Semblance of Heterogeneity in Collective Cell Migration

One-Shot Single-Cell Proteome and Metabolome Analysis Strategy for the Same Single Cell

Characterizing the profiles of proteome and metabolome at the single-cell level is of great significance in single-cell multiomic studies. Herein, we proposed a novel strategy called one-shot single-cell proteome and metabolome analysis (scPMA) to acquire the proteome and metabolome information in a single-cell individual in one injection of LC-MS/MS analysis. Based on the scPMA strategy, a total workflow was developed to achieve the single-cell capture, nanoliter-scale sample pretreatment, one-shot LC injection and separation of the enzyme-digested peptides and metabolites, and dual-zone MS/MS detection for proteome and metabolome profiling. Benefiting from the scPMA strategy, we realized dual-omic analysis of single tumor cells, including A549, HeLa, and HepG2 cells with 816, 578, and 293 protein groups and 72, 91, and 148 metabolites quantified on average. A single-cell perspective experiment for investigating the doxorubicin-induced antitumor effects in both the proteome and metabolome aspects was also performed.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Intrinsic statistical separation of subpopulations in heterogeneous collective motion via dimensionality reduction

Collective motion of locally interacting agents is found ubiquitously throughout nature. The inability to probe individuals has driven longstanding interest in the development of methods for inferring the underlying interactions. In the context of heterogeneous collectives, where the population consists of individuals driven by different interactions, existing approaches require some knowledge about the heterogeneities or underlying interactions. Here, we investigate the feasibility of identifying the identities in a heterogeneous collective without such prior knowledge. We numerically explore the behavior of a heterogeneous Vicsek model and find sufficiently long trajectories intrinsically cluster in a principal component analysis-based dimensionally reduced model-agnostic description of the data. We identify how heterogeneities in each parameter in the model (interaction radius, noise, population proportions) dictate this clustering. Finally, we show the generality of this phenomenon by finding similar behavior in a heterogeneous D'Orsogna model. Altogether, our results establish and quantify the intrinsic model-agnostic statistical disentanglement of identities in heterogeneous collectives.

Unravelling the nexus: Towards a unified model of development, ageing, and cancer

This work presents a comprehensive model that aims to unify our understanding of embryogenesis, ageing, and cancer. While there have been previous attempts to construct models separately for two of these phenomena (such as embryogenesis and cancer, ageing and cancer), models encompassing all three are relatively scarce, if not entirely absent. The model's most notable feature is the presence of driver cells throughout the body, which may correspond to Spemann's organisers. These driver cells play a vital role in propelling development as they dynamically emerge from non-driver cells and inhabit specialised niches. Remarkably, this continuous process persists throughout an organism's entire lifespan, signifying that development unfolds from conception to the end of life. Driver cells orchestrate change events through the induction of distinctive epigenetic patterns of gene activation. Events occurring at young age drive development, are subject to high evolutionary pressure and hence carefully optimised. Events occurring after reproduction age are subject to decreasing evolutionary pressure: for this reason, such events are "pseudorandom" -deterministic but erratic. Some of these events lead to age-related benign conditions, such as gray hair. Some lead to serious age-related diseases, such as diabetes and Alzheimer's disease. Furthermore, some of these events might perturb epigenetically key pathways involved in driver activation and formation, leading to cancer. In our model, this driver cell-based mechanism represents the backbone of multicellular biology: understanding and correcting its functioning may give the chance to solve a wide range of conditions at once.

Cell segregation via differential collision modes between heterotypic cell populations

In tissue development and regeneration, the establishment of sharp boundaries between heterotypic cells is essential for the differentiation of tissue functions. During the dynamic rearrangements of constituent cells that result from cell division and collective migration, the segregation boundary encounters various challenges. Several studies have suggested that cortical actomyosin structures play a crucial role in the maintenance of the boundary interface of segregated cell populations, implicating actin-mediated stresses. Examining physical cellular properties such as motility, traction, and intercellular stress, we investigated the formation and maintenance of the stable segregation between epithelial and mesenchymal cell populations devoid of heterotypic adhesions. At the contact boundary, the homotypic adhesion-mediated epithelial aggregates exerted collision-mediated compression against the surrounding mesenchymal cells. Our results demonstrated that heterotypic cell populations established a robust interfacial boundary by accumulating stress from active collisions and repulsions between two dissimilar cell types. Furthermore, the moment of the heterotypic collisions was identified by the existence of a sharp rise in maximum shear stress within the cell cluster.

Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population

Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it is challenging to infer the interaction rules directly from data. In the field of equation discovery, the weak-form sparse identification of nonlinear dynamics (WSINDy) methodology has been shown to be computationally efficient for identifying the governing equations of complex systems from noisy data. Motivated by the success of IPS models to describe the spatial movement of organisms, we develop WSINDy for the second-order IPS to learn equations for communities of cells. Our approach learns the directional interaction rules for each individual cell that in aggregate govern the dynamics of a heterogeneous population of migrating cells. To sort a cell according to the active classes present in its model, we also develop a novel ad hoc classification scheme (which accounts for the fact that some cells do not have enough evidence to accurately infer a model). Aggregated models are then constructed hierarchically to simultaneously identify different species of cells present in the population and determine best-fit models for each species. We demonstrate the efficiency and proficiency of the method on several test scenarios, motivated by common cell migration experiments.

Disentangling intrinsic motion from neighborhood effects in heterogeneous collective motion

Most real-world collectives, including animal groups, pedestrian crowds, active particles, and living cells, are heterogeneous. The differences among individuals in their intrinsic properties have emergent effects at the group level. It is often of interest to infer how the intrinsic properties differ among the individuals based on their observed movement patterns. However, the true individual properties may be masked by the nonlinear interactions in the collective. We investigate the inference problem in the context of a bidisperse collective with two types of agents, where the goal is to observe the motion of the collective and classify the agents according to their types. Since collective effects, such as jamming and clustering, affect individual motion, the information in an agent's own movement is insufficient for accurate classification. A simple observer algorithm, based only on individual velocities, cannot accurately estimate the level of heterogeneity of the system and often misclassifies agents. We propose a novel approach to the classification problem, where collective effects on an agent's motion are explicitly accounted for. We use insights about the phenomenology of collective motion to quantify the effect of the neighborhood on an agent's motion using a neighborhood parameter. Such an approach can distinguish between agents of two types, even when their observed motion is identical. This approach estimates the level of heterogeneity much more accurately and achieves significant improvements in classification. Our results demonstrate that explicitly accounting for neighborhood effects is often necessary to correctly infer intrinsic properties of individuals.

Capturing Biomarkers and Molecular Targets in Cellular Landscapes From Dynamic Reaction Network Models and Machine Learning

Computational dynamic ODE models of cell function describing biochemical reactions have been created for decades, but on a small scale. Still, they have been highly effective in describing and predicting behaviors. For example, oscillatory phospho-ERK levels were predicted and confirmed in MAPK signaling encompassing both positive and negative feedback loops. These models typically were limited and not adapted to large datasets so commonly found today. But importantly, ODE models describe reaction networks in well-mixed systems representing the cell and can be simulated with ordinary differential equations that are solved deterministically. Stochastic solutions, which can account for noisy reaction networks, in some cases, also improve predictions. Today, dynamic ODE models rarely encompass an entire cell even though it might be expected that an upload of the large genomic, transcriptomic, and proteomic datasets may allow whole cell models. It is proposed here to combine output from simulated dynamic ODE models, completed with omics data, to discover both biomarkers in cancer a priori and molecular targets in the Machine Learning setting.

Seven challenges in the multiscale modeling of multicellular tissues

The growth and dynamics of multicellular tissues involve tightly regulated and coordinated morphogenetic cell behaviors, such as shape changes, movement, and division, which are governed by subcellular machinery and involve coupling through short- and long-range signals. A key challenge in the fields of developmental biology, tissue engineering and regenerative medicine is to understand how relationships between scales produce emergent tissue-scale behaviors. Recent advances in molecular biology, live-imaging and ex vivo techniques have revolutionized our ability to study these processes experimentally. To fully leverage these techniques and obtain a more comprehensive understanding of the causal relationships underlying tissue dynamics, computational modeling approaches are increasingly spanning multiple spatial and temporal scales, and are coupling cell shape, growth, mechanics, and signaling. Yet such models remain challenging: modeling at each scale requires different areas of technical skills, while integration across scales necessitates the solution to novel mathematical and computational problems. This review aims to summarize recent progress in multiscale modeling of multicellular tissues and to highlight ongoing challenges associated with the construction, implementation, interrogation, and validation of such models. This article is categorized under: Reproductive System Diseases > Computational Models Metabolic Diseases > Computational Models Cancer > Computational Models.

Matrix feedback enables diverse higher-order patterning of the extracellular matrix

The higher-order patterning of extra-cellular matrix in normal and pathological tissues has profound consequences on tissue function. Whilst studies have documented both how fibroblasts create and maintain individual matrix fibers and how cell migration is altered by the fibers they interact with, a model unifying these two aspects of tissue organization is lacking. Here we use computational modelling to understand the effect of this interconnectivity between fibroblasts and matrix at the mesoscale level. We created a unique adaptation to the Vicsek flocking model to include feedback from a second layer representing the matrix, and use experimentation to parameterize our model and validate model-driven hypotheses. Our two-layer model demonstrates that feedback between fibroblasts and matrix increases matrix diversity creating higher-order patterns. The model can quantitatively recapitulate matrix patterns of tissues in vivo. Cells follow matrix fibers irrespective of when the matrix fibers were deposited, resulting in feedback with the matrix acting as temporal 'memory' to collective behaviour, which creates diversity in topology. We also establish conditions under which matrix can be remodelled from one pattern to another. Our model elucidates how simple rules defining fibroblast-matrix interactions are sufficient to generate complex tissue patterns.

Mathematical models of tumor cell proliferation: A review of the literature

INTRODUCTION

A defining hallmark of cancer is aberrant cell proliferation. Efforts to understand the generative properties of cancer cells span all biological scales: from genetic deviations and alterations of metabolic pathways to physical stresses due to overcrowding, as well as the effects of therapeutics and the immune system. While these factors have long been studied in the laboratory, mathematical and computational techniques are being increasingly applied to help understand and forecast tumor growth and treatment response. Advantages of mathematical modeling of proliferation include the ability to simulate and predict the spatiotemporal development of tumors across multiple experimental scales. Central to proliferation modeling is the incorporation of available biological data and validation with experimental data. Areas covered: We present an overview of past and current mathematical strategies directed at understanding tumor cell proliferation. We identify areas for mathematical development as motivated by available experimental and clinical evidence, with a particular emphasis on emerging, non-invasive imaging technologies. Expert commentary: The data required to legitimize mathematical models are often difficult or (currently) impossible to obtain. We suggest areas for further investigation to establish mathematical models that more effectively utilize available data to make informed predictions on tumor cell proliferation.

The devil is in the mesoscale: Mechanical and behavioural heterogeneity in collective cell movement

Heterogeneity within cell populations can be an important aspect affecting their collective movement and tissue-mechanical properties, determining for example their effective viscoelasticity. Differences in cell-level properties and behaviour within a group of moving cells can give rise to unexpected and non-intuitive behaviours at the tissue level. Such emergent phenomena often manifest themselves through spatiotemporal patterns at an intermediate 'mesoscale' between cell and tissue scales, typically involving tens of cells. Focussing on the development of embryonic animal tissues, we review recent evidence for the importance of heterogeneity at the mesoscale for collective cell migration and convergence and extension movements. We further discuss approaches to incorporate heterogeneity into computational models to complement experimental investigations.

PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems

Many multicellular systems problems can only be understood by studying how cells move, grow, divide, interact, and die. Tissue-scale dynamics emerge from systems of many interacting cells as they respond to and influence their microenvironment. The ideal "virtual laboratory" for such multicellular systems simulates both the biochemical microenvironment (the "stage") and many mechanically and biochemically interacting cells (the "players" upon the stage). PhysiCell-physics-based multicellular simulator-is an open source agent-based simulator that provides both the stage and the players for studying many interacting cells in dynamic tissue microenvironments. It builds upon a multi-substrate biotransport solver to link cell phenotype to multiple diffusing substrates and signaling factors. It includes biologically-driven sub-models for cell cycling, apoptosis, necrosis, solid and fluid volume changes, mechanics, and motility "out of the box." The C++ code has minimal dependencies, making it simple to maintain and deploy across platforms. PhysiCell has been parallelized with OpenMP, and its performance scales linearly with the number of cells. Simulations up to 105-106 cells are feasible on quad-core desktop workstations; larger simulations are attainable on single HPC compute nodes. We demonstrate PhysiCell by simulating the impact of necrotic core biomechanics, 3-D geometry, and stochasticity on the dynamics of hanging drop tumor spheroids and ductal carcinoma in situ (DCIS) of the breast. We demonstrate stochastic motility, chemical and contact-based interaction of multiple cell types, and the extensibility of PhysiCell with examples in synthetic multicellular systems (a "cellular cargo delivery" system, with application to anti-cancer treatments), cancer heterogeneity, and cancer immunology. PhysiCell is a powerful multicellular systems simulator that will be continually improved with new capabilities and performance improvements. It also represents a significant independent code base for replicating results from other simulation platforms. The PhysiCell source code, examples, documentation, and support are available under the BSD license at http://PhysiCell.MathCancer.org and http://PhysiCell.sf.net.