From understanding the development landscape of the canonical fate-switch pair to constructing a dynamic landscape for two-step neural differentiation

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, that infers absolute RNA velocity, reconstructs continuous vector-field functions 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.

Noise distorts the epigenetic landscape and shapes cell-fate decisions

The Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process. Recent single-cell transcriptomic data provide new opportunities for quantifying this originally conceptual tool, offering insight into the gene regulatory networks underlying cellular development. While many methods for constructing the landscape have been proposed, by far the most commonly employed approach is based on computing the landscape as the negative logarithm of the steady-state probability distribution. Here, we use simple models to highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape. We further discuss how the presence of noise has important implications for the identifiability of the regulatory dynamics from experimental data. A record of this paper's transparent peer review process is included in the supplemental information.

Inferring Causal Gene Regulatory Networks from Coupled Single-Cell Expression Dynamics Using Scribe

Here, we present Scribe (https://github.com/aristoteleo/Scribe-py), a toolkit for detecting and visualizing causal regulatory interactions between genes and explore the potential for single-cell experiments to power network reconstruction. Scribe employs restricted directed information to determine causality by estimating the strength of information transferred from a potential regulator to its downstream target. We apply Scribe and other leading approaches for causal network reconstruction to several types of single-cell measurements and show that there is a dramatic drop in performance for "pseudotime"-ordered single-cell data compared with true time-series data. We demonstrate that performing causal inference requires temporal coupling between measurements. We show that methods such as "RNA velocity" restore some degree of coupling through an analysis of chromaffin cell fate commitment. These analyses highlight a shortcoming in experimental and computational methods for analyzing gene regulation at single-cell resolution and suggest ways of overcoming it.

CALISTA: Clustering and LINEAGE Inference in Single-Cell Transcriptional Analysis

We present Clustering and Lineage Inference in Single-Cell Transcriptional Analysis (CALISTA), a numerically efficient and highly scalable toolbox for an end-to-end analysis of single-cell transcriptomic profiles. CALISTA includes four essential single-cell analyses for cell differentiation studies, including single-cell clustering, reconstruction of cell lineage specification, transition gene identification, and cell pseudotime ordering, which can be applied individually or in a pipeline. In these analyses, we employ a likelihood-based approach where single-cell mRNA counts are described by a probabilistic distribution function associated with stochastic gene transcriptional bursts and random technical dropout events. We illustrate the efficacy of CALISTA using single-cell gene expression datasets from different single-cell transcriptional profiling technologies and from a few hundreds to tens of thousands of cells. CALISTA is freely available on https://www.cabselab.com/calista.

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.

Approximating the energy landscape of a two-dimensional bistable gene autoregulation model by separating slow and fast dynamics

The energy landscape is widely used to quantify the stability of multistable nonlinear systems, such as bistable gene regulation networks. In physics, the potential can be obtained through integration only for gradient systems. However, multidimensional nonlinear systems are often nongradient, for which the potential is calculated by decomposing the dynamics to gradient and nongradient parts. This potential is then called a quasipotential. Given that one-dimensional (1D) systems can be regarded as gradient systems, we attempt to separate the two-dimensional (2D) system into two 1D systems working on distinct timescales, and the potential can be easily calculated for the two 1D systems separately. This method is used in this study to estimate the energy landscape of a two-variable gene autoregulation model. This elegant and comprehensive method is accessible for 2D nonlinear systems in which the dynamics can be divided into slow and fast parts.

Reversed graph embedding resolves complex single-cell trajectories

Single-cell trajectories can unveil how gene regulation governs cell fate decisions. However, learning the structure of complex trajectories with multiple branches remains a challenging computational problem. We present Monocle 2, an algorithm that uses reversed graph embedding to describe multiple fate decisions in a fully unsupervised manner. We applied Monocle 2 to two studies of blood development and found that mutations in the genes encoding key lineage transcription factors divert cells to alternative fates.

Reversed graph embedding resolves complex single-cell trajectories

Single-cell trajectories can unveil how gene regulation governs cell fate decisions. However, learning the structure of complex trajectories with multiple branches remains a challenging computational problem. We present Monocle 2, an algorithm that uses reversed graph embedding to describe multiple fate decisions in a fully unsupervised manner. We applied Monocle 2 to two studies of blood development and found that mutations in the genes encoding key lineage transcription factors divert cells to alternative fates.

A predictive computational framework for direct reprogramming between human cell types

Transdifferentiation, the process of converting from one cell type to another without going through a pluripotent state, has great promise for regenerative medicine. The identification of key transcription factors for reprogramming is currently limited by the cost of exhaustive experimental testing of plausible sets of factors, an approach that is inefficient and unscalable. Here we present a predictive system (Mogrify) that combines gene expression data with regulatory network information to predict the reprogramming factors necessary to induce cell conversion. We have applied Mogrify to 173 human cell types and 134 tissues, defining an atlas of cellular reprogramming. Mogrify correctly predicts the transcription factors used in known transdifferentiations. Furthermore, we validated two new transdifferentiations predicted by Mogrify. We provide a practical and efficient mechanism for systematically implementing novel cell conversions, facilitating the generalization of reprogramming of human cells. Predictions are made available to help rapidly further the field of cell conversion.

Modeling the epigenetic attractors landscape: toward a post-genomic mechanistic understanding of development

Robust temporal and spatial patterns of cell types emerge in the course of normal development in multicellular organisms. The onset of degenerative diseases may result from altered cell fate decisions that give rise to pathological phenotypes. Complex networks of genetic and non-genetic components underlie such normal and altered morphogenetic patterns. Here we focus on the networks of regulatory interactions involved in cell-fate decisions. Such networks modeled as dynamical non-linear systems attain particular stable configurations on gene activity that have been interpreted as cell-fate states. The network structure also restricts the most probable transition patterns among such states. The so-called Epigenetic Landscape (EL), originally proposed by C. H. Waddington, was an early attempt to conceptually explain the emergence of developmental choices as the result of intrinsic constraints (regulatory interactions) shaped during evolution. Thanks to the wealth of molecular genetic and genomic studies, we are now able to postulate gene regulatory networks (GRN) grounded on experimental data, and to derive EL models for specific cases. This, in turn, has motivated several mathematical and computational modeling approaches inspired by the EL concept, that may be useful tools to understand and predict cell-fate decisions and emerging patterns. In order to distinguish between the classical metaphorical EL proposal of Waddington, we refer to the Epigenetic Attractors Landscape (EAL), a proposal that is formally framed in the context of GRNs and dynamical systems theory. In this review we discuss recent EAL modeling strategies, their conceptual basis and their application in studying the emergence of both normal and pathological developmental processes. In addition, we discuss how model predictions can shed light into rational strategies for cell fate regulation, and we point to challenges ahead.

Classification of transient behaviours in a time-dependent toggle switch model

BACKGROUND

Waddington's epigenetic landscape is an intuitive metaphor for the developmental and evolutionary potential of biological regulatory processes. It emphasises time-dependence and transient behaviour. Nowadays, we can derive this landscape by modelling a specific regulatory network as a dynamical system and calculating its so-called potential surface. In this sense, potential surfaces are the mathematical equivalent of the Waddingtonian landscape metaphor. In order to fully capture the time-dependent (non-autonomous) transient behaviour of biological processes, we must be able to characterise potential landscapes and how they change over time. However, currently available mathematical tools focus on the asymptotic (steady-state) behaviour of autonomous dynamical systems, which restricts how biological systems are studied.

RESULTS

We present a pragmatic first step towards a methodology for dealing with transient behaviours in non-autonomous systems. We propose a classification scheme for different kinds of such dynamics based on the simulation of a simple genetic toggle-switch model with time-variable parameters. For this low-dimensional system, we can calculate and explicitly visualise numerical approximations to the potential landscape. Focussing on transient dynamics in non-autonomous systems reveals a range of interesting and biologically relevant behaviours that would be missed in steady-state analyses of autonomous systems. Our simulation-based approach allows us to identify four qualitatively different kinds of dynamics: transitions, pursuits, and two kinds of captures. We describe these in detail, and illustrate the usefulness of our classification scheme by providing a number of examples that demonstrate how it can be employed to gain specific mechanistic insights into the dynamics of gene regulation.

CONCLUSIONS

The practical aim of our proposed classification scheme is to make the analysis of explicitly time-dependent transient behaviour tractable, and to encourage the wider use of non-autonomous models in systems biology. Our method is applicable to a large class of biological processes.

Chemotactic responses of neural stem cells to SDF-1α correlate closely with their differentiation status

Chemotaxis of neural stem/progenitor cells (NSCs) is regulated by a variety of factors, and much effort has been devoted to the delineation of factors that are involved in NSC migration. However, the relationship between NSC chemotactic migration and differentiation remains uncharacterized. In the present study, by comparing the transfilter migration rate, single-cell migration speed, and directional efficiency of NSCs in stromal cell-derived factor-1 alpha (SDF-1α)-induced Boyden chamber and Dunn chamber chemotaxis assays, we demonstrate that NSCs in varying differentiation stages possess different migratory capacity. Furthermore, F-actin microfilament reorganization upon stimulation varies greatly among separate differentiation states. We show that signaling pathways involved in NSC migration, such as PI3K/Akt and mitogen-activated protein kinase (MAPK) (ERK1/2, JNK, and p38 MAPK) pathways, are differentially activated by SDF-1α among each NSC differentiation stages, and the extent to which these pathways participate in cell chemotaxis exhibits a differentiation stage-dependent manner. Taken together, these results suggest that the differentiation of NSCs influences their chemotactic responses to SDF-1α, providing new insight into the optimization of the therapeutic efficacy of NSCs for neural regeneration and nerve repair after injury.