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Temporal dynamics of gene expression inform cellular and molecular perturbations associated with disease development and evolution. Given the complexity of high-dimensional temporal genomic data, an analytic framework guided by a robust theory is needed to interpret time-sequential changes and to predict system dynamics. Here we model temporal dynamics of the transcriptome of peripheral blood mononuclear cells in a two-dimensional state-space representing states of health and leukemia using time-sequential bulk RNA-seq data from a murine model of acute myeloid leukemia (AML). The state-transition model identified critical points that accurately predict AML development and identifies stepwise transcriptomic perturbations that drive leukemia progression. The geometry of the transcriptome state-space provided a biological interpretation of gene dynamics, aligned gene signals that are not synchronized in time across mice, and allowed quantification of gene and pathway contributions to leukemia development. Our state-transition model synthesizes information from multiple cell types in the peripheral blood and identifies critical points in the transition from health to leukemia to guide interpretation of changes in the transcriptome as a whole to predict disease progression.Significance:These findings apply the theory of state transitions to model the initiation and development of acute myeloid leukemia, identifying transcriptomic perturbations that accurately predict time to disease development.See related commentary by Kuijjer, p. 3072

Table S1. Differentially expressed genes for c_1 vs c_1^* Table S2. Differentially expressed genes for c_2 vs c_1^* Table S3. Differentially expressed genes for c_3 vs c_1^* Table S4. Differentially expressed genes for c_2 vs c_1 Table S5. Differentially expressed genes for c_3 vs c_1 Table S6. Differentially expressed genes for c_3 vs c_2 Tables S7-S10. Differentially expressed genes for early, transition, persistent, and leukemia events. Tables S11-S14. GO terms enriched for early, transition, persistent, and leukemia events. Table S15. Top 1% of eigengenes.

Figure S1. Details of animal model and fusion gene CM, Figure S2. Ex vivo flow cytometry analysis of bone marrow, Figure S3. Details of principal component analysis, Figure S4. Comparison of state-space construction with different dimension reduction methods, Figure S5. Hierarchical clustering of time-series RNA-seq data and relation to state-space, Figure S6. Details of critical point estimation, construction of quasi-potential, and state-space dynamics, Figure S7. Correlation of state-space geometry with Kit and CM gene expression. Sensitivity of state-space geometry to inclusion of Kit and CM, Figure S8. Volcano plots of critical-point based differential gene expression analysis, Figure S9. Heatmaps of selected GO pathways in early, transition, persistent, and leukemic events, Figure S10. Computation of eigengene angle in state-space, Figure S11. Details of principal component analysis of validation cohorts and state-space dynamics, Figure S12. Mean-squared displacement analysis of particle trajectories in state-space and calibration of Fokker-Planck diffusion coefficient with training cohort, Figure S13. Sensitivity analysis of state-space construction to sample and normalization thresholds, Figure S14. Bootstrap cross validation of state-space construction.

In this supplement we provide additional data and methods to support our results. In particular, we show: details of our mouse model of AML; demonstrate the robustness of our state-space construction to normalization methods and gene selection criteria; compare dimension reduction methods; show bootstrap cross-validation of our predictions; compare hierarchical clustering with our state-space approach; and finally, provide full lists of differentially expressed genes and gene ontology (GO) term enrichment.

MiR-126 and miR-155 are key microRNAs (miRNAs) that regulate, respectively, hematopoietic cell quiescence and proliferation. Herein we showed that in acute myeloid leukemia (AML), the biogenesis of these two miRNAs is interconnected through a network of regulatory loops driven by the FMS-like tyrosine kinase 3-internal tandem duplication (FLT3-ITD). In fact, FLT3-ITD induces the expression of miR-155 through a noncanonical mechanism of miRNA biogenesis that implicates cytoplasmic Drosha ribonuclease III (DROSHA). In turn, miR-155 down-regulates SH2-containing inositol phosphatase 1 (SHIP1), thereby increasing phosphor-protein kinase B (AKT) that in turn serine-phosphorylates, stabilizes, and activates Sprouty related EVH1 domain containing 1 (SPRED1). Activated SPRED1 inhibits the RAN/XPO5 complex and blocks the nucleus-to-cytoplasm transport of pre-miR-126, which cannot then complete the last steps of biogenesis. The net result is aberrantly low levels of mature miR-126 that allow quiescent leukemia blasts to be recruited into the cell cycle and proliferate. Thus, miR-126 down-regulation in proliferating AML blasts is downstream of FLT3-ITD–dependent miR-155 expression that initiates a complex circuit of concatenated regulatory feedback (i.e., miR-126/SPRED1, miR-155/human dead-box protein 3 [DDX3X]) and feed-forward (i.e., miR-155/SHIP1/AKT/miR-126) regulatory loops that eventually converge into an output signal for leukemic growth.

The lncRNA Xist forms ∼50 diffraction-limited foci to transcriptionally silence one X chromosome. How this small number of RNA foci and interacting proteins regulate a much larger number of X-linked genes is unknown. We show that Xist foci are locally confined, contain ∼2 RNA molecules, and nucleate supramolecular complexes (SMACs) that include many copies of the critical silencing protein SPEN. Aggregation and exchange of SMAC proteins generate local protein gradients that regulate broad, proximal chromatin regions. Partitioning of numerous SPEN molecules into SMACs is mediated by their intrinsically disordered regions and essential for transcriptional repression. Polycomb deposition via SMACs induces chromatin compaction and the increase in SMACs density around genes, which propagates silencing across the X chromosome. Our findings introduce a mechanism for functional nuclear compartmentalization whereby crowding of transcriptional and architectural regulators enables the silencing of many target genes by few RNA molecules.

We study the dynamics and statistical mechanical equilibria of a neutral two-dimensional point vortex gas with Coulomb-like interactions confined in a squared and a rectangular domain. Using a punctuated Hamiltonian model in which we model the process of vortex-antivortex annihilation in superfluids by removing vortex dipoles, we show that this leads to evaporative heating of the system. Consequently, the vortex gas enters the negative temperature regime and subsequently relaxes to a maximum entropy configuration. We demonstrate that the large scale flows that emerge in this regime can be explained by using an equilibrium statistical mechanical mean field theory of point vortices based on a Poisson-Boltzmann (PB) equation. In particular, we observe that the emergent large scale flows in our point vortex simulations in the squared domain give rise to a spontaneous acquisition of angular momentum whereas the flows in the rectangular domain prefers a state with zero angular momentum. In addition to the observed qualitative agreement between the dynamical simulations and the theory that we demonstrate for the two geometries, we also present an approach that allows us to accurately compute a coarse-grained vorticity field, and henceforth recover the entropy from our dynamical runs. This allows us to perform a quantitative comparison between the dynamical point vortex simulations and the statistical mechanical predictions of the mean field theory thereby allowing us to clearly assert the validity of the assumptions of the statistical approaches as applied to this system with long-range interactions.

The long non-coding RNA Xist exploits numerous effector proteins to progressively induce gene silencing across the X chromosome and form the inactive X (Xi)-compartment. The mechanism underlying formation of the chromosome-wide Xi-compartment is poorly understood. Here, we find that formation of the Xi-compartment is induced by ∼50 locally confined granules, where two Xist RNA molecules nucleate supra-molecular complexes (SMCs) of interacting proteins. Xist-SMCs are transient structures that concentrate rapidly recycling proteins in the X by increasing protein binding affinity. We find that gene silencing originates at Xist-SMCs and propagates across the entire chromosome over time, achieved by Polycomb-mediated coalescence of chromatin regions and aggregation, via its intrinsically disordered domains, of the critical silencing factor SPEN. Our results suggest a new model for X chromosome inactivation, in which Xist RNA induces macromolecular crowding of heterochromatinizing proteins near distinct sites which ultimately increases their density throughout the chromosome. This mechanism enables deterministic gene silencing without the need for Xist ribonucleoprotein complex-chromatin interactions at each target gene.

Temporal dynamics of gene expression inform cellular and molecular perturbations associated with disease development and evolution. Given the complexity of high-dimensional temporal genomic data, an analytic framework guided by a robust theory is needed to interpret time-sequential changes and to predict system dynamics. Here we model temporal dynamics of the transcriptome of peripheral blood mononuclear cells in a two-dimensional state-space representing states of health and leukemia using time-sequential bulk RNA-seq data from a murine model of acute myeloid leukemia (AML). The state-transition model identified critical points that accurately predict AML development and identifies stepwise transcriptomic perturbations that drive leukemia progression. The geometry of the transcriptome state-space provided a biological interpretation of gene dynamics, aligned gene signals that are not synchronized in time across mice, and allowed quantification of gene and pathway contributions to leukemia development. Our state-transition model synthesizes information from multiple cell types in the peripheral blood and identifies critical points in the transition from health to leukemia to guide interpretation of changes in the transcriptome as a whole to predict disease progression. Significance: These findings apply the theory of state transitions to model the initiation and development of acute myeloid leukemia, identifying transcriptomic perturbations that accurately predict time to disease development. See related commentary by Kuijjer, p. 3072

Chimeric antigen receptor (CAR) T-cell therapy has shown promise in the treatment of hematological cancers and is currently being investigated for solid tumors including high-grade glioma brain tumors. There is a desperate need to quantitatively study the factors that contribute to the efficacy of CAR T-cell therapy in solid tumors. In this work we use a mathematical model of predator-prey dynamics to explore the kinetics of CAR T-cell killing in glioma: the Chimeric Antigen Receptor t-cell treatment Response in GliOma (CARRGO) model. The model includes rates of cancer cell proliferation, CAR T-cell killing, CAR T-cell proliferation and exhaustion, and CAR T-cell persistence. We use patient-derived and engineered cancer cell lines with an in vitro real-time cell analyzer to parameterize the CARRGO model. We observe that CAR T-cell dose correlates inversely with the killing rate and correlates directly with the net rate of proliferation and exhaustion. This suggests that at a lower dose of CAR T-cells, individual T-cells kill more cancer cells but become more exhausted as compared to higher doses. Furthermore, the exhaustion rate was observed to increase significantly with tumor growth rate and was dependent on level of antigen expression. The CARRGO model highlights nonlinear dynamics involved in CAR T-cell therapy and provides novel insights into the kinetics of CAR T-cell killing. The model suggests that CAR T-cell treatment may be tailored to individual tumor characteristics including tumor growth rate and antigen level to maximize therapeutic benefit.Statement of SignificanceWe utilize a mathematical model to deconvolute the nonlinear contributions of CAR T-cell proliferation and exhaustion to predict therapeutic efficacy and dependence on CAR T-cell dose and target antigen levels.

Chimeric antigen receptor (CAR) T-cell therapy is an emerging targeted immunotherapy which has shown success in liquid cancers such as leukemias. CAR T-cells are also being used for the treatment of solid tumors such as glioblastoma, which is a primary brain tumor. Ongoing phase I trials have been designed to evaluate CAR T-cell dosing, scheduling, and route of administration in order to understand and improve the efficacy of CAR T-cell therapy. A better understanding of factors leading to the success of CAR T-cell immunotherapy for solid tumors will be necessary to improve outcomes for patients with solid tumors and to advance the field of CAR T-cell immuno-oncology. Here we use mathematical model to explore factors in determining a successful response to CAR T-cell therapy: proliferation, persistence, and killing capacity of CAR T-cells. Using a novel in vitro experimental apparatus, we are able to measure the density of cancer cells over several days in 15 minute interval time resolution. This highly temporally resolved data provides a unique opportunity to confidently estimate parameters of the model and to provide insights into the dynamics of CAR T-cell proliferation, persistence, and killing capacity. Furthermore we explore the relationship between these factor with CAR T-cell dose level. We will show results from experiments using patient-derived cancer cell lines as well as cancer cells engineered to express specific levels of the target antigen (IL13Rα2) to quantitatively evaluate the roles of proliferation, persistence, and killing in cells with different levels of antigen expression. We will discuss the interpretation of the model parameters and demonstrate the clinical value of this analysis through an application of CAR T-cell treatment tailored to the dynamics of an individual patient’s cancer growth rate.

Temporal dynamics of gene expression are informative of changes associated with disease development and evolution. Given the complexity of high-dimensional temporal datasets, an analytical framework guided by a robust theory is needed to interpret time-sequential changes and to predict system dynamics. Herein, we use acute myeloid leukemia as a proof-of-principle to model gene expression dynamics in a transcriptome state-space constructed based on time-sequential RNA-sequencing data. We describe the construction of a state-transition model to identify state-transition critical points which accurately predicts leukemia development. We show an analytical approach based on state-transition critical points identified step-wise transcriptomic perturbations driving leukemia progression. Furthermore, the gene(s) trajectory and geometry of the transcriptome state-space provides biologically-relevant gene expression signals that are not synchronized in time, and allows quantification of gene(s) contribution to leukemia development. Therefore, our state-transition model can synthesize information, identify critical points to guide interpretation of transcriptome trajectories and predict disease development.Graphical AbstractIn briefThe theory of state-transition is applied to acute myeloid leukemia (AML) to model transcriptome dynamics and trajectories in a state-space, and is used to identify critical points corresponding to critical transcriptomic perturbations that predict leukemia development.HighlightsLeukemia transcriptome dynamics are modeled as movement in transcriptome state-spaceState-transition model and critical points accurately predicts leukemia developmentCritical point-based approach identifies step-wise transcriptome events in leukemiaState-based geometric analysis provides quantification of leukemogenic contribution

MiRNAs are small noncoding RNAs that control gene expression by binding to cognate sites in the 3′ untranslated region (3′ UTR) of target messenger RNAs (mRNAs). MiRNAs are transcribed as primary (pri) mRNAs and processed into precursor (pre) miRNAs by nuclear DROSHA before being exported into the cytoplasm via the Exportin 5 (XPO5)/RAN-GTP complex. Once in the cytoplasm, pre-miRNAs are further processed by Dicer into mature miRNAs. The FMS-like tyrosine kinase 3 internal tandem duplication (FLT3-ITD) is one of the most common mutations in acute myeloid leukemia (AML) and confers growth and survival advantages to leukemia blasts. Among miRNAs, miR-155 has emerged as one of the most significantly upregulated in the FLT3-ITD+ AML and has been shown to play a pivotal role in uncontrolled blast hyperproliferation and survival. Herein, we report a previously unrecognized activity of FLT3-ITD that leads to deregulation of miR-155 expression by providing the evidence for the existence of FLT3-dependent non-canonical mechanisms of miRNA biogenesis. We initially observed that FLT3-ITD blocked the biogenesis of intronic miRNAs via inhibition of the "gatekeeper" XPO5/RAN-GTP complex that allow nucleus-to-cytoplasm pre-miRNA transport. By using in vitro phosphorylation assay with [32P]-ATP labeling, we demonstrated that FLT3-ITD phosphorylates a Sprouty related EVH1 domain-containing protein 1 (SPRED1), and that phospho-SPRED1 in turn inhibited the XPO5/RAN-GTP complex thereby halting transportation of pre-miRNAs from the nucleus to cytoplasm. This resulted in a decrease of several intronic miRNAs involved in normal hematopoiesis (i.e., miR-29b, miR-181a, miR-146b, miR-126). Accordingly, knocking down of SPRED1 expression in FLT3-ITD+ AML cells resulted in increased production of mature intronic miRNAs. Since the XPO5/RAN-GTP complex is the main gatekeeper for miRNA biogenesis, these results appeared in contradiction with the miR-155 upregulation which has been invariably observed in FLT3-ITD+ AML blasts. Differently from intronic miRNAs, miR-155 is hosted at the genomic site of long non-coding RNA (lnc-RNA) and we therefore hypothesized that it follows a different path of biogenesis. In fact forced expression of FLT3-ITD in lin-Sca1+kit+ (LSK) cells decreased intronic miRNA biogenesis (i.e., miR-126) and increase production of lnc-RNA hosted miRNAs (i.e., miR-155). Accordingly, we demonstrated that upon FLT3-ITD activation, AKT phosphorylated DDX3X, a DEAD-box RNA helicase protein thereby reducing its ability to bind heterogeneous nuclear Ribonucleoprotein U (hnRNP U), a component of the hnRNP complex associated with pre-mRNA splicing. Consequently, in FLT3-ITD cells, BIC-155 splicing is decreased. In fact, we measured significant increased levels of phospho-DDX3X and unspliced BIC-155 in primary FLT3-ITD+ blasts compared with FLT3-ITD- AML blasts. In consistent, DDX3X knock-down (KO) in FLT3-ITD- cells decreased BIC-155 splicing whereas DDX3X re-expression reversed these effects. The excess of unspliced BIC-155 RNA then bound to nuclear RNA export factor 1 (NXF1), a shuttle protein that transports poly A+ RNAs from the nucleus to the cytoplasm. In consistent, NXF1 KO blocked unspliced BIC-155 nucleus-to-cytoplasm transportation. In FLT3-ITD+ blasts, once in the cytoplasm, the unspliced BIC-155 RNA was then processed by cytoplasmic isoforms of DROSHA, as demonstrated using immunostaining, RNA Immunoprecipitation (RIP), and other gain- and loss-of-function experiments. Furthermore, overexpression of cytoplasmic DROSHA but not nuclear DROSHA isoform increased the processing of unspliced BIC-155 to mature miR-155. None of the intronic miRNAs studies interacted with cytoplasmic DROSHA. The bound of BIC-155 RNA with cytoplasmic DROSHA was unique of FLT3-ITD+ blasts, as it was not observed in FLT3-ITD- blasts. Thus, our results indicate a two-fold activity of FLT3-ITD that leads to decreased levels of intronic miRNAs via XPO5/RAN-GTP blockage and upregulation of other lnc-RNA hosted miRNAs via cytoplasmic DROSHA activation. The net result is suppression of intronic miRNAs that participates to the regulation of normal hematopoiesis and upregulation of lnc-RNA-hosted miRNA, especially miR-155 that contribute to aberrant blast hyperproliferation in the FLT3-ITD AML phenotype (Figure 1). Disclosures No relevant conflicts of interest to declare.

We study the relaxation of a 2D ultracold Bose-gas from a nonequilibrium initial state containing vortex excitations in experimentally realizable square and rectangular traps. We show that the subsystem of vortex gas excitations results in the spontaneous emergence of a coherent superfluid flow with a non-zero coarse-grained vorticity field. The streamfunction of this emergent quasi-classical 2D flow is governed by a Boltzmann-Poisson equation. This equation reveals that maximum entropy states of a neutral vortex gas that describe the spectral condensation of energy can be classified into types of flow depending on whether or not the flow spontaneously acquires angular momentum. Numerical simulations of a neutral point vortex model and a Bose gas governed by the 2D Gross-Pitaevskii equation in a square reveal that a large scale monopole flow field with net angular momentum emerges that is consistent with predictions of the Boltzmann-Poisson equation. The results allow us to characterise the spectral energy condensate in a 2D quantum fluid that bears striking similarity with similar flows observed in experiments of 2D classical turbulence. By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum., 9 pages, 9 figures

Chimeric antigen receptor (CAR) T-cell therapy is a promising emerging area of immunotherapy for the treatment of recurrent glioblastoma. In this therapy, T-cells are genetically modified to target tumor-specific antigens. Efficacy of CAR T-cell therapy depends on several factors, including CAR T-cell proliferation, persistence, and tumor cell killing capacity. Here we use a mathematical model to investigate the role of these three factors in determining response of recurrent GBM to this novel immunotherapy. Additionally, the impact of dosing and scheduling of CAR T-cell infusions on the therapeutic response is explored. We model the interaction between the two cell populations (cancer cells and CAR T-cells) using an ordinary differential equation based formalism. The growth and death of cancer cells are simulated as rates of proliferation and interaction between cancer cells and CAR T-cells, respectively. Biological data was used to parameterize the model. Analysis of the dynamics of interaction between cancer cells and CAR T-cells was performed to determine the maximum efficacy of a single and multiple doses of CAR T-cells. Our mathematical model and analysis shows that a critical parameter for the success of CAR T-cell therapy is the ratio of cancer cell proliferation to the killing capacity of the CAR T-cells. We quantify the dose level of CAR T-cells required to eliminate the cancer cell population. Furthermore, we use the mathematical model to predict the time to progression for specific dose levels, which may help in optimizing and scheduling multiple doses of CAR T-cell monotherapy. We compare the mathematical results with patient data from an ongoing dose-escalation study (NCT02208362) using central memory derived IL13Rα2-targeted CAR T-cell therapy for recurrent glioblastoma.