Mapping transcriptomic vector fields of single cells.

Single-cell (sc)RNA-seq, together with RNA velocity and metabolic labeling, reveals cellular states and transitions at unprecedented resolution. Fully exploiting these data, however, requires kinetic models capable of unveiling governing regulatory functions. Here, we introduce an analytical framework dynamo (https://github.com/aristoteleo/dynamo-release), which infers absolute RNA velocity, reconstructs continuous vector fields that predict cell fates, employs differential geometry to extract underlying regulations, and ultimately predicts optimal reprogramming paths and perturbation outcomes. We highlight dynamo's power to overcome fundamental limitations of conventional splicing-based RNA velocity analyses to enable accurate velocity estimations on a metabolically labeled human hematopoiesis scRNA-seq dataset. Furthermore, differential geometry analyses reveal mechanisms driving early megakaryocyte appearance and elucidate asymmetrical regulation within the PU.1-GATA1 circuit. Leveraging the least-action-path method, dynamo accurately predicts drivers of numerous hematopoietic transitions. Finally, in silico perturbations predict cell-fate diversions induced by gene perturbations. Dynamo, thus, represents an important step in advancing quantitative and predictive theories of cell-state transitions.

The complex landscape of haematopoietic lineage commitments is encoded in the coarse-grained endogenous network.

Haematopoietic lineage commitments are presented by a canonical roadmap in which haematopoietic stem cells or multipotent progenitors (MPPs) bifurcate into progenitors of more restricted lineages and ultimately mature to terminally differentiated cells. Although transcription factors playing significant roles in cell-fate commitments have been extensively studied, integrating such knowledge into the dynamic models to understand the underlying biological mechanism remains challenging. The hypothesis and modelling approach of the endogenous network has been developed previously and tested in various biological processes and is used in the present study of haematopoietic lineage commitments. The endogenous network is constructed based on the key transcription factors and their interactions that determine haematopoietic cell-fate decisions at each lineage branchpoint. We demonstrate that the process of haematopoietic lineage commitments can be reproduced from the landscape which orchestrates robust states of network dynamics and their transitions. Furthermore, some non-trivial characteristics are unveiled in the dynamical model. Our model also predicted previously under-represented regulatory interactions and heterogeneous MPP states by which distinct differentiation routes are intermediated. Moreover, network perturbations resulting in state transitions indicate the effects of ectopic gene expression on cellular reprogrammes. This study provides a predictive model to integrate experimental data and uncover the possible regulatory mechanism of haematopoietic lineage commitments.

KLHL22 maintains PD-1 homeostasis and prevents excessive T cell suppression.

Aberrant programmed cell death protein 1 (PD-1) expression on the surface of T cells is known to inhibit T cell effector activity and to play a pivotal role in tumor immune escape; thus, maintaining an appropriate level of PD-1 expression is of great significance. We identified KLHL22, an adaptor of the Cul3-based E3 ligase, as a major PD-1-associated protein that mediates the degradation of PD-1 before its transport to the cell surface. KLHL22 deficiency leads to overaccumulation of PD-1, which represses the antitumor response of T cells and promotes tumor progression. Importantly, KLHL22 was markedly decreased in tumor-infiltrating T cells from colorectal cancer patients. Meanwhile, treatment with 5-fluorouracil (5-FU) could increase PD-1 expression by inhibiting the transcription of KLHL22. These findings reveal that KLHL22 plays a crucial role in preventing excessive T cell suppression by maintaining PD-1 expression homeostasis and suggest the therapeutic potential of 5-FU in combination with anti-PD-1 in colorectal cancer patients.

Toward a translationally independent RNA-based synthetic oscillator using deactivated CRISPR-Cas.

In synthetic circuits, CRISPR-Cas systems have been used effectively for endpoint changes from an initial state to a final state, such as in logic gates. Here, we use deactivated Cas9 (dCas9) and deactivated Cas12a (dCas12a) to construct dynamic RNA ring oscillators that cycle continuously between states over time in bacterial cells. While our dCas9 circuits using 103-nt guide RNAs showed irregular fluctuations with a wide distribution of peak-to-peak period lengths averaging approximately nine generations, a dCas12a oscillator design with 40-nt CRISPR RNAs performed much better, having a strongly repressed off-state, distinct autocorrelation function peaks, and an average peak-to-peak period length of ∼7.5 generations. Along with free-running oscillator circuits, we measure repression response times in open-loop systems with inducible RNA steps to compare with oscillator period times. We track thousands of cells for 24+ h at the single-cell level using a microfluidic device. In creating a circuit with nearly translationally independent behavior, as the RNAs control each others' transcription, we present the possibility for a synthetic oscillator generalizable across many organisms and readily linkable for transcriptional control.

Adaptive Landscape Shaped by Core Endogenous Network Coordinates Complex Early Progenitor Fate Commitments in Embryonic Pancreas.

The classical development hierarchy of pancreatic cell fate commitments describes that multipotent progenitors (MPs) first bifurcate into tip cells and trunk cells, and then these cells give rise to acinar cells and endocrine/ductal cells separately. However, lineage tracings reveal that pancreatic progenitors are highly heterogeneous in tip and trunk domains in embryonic pancreas. The progenitor fate commitments from multipotency to unipotency during early pancreas development is insufficiently characterized. In pursuing a mechanistic understanding of the complexity in progenitor fate commitments, we construct a core endogenous network for pancreatic lineage decisions based on genetic regulations and quantified its intrinsic dynamic properties using dynamic modeling. The dynamics reveal a developmental landscape with high complexity that has not been clarified. Not only well-characterized pancreatic cells are reproduced, but also previously unrecognized progenitors-tip progenitor (TiP), trunk progenitor (TrP), later endocrine progenitor (LEP), and acinar progenitors (AciP/AciP2) are predicted. Further analyses show that TrP and LEP mediate endocrine lineage maturation, while TiP, AciP, AciP2 and TrP mediate acinar and ductal lineage maturation. The predicted cell fate commitments are validated by analyzing single-cell RNA sequencing (scRNA-seq) data. Significantly, this is the first time that a redefined hierarchy with detailed early pancreatic progenitor fate commitment is obtained.

Stochastic antagonism between two proteins governs a bacterial cell fate switch.

Cell fate decision circuits must be variable enough for genetically identical cells to adopt a multitude of fates, yet ensure that these states are distinct, stably maintained, and coordinated with neighboring cells. A long-standing view is that this is achieved by regulatory networks involving self-stabilizing feedback loops that convert small differences into long-lived cell types. We combined regulatory mutants and in vivo reconstitution with theory for stochastic processes to show that the marquee features of a cell fate switch in Bacillus subtilis-discrete states, multigenerational inheritance, and timing of commitments-can instead be explained by simple stochastic competition between two constitutively produced proteins that form an inactive complex. Such antagonistic interactions are commonplace in cells and could provide powerful mechanisms for cell fate determination more broadly.

Publisher Correction: Potential landscape of high dimensional nonlinear stochastic dynamics with large noise.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Correction to: 'Dynamical modelling of secondary metabolism and metabolic switches in Streptomyces xiamenensis 318'.

[This corrects the article DOI: 10.1098/rsos.190418.].

Dynamical modelling of secondary metabolism and metabolic switches in Streptomyces xiamenensis 318.

The production of secondary metabolites, while important for bioengineering purposes, presents a paradox in itself. Though widely existing in plants and bacteria, they have no definite physiological roles. Yet in both native habitats and laboratories, their production appears robust and follows apparent metabolic switches. We show in this work that the enzyme-catalysed process may improve the metabolic stability of the cells. The latter can be responsible for the overall metabolic behaviours such as dynamic metabolic landscape, metabolic switches and robustness, which can in turn affect the genetic formation of the organism in question. Mangrove-derived Streptomyces xiamenensis 318, with a relatively compact genome for secondary metabolism, is used as a model organism in our investigation. Integrated studies via kinetic metabolic modelling, transcriptase measurements and metabolic profiling were performed on this strain. Our results demonstrate that the secondary metabolites increase the metabolic fitness of the organism via stabilizing the underlying metabolic network. And the fluxes directing to NADH, NADPH, acetyl-CoA and glutamate provide the key switches for the overall and secondary metabolism. The information may be helpful for improving the xiamenmycin production on the strain.

Endogenous Molecular-Cellular Network Cancer Theory: A Systems Biology Approach.

In light of ever apparent limitation of the current dominant cancer mutation theory, a quantitative hypothesis for cancer genesis and progression, endogenous molecular-cellular network hypothesis has been proposed from the systems biology perspective, now for more than 10 years. It was intended to include both the genetic and epigenetic causes to understand cancer. Its development enters the stage of meaningful interaction with experimental and clinical data and the limitation of the traditional cancer mutation theory becomes more evident. Under this endogenous network hypothesis, we established a core working network of hepatocellular carcinoma (HCC) according to the hypothesis and quantified the working network by a nonlinear dynamical system. We showed that the two stable states of the working network reproduce the main known features of normal liver and HCC at both the modular and molecular levels. Using endogenous network hypothesis and validated working network, we explored genetic mutation pattern in cancer and potential strategies to cure or relieve HCC from a totally new perspective. Patterns of genetic mutations have been traditionally analyzed by posteriori statistical association approaches in light of traditional cancer mutation theory. One may wonder the possibility of a priori determination of any mutation regularity. Here, we found that based on the endogenous network theory the features of genetic mutations in cancers may be predicted without any prior knowledge of mutation propensities. Normal hepatocyte and cancerous hepatocyte stable states, specified by distinct patterns of expressions or activities of proteins in the network, provide means to directly identify a set of most probable genetic mutations and their effects in HCC. As the key proteins and main interactions in the network are conserved through cell types in an organism, similar mutational features may also be found in other cancers. This analysis yielded straightforward and testable predictions on an accumulated and preferred mutation spectrum in normal tissue. The validation of predicted cancer state mutation patterns demonstrates the usefulness and potential of a causal dynamical framework to understand and predict genetic mutations in cancer. We also obtained the following implication related to HCC therapy, (1) specific positive feedback loops are responsible for the maintenance of normal liver and HCC; (2) inhibiting proliferation and inflammation-related positive feedback loops, and simultaneously inducing liver-specific positive feedback loop is predicated as the potential strategy to cure or relieve HCC; (3) the genesis and regression of HCC is asymmetric. In light of the characteristic property of the nonlinear dynamical system, we demonstrate that positive feedback loops must be existed as a simple and general molecular basis for the maintenance of phenotypes such as normal liver and HCC, and regulating the positive feedback loops directly or indirectly provides potential strategies to cure or relieve HCC.

Potential landscape of high dimensional nonlinear stochastic dynamics with large noise.

Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including the cell-fate decision in developmental processes as well as the genesis and progression of cancers. While various attempts have been made to construct potential landscape in high dimensional systems and to estimate transition rates, they are practically limited to the cases where either noise is small or detailed balance condition holds. A general and practical approach to investigate real-world nonequilibrium systems, which are typically high-dimensional and subject to large multiplicative noise and the breakdown of detailed balance, remains elusive. Here, we formulate a computational framework that can directly compute the relative probabilities between locally stable states of such systems based on a least action method, without the necessity of simulating the steady-state distribution. The method can be applied to systems with arbitrary noise intensities through A-type stochastic integration, which preserves the dynamical structure of the deterministic counterpart dynamics. We demonstrate our approach in a numerically accurate manner through solvable examples. We further apply the method to investigate the role of noise on tumor heterogeneity in a 38-dimensional network model for prostate cancer, and provide a new strategy on controlling cell populations by manipulating noise strength.

Beyond cancer genes: colorectal cancer as robust intrinsic states formed by molecular interactions.

Colorectal cancer (CRC) has complex pathological features that defy the linear-additive reasoning prevailing in current biomedicine studies. In pursuing a mechanistic understanding behind such complexity, we constructed a core molecular-cellular interaction network underlying CRC and investigated its nonlinear dynamical properties. The hypothesis and modelling method has been developed previously and tested in various cancer studies. The network dynamics reveal a landscape of several attractive basins corresponding to both normal intestinal phenotype and robust tumour subtypes, identified by their different molecular signatures. Comparison between the modelling results and gene expression profiles from patients collected at the second affiliated hospital of Zhejiang University is presented as validation. The numerical 'driving' experiment suggests that CRC pathogenesis may depend on pathways involved in gastrointestinal track development and molecules associated with mesenchymal lineage differentiation, such as Stat5, BMP, retinoic acid signalling pathways, Runx and Hox transcription families. We show that the multi-faceted response to immune stimulation and therapies, as well as different carcinogenesis and metastasis routes, can be straightforwardly understood and analysed under such a framework.

PCAF/GCN5-Mediated Acetylation of RPA1 Promotes Nucleotide Excision Repair.

The RPA complex can integrate multiple stress signals into diverse responses by activating distinct DNA repair pathways. However, it remains unclear how RPA1 elects to activate a specific repair pathway during different types of DNA damage. Here, we report that PCAF/GCN5-mediated K163 acetylation of RPA1 is crucial for nucleotide excision repair (NER) but is dispensable for other DNA repair pathways. Mechanistically, we demonstrate that the acetylation of RPA1 is critical for the steady accumulation of XPA at damaged DNA sites and preferentially activates the NER pathway. DNA-PK phosphorylates and activates PCAF upon UV damage and consequently promotes the acetylation of RPA1. Moreover, the acetylation of RPA1 is tightly regulated by HDAC6 and SIRT1. Together, our results demonstrate that the K163 acetylation of RPA1 plays a key role in the repair of UV-induced DNA damage and reveal how the specific RPA1 modification modulates the choice of distinct DNA repair pathways.

Decoding early myelopoiesis from dynamics of core endogenous network.

A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network perspective. Indeed, there are numerical difficulties even for those who were determined to explore along this direction. Undeterred, seven years ago a group of Chinese scientists started a program aiming to obtain quantitative connections between tumors and network dynamics. Many interesting results have been obtained. In this paper we wish to test such idea from a different angle: the connection between a normal biological process and the network dynamics. We have taken early myelopoiesis as our biological model. A standard roadmap for the cell-fate diversification during hematopoiesis has already been well established experimentally, yet little was known for its underpinning dynamical mechanisms. Compounding this difficulty there were additional experimental challenges, such as the seemingly conflicting hematopoietic roadmaps and the cell-fate inter-conversion events. With early myeloid cell-fate determination in mind, we constructed a core molecular endogenous network from well-documented gene regulation and signal transduction knowledge. Turning the network into a set of dynamical equations, we found computationally several structurally robust states. Those states nicely correspond to known cell phenotypes. We also found the states connecting those stable states. They reveal the developmental routes-how one stable state would most likely turn into another stable state. Such interconnected network among stable states enabled a natural organization of cell-fates into a multi-stable state landscape. Accordingly, both the myeloid cell phenotypes and the standard roadmap were explained mechanistically in a straightforward manner. Furthermore, recent challenging observations were also explained naturally. Moreover, the landscape visually enables a prediction of a pool of additional cell states and developmental routes, including the non-sequential and cross-branch transitions, which are testable by future experiments. In summary, the endogenous network dynamics provide an integrated quantitative framework to understand the heterogeneity and lineage commitment in myeloid progenitors.

Cancer as robust intrinsic state shaped by evolution: a key issues review.

Cancer is a complex disease: its pathology cannot be properly understood in terms of independent players-genes, proteins, molecular pathways, or their simple combinations. This is similar to many-body physics of a condensed phase that many important properties are not determined by a single atom or molecule. The rapidly accumulating large 'omics' data also require a new mechanistic and global underpinning to organize for rationalizing cancer complexity. A unifying and quantitative theory was proposed by some of the present authors that cancer is a robust state formed by the endogenous molecular-cellular network, which is evolutionarily built for the developmental processes and physiological functions. Cancer state is not optimized for the whole organism. The discovery of crucial players in cancer, together with their developmental and physiological roles, in turn, suggests the existence of a hierarchical structure within molecular biology systems. Such a structure enables a decision network to be constructed from experimental knowledge. By examining the nonlinear stochastic dynamics of the network, robust states corresponding to normal physiological and abnormal pathological phenotypes, including cancer, emerge naturally. The nonlinear dynamical model of the network leads to a more encompassing understanding than the prevailing linear-additive thinking in cancer research. So far, this theory has been applied to prostate, hepatocellular, gastric cancers and acute promyelocytic leukemia with initial success. It may offer an example of carrying physics inquiring spirit beyond its traditional domain: while quantitative approaches can address individual cases, however there must be general rules/laws to be discovered in biology and medicine.

Comment on "Construction of the landscape for multi-stable systems: Potential landscape, quasi-potential, A-type integral and beyond" [J. Chem. Phys. 144, 094109 (2016)].

Connections between a "SDE decomposition" to other frameworks constructing landscape in non-equilibrium processes were discussed by Zhou and Li [J. Chem. Phys. 144, 094109 (2016)]. It was speculated that the SDE decomposition would not be generally unique. In this comment, we demonstrate both mathematically and physically that the speculation is incorrect and the uniqueness is guaranteed under appropriate conditions. A few related issues are also clarified, such as the limitation of obtaining potential function from steady state distribution. Current demonstration may lead to a better understanding on the structure and robustness of the decomposition framework.

Towards stable kinetics of large metabolic networks: Nonequilibrium potential function approach.

While the biochemistry of metabolism in many organisms is well studied, details of the metabolic dynamics are not fully explored yet. Acquiring adequate in vivo kinetic parameters experimentally has always been an obstacle. Unless the parameters of a vast number of enzyme-catalyzed reactions happened to fall into very special ranges, a kinetic model for a large metabolic network would fail to reach a steady state. In this work we show that a stable metabolic network can be systematically established via a biologically motivated regulatory process. The regulation is constructed in terms of a potential landscape description of stochastic and nongradient systems. The constructed process draws enzymatic parameters towards stable metabolism by reducing the change in the Lyapunov function tied to the stochastic fluctuations. Biologically it can be viewed as interplay between the flux balance and the spread of workloads on the network. Our approach allows further constraints such as thermodynamics and optimal efficiency. We choose the central metabolism of Methylobacterium extorquens AM1 as a case study to demonstrate the effectiveness of the approach. Growth efficiency on carbon conversion rate versus cell viability and futile cycles is investigated in depth.

From molecular interaction to acute promyelocytic leukemia: Calculating leukemogenesis and remission from endogenous molecular-cellular network.

Acute promyelocytic leukemia (APL) remains the best example of a malignancy that can be cured clinically by differentiation therapy. We demonstrate that APL may emerge from a dynamical endogenous molecular-cellular network obtained from normal, non-cancerous molecular interactions such as signal transduction and translational regulation under physiological conditions. This unifying framework, which reproduces APL, normal progenitor, and differentiated granulocytic phenotypes as different robust states from the network dynamics, has the advantage to study transition between these states, i.e. critical drivers for leukemogenesis and targets for differentiation. The simulation results quantitatively reproduce microarray profiles of NB4 and HL60 cell lines in response to treatment and normal neutrophil differentiation, and lead to new findings such as biomarkers for APL and additional molecular targets for arsenic trioxide therapy. The modeling shows APL and normal states mutually suppress each other, both in "wiring" and in dynamical cooperation. Leukemogenesis and recovery under treatment may be a consequence of spontaneous or induced transitions between robust states, through "passes" or "dragging" by drug effects. Our approach rationalizes leukemic complexity and constructs a platform towards extending differentiation therapy by performing "dry" molecular biology experiments.

Endogenous network states predict gain or loss of functions for genetic mutations in hepatocellular carcinoma.

Cancers have been typically characterized by genetic mutations. Patterns of such mutations have traditionally been analysed by posteriori statistical association approaches. One may ponder the possibility of a priori determination of any mutation regularity. Here by exploring biological processes implied in a mechanistic theory recently developed (the endogenous molecular-cellular network theory), we found that the features of genetic mutations in cancers may be predicted without any prior knowledge of mutation propensities. With hepatocellular carcinoma (HCC) as an example, we found that the normal hepatocyte and cancerous hepatocyte can be represented by robust stable states of one single endogenous network. These stable states, specified by distinct patterns of expressions or activities of proteins in the network, provide means to directly identify a set of most probable genetic mutations and their effects in HCC. As the key proteins and main interactions in the network are conserved through cell types in an organism, similar mutational features may also be found in other cancers. This analysis yielded straightforward and testable predictions on accumulated and preferred mutation spectra in normal tissue. The validation of predicted cancer state mutation patterns demonstrates the usefulness and potential of a causal dynamical framework to understand and predict genetic mutations in cancer.

Core level regulatory network of osteoblast as molecular mechanism for osteoporosis and treatment.

To develop and evaluate the long-term prophylactic treatment for chronic diseases such as osteoporosis requires a clear view of mechanism at the molecular and systems level. While molecular signaling pathway studies for osteoporosis are extensive, a unifying mechanism is missing. In this work, we provide experimental and systems-biology evidences that a tightly connected top-level regulatory network may exist, which governs the normal and osteoporotic phenotypes of osteoblast. Specifically, we constructed a hub-like interaction network from well-documented cross-talks among estrogens, glucocorticoids, retinoic acids, peroxisome proliferator-activated receptor, vitamin D receptor and calcium-signaling pathways. The network was verified with transmission electron microscopy and gene expression profiling for bone tissues of ovariectomized (OVX) rats before and after strontium gluconate (GluSr) treatment. Based on both the network structure and the experimental data, the dynamical modeling predicts calcium and glucocorticoids signaling pathways as targets for GluSr treatment. Modeling results further reveal that in the context of missing estrogen signaling, the GluSr treated state may be an outcome that is closest to the healthy state.