonal level is of interest in understanding how hematopoietic stem and progenitor cells (HSPCs) and their progeny interact with bone marrow (BM) niches during regeneration. We tagged rhesus macaque autologous HSPCs with genetic barcodes, allowing clonal tracking over time and space after transplantation. We found marked geographic segregation of CD34(+) HSPCs for at least 6 mo posttransplantation, followed by very gradual clonal mixing at different BM sites over subsequent months to years. Clonal mapping was used to document local production of granulocytes, monocytes, B cells, and CD56(+) natural killer (NK) cells. In contrast, CD16(+)CD56(-) NK cells were not produced in the BM, and in fact were clonally distinct from multipotent progenitors producing all other lineages. Most surprisingly, we documented local BM production of CD3(+) T cells early after transplantation, using both clonal mapping and intravascular versus tissue-resident T cell staining, suggesting a thymus-independent T cell developmental pathway operating during BM regeneration, perhaps before thymic recovery.

Autologous transplantation of hematopoietic stem and progenitor cells lentivirally labeled with unique oligonucleotide barcodes flanked by sequencing primer targets enables quantitative assessment of the self-renewal and differentiation patterns of these cells in a myeloablative rhesus macaque model. Compared with other approaches to clonal tracking, this approach is highly quantitative and reproducible. We documented stable multipotent long-term hematopoietic clonal output of monocytes, granulocytes, B cells, and T cells from a polyclonal pool of hematopoietic stem and progenitor cells in 4 macaques observed for up to 49 months posttransplantation. A broad range of clonal behaviors characterized by contribution level and biases toward certain cell types were extremely stable over time. Correlations between granulocyte and monocyte clonalities were greatest, followed by correlations between these cell types and B cells. We also detected quantitative expansion of T cell-biased clones consistent with an adaptive immune response. In contrast to recent data from a nonquantitative murine model, there was little evidence for clonal succession after initial hematopoietic reconstitution. These findings have important implications for human hematopoiesis, given the similarities between macaque and human physiologies.

Natural killer (NK) cells are defined as lymphocytes capable of target cell killing and cytokine production independent of somatic antigen receptor recombination. Challenging the paradigm of continuous production of non-specific cytotoxic NK cells from undifferentiated precursors, a subset of murine NK cells sharing many properties with cytotoxic effector T cells was shown to specifically respond to a viral infection, resulting in expansion and protective immunity upon adoptive transfer, uncovering unexpected "adaptive" capabilities for NK cells. In humans, CD56dimCD16+ NK cells expressing NKG2C and variegated patterns of KIR are associated with Cytomegalovirus (CMV) infection, and may represent human analogs of murine adaptive NK cells. In contrast to CD56bright and canonical CD56dim NK cells, we recently showed that human adaptive NK cells lack expression of specific signaling proteins and transcription factors, and epigenetically resemble CD8+ effector T cells, suggesting shared pathogen-driven developmental pathways (Schulms et al, 2015). NK cell heterogeneity, ontogeny, and mechanisms sustaining NK cell memory are poorly understood, particularly in humans, because in contrast to adaptive T and B cells, clonal tracking of NK cells based on receptor gene structure is not possible. We applied autologous transplantation of genetically barcoded CD34+ rhesus macaque hematopoietic stem and progenitor cells (HSPC) to interrogate the landscape of NK cell production and expansion at a clonal level. We followed 3 monkeys for up to 4 years post-transplantation, and observed a distinct clonal ontogeny for CD56-CD16+ (corresponding to human CD56dimCD16+ NK) versus CD56+CD16- rhesus NK cells. CD56-CD16+ NK were oligoclonal, and dominated by small numbers of highly biased clones, a pattern showing little overlap with highly polyclonal multipotent contributions to T, B, myeloid and CD56+CD16- NK cell lineages. There were clear expansions and contractions of groups of these highly biased CD56-CD16+ NK cell clones over time, with individual clones contributing up to 20% to this lineage, similar to patterns of waxing and waning T cell clones, suggesting responses of both cell types to extrinsic cues such as viruses. In contrast, all other lineages, including CD56+CD16- NK cells, were characterized by very stable contributions from long-term engrafting multipotent HSPC clones over time. The highly biased, greatly expanded, and waxing and waning CD56-CD16+ NK cell clones were specifically enriched in a subpopulation of CD56+CD16- NK with high KIR and low SYK expression,and decreased methylation at IFNG the CNS1 locus, analogous to human CMV-associated adaptive NK cells. This population of cells was increased in CMV+ compared to CMV- macaques; our transplanted macaques were CMV+. Canonical CD56+CD16- NK cells, lacking an adaptive phenotype, had clonal patterns similar to CD56+CD16- NK cells. We profoundly depleted CD56-CD16+ NK cells with an anti-CD16 antibody, and observed rapid regeneration of the same CD56-CD16+ NK clonal pattern, without recruitment of contributions from multipotent HSPC via CD56+CD16- putative precursor NK cells. There was a marked increase in cycling of CD56-CD16dim NK cells just prior to reappearance of CD56-CD16bright NK cells, and no change in cycling of CD56+CD16- cells. Thus, adaptive NK cell clones, both at steady state and under regenerative stress do not appear to require ongoing production from HSPC via CD56+CD16- precursors. These results suggest that adaptive NK cells or their immediate precursors have acquired self-renewal properties and high proliferative potential, with clonal restriction potentially based selection and expansion of cells with specific, epigenetically-controlled receptor expression able to interact with external stimuli such as viruses. In conclusion, via tracking of individual NK cell clonal histories in rhesus macaques, we provide the first direct evidence for persistence of adaptive NK cell clones in any species, offering potential insights into the acquisition of NK cell memory.

The classical model of hematopoiesis states that differentiation proceeds from hematopoietic stem cells (HSC) to mature blood cells via specified multipotent and bipotent progenitors, such as the common myeloid progenitor (CMP), common lymphoid progenitor (CLP), erythrocyte-megakaryoctye progenitor and granulocyte-monocyte progenitor. However, recent studies question this assumption and suggest that these intermediates are neither required nor prevalent. As an example, analyses of binarized data from murine barcoding experiments (Perie et al, Cell Reports, 2014) raise the possibility that hematopoiesis progresses via a random loss of potentials rather than discrete steps. Additionally, Notta et al (Science, 2015) showed that oligopotent progenitor cells form only a negligible component in the hierarchy by studying the distribution of progenitors in human marrow, leading them to infer that HSC and earliest multipotent progenitors differentiate directly into unipotent cells. Although these data challenge fundamental beliefs, the quantitative contributions of HSC and progenitors to cell lineages could not be tracked in individual mice or persons over time.