Using fluctuation analysis to establish causal relations between cellular events without experimental perturbation

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.

Filopodial protrusion driven by density-dependent Ena-TOCA-1 interactions

Filopodia are narrow actin-rich protrusions with important roles in neuronal development where membrane-binding adaptor proteins, such as I-BAR- and F-BAR-domain-containing proteins, have emerged as upstream regulators that link membrane interactions to actin regulators such as formins and proteins of the Ena/VASP family. Both the adaptors and their binding partners are part of diverse and redundant protein networks that can functionally compensate for each other. To explore the significance of the F-BAR domain-containing neuronal membrane adaptor TOCA-1 (also known as FNBP1L) in filopodia we performed a quantitative analysis of TOCA-1 and filopodial dynamics in Xenopus retinal ganglion cells, where Ena/VASP proteins have a native role in filopodial extension. Increasing the density of TOCA-1 enhances Ena/VASP protein binding in vitro, and an accumulation of TOCA-1, as well as its coincidence with Ena, correlates with filopodial protrusion in vivo. Two-colour single-molecule localisation microscopy of TOCA-1 and Ena supports their nanoscale association. TOCA-1 clusters promote filopodial protrusion and this depends on a functional TOCA-1 SH3 domain and activation of Cdc42, which we perturbed using the small-molecule inhibitor CASIN. We propose that TOCA-1 clusters act independently of membrane curvature to recruit and promote Ena activity for filopodial protrusion.

Quantifying the phenotypic information in mRNA abundance

Quantifying the dependency between mRNA abundance and downstream cellular phenotypes is a fundamental open problem in biology. Advances in multimodal single‐cell measurement technologies provide an opportunity to apply new computational frameworks to dissect the contribution of individual genes and gene combinations to a given phenotype. Using an information theory approach, we analyzed multimodal data of the expression of 83 genes in the Ca²⁺ signaling network and the dynamic Ca²⁺ response in the same cell. We found that the overall expression levels of these 83 genes explain approximately 60% of Ca²⁺ signal entropy. The average contribution of each single gene was 17%, revealing a large degree of redundancy between genes. Using different heuristics, we estimated the dependency between the size of a gene set and its information content, revealing that on average, a set of 53 genes contains 54% of the information about Ca²⁺ signaling. Our results provide the first direct quantification of information content about complex cellular phenotype that exists in mRNA abundance measurements.

Granger-causal inference of the lamellipodial actin regulator hierarchy by live cell imaging without perturbation

Many cell regulatory systems implicate nonlinearity and redundancy among components. The regulatory network governing lamellipodial and lamellar actin structures is prototypical of such a system, containing tens of actin-nucleating and -modulating molecules with functional overlap and feedback loops. Due to instantaneous and long-term compensation, phenotyping the system response to perturbation provides limited information on the roles the targeted component plays in the unperturbed system. Accordingly, how individual actin regulators contribute to lamellipodial dynamics remains ambiguous. Here, we present a perturbation-free reconstruction of cause-effect relations among actin regulators by applying Granger-causal inference to constitutive image fluctuations that indicate regulator recruitment as a proxy for activity. Our analysis identifies distinct zones of actin regulator activation and of causal effects on filament assembly and delineates actin-dependent and actin-independent regulator roles in controlling edge motion. We propose that edge motion is driven by assembly of two independently operating actin filament systems.

Leading edge maintenance in migrating cells is an emergent property of branched actin network growth

Animal cell migration is predominantly driven by the coordinated, yet stochastic, polymerization of thousands of nanometer-scale actin filaments across micron-scale cell leading edges. It remains unclear how such inherently noisy processes generate robust cellular behavior. We employed high-speed imaging of migrating neutrophil-like HL-60 cells to explore the fine-scale shape fluctuations that emerge and relax throughout the process of leading edge maintenance. We then developed a minimal stochastic model of the leading edge that reproduces this stable relaxation behavior. Remarkably, we find lamellipodial stability naturally emerges from the interplay between branched actin network growth and leading edge shape – with no additional feedback required – based on a synergy between membrane-proximal branching and lateral spreading of filaments. These results thus demonstrate a novel biological noise-suppression mechanism based entirely on system geometry. Furthermore, our model suggests that the Arp2/3-mediated ~70–80° branching angle optimally smooths lamellipodial shape, addressing its long-mysterious conservation from protists to mammals.

In every human cell, there are tens of millions of proteins which work together to control everything from the cell’s shape to its behavior. One of the most abundant proteins is actin, which organizes itself into filaments that mechanically support the cell and help it to move.

These filaments are very dynamic, with individual actin molecules constantly being added or removed. This allows the cell to build large structures with distinct shapes and properties. Many motile cells, for example, have a structure called a lamellipodium which protrudes at their ‘leading edge’ and pushes them forward. The lamellipodium has a very robust shape that does not vary much between different cell types, or change significantly as cells migrate. But how the tens of thousands of actin molecules inside the lamellipodium organize themselves into this large, stable structure is not fully understood.

To investigate, Garner and Theriot used high-speed video microscopy to track the shape of human cells cultured in the laboratory. As the cells crawled along a glass surface, their leading edge undulated like strings being plucked on a guitar. A computer simulation showed that these ripples can be caused by filaments randomly adding and removing actin molecules.

While these random movements could destabilize the structure of the leading edge, the simulation suggests that another aspect of actin filament growth smooths out any fluctuations in the lamellipodium’s shape. Actin networks in the lamellipodium have a branched configuration, with new strands emerging off each other at an angle like branches in a tree. Garner and Theriot found that the specific angle in which new filaments are added smooths out the lamellipodium’s shape, which may explain why this geometry has persisted throughout evolution.

These findings suggest that the way in which actin filaments join together helps to maintain the shape of large cellular structures. In the future, scientists could use this design principle to build molecular machines that can self-organize into microstructures. These engineered constructs could be used to modulate the activity of living cells that have been damaged by disease.

Morphogenesis: Guiding Embryonic Development with Light

Embryonic development is controlled by dynamic signaling systems that are translated into patterns of gene expression. Optogenetics has now been used to rescue genetic loss of Drosophila terminal patterning, bringing us a step closer to reconstruct morphogenesis synthetically.

Dynamics as a cause for the nanoscale organization of the genome

Chromatin ‘blobs’ were recently identified by live super-resolution imaging of labeled nucleosomes as pervasive but fleeting structural entities. However, the mechanisms leading to the formation of these blobs and their functional implications are unknown. We explore here whether causal relationships exist between parameters that characterize the chromatin blob dynamics and structure, by adapting a framework for spatio-temporal Granger-causality inference. Our analysis reveals that chromatin dynamics is a key determinant for both blob area and local density. Such causality, however, could be demonstrated only in 10–20% of the nucleus, suggesting that chromatin dynamics and structure at the nanometer scale are dominated by stochasticity. We show that the theory of active semiflexible polymers can be invoked to provide potential mechanisms leading to the organization of chromatin into blobs. Our results represent a first step toward elucidating the mechanisms that govern the dynamic and stochastic organization of chromatin in the cell nucleus.

Probing the Functional Role of Physical Motion in Development

Spatiotemporal organization during development has frequently been proposed to be explainable by reaction-transport models, where biochemical reactions couple to physical motion. However, whereas genetic tools allow causality of molecular players to be dissected via perturbation experiments, the functional role of physical transport processes, such as diffusion and cytoplasmic streaming, frequently remains untestable. This Perspective explores the challenges of validating reaction-transport hypotheses and highlights new opportunities provided by perturbation approaches that specifically target physical transport mechanisms. Using these methods, experimental physics may begin to catch up with molecular biology and find ways to test roles of diffusion and flows in development.

Discovery of functional interactions among actin regulators by analysis of image fluctuations in an unperturbed motile cell system

Cell migration is driven by propulsive forces derived from polymerizing actin that pushes and extends the plasma membrane. The underlying actin network is constantly undergoing adaptation to new mechano-chemical environments and intracellular conditions. As such, mechanisms that regulate actin dynamics inherently contain multiple feedback loops and redundant pathways. Given the highly adaptable nature of such a system, studies that use only perturbation experiments (e.g. knockdowns, overexpression, pharmacological activation/inhibition, etc.) are challenged by the nonlinearity and redundancy of the pathway. In these pathway configurations, perturbation experiments at best describe the function(s) of a molecular component in an adapting (e.g. acutely drug-treated) or fully adapted (e.g. permanent gene silenced) cell system, where the targeted component now resides in a non-native equilibrium. Here, we propose how quantitative live-cell imaging and analysis of constitutive fluctuations of molecular activities can overcome these limitations. We highlight emerging actin filament barbed-end biology as a prime example of a complex, nonlinear molecular process that requires a fluctuation analytic approach, especially in an unperturbed cellular system, to decipher functional interactions of barbed-end regulators, actin polymerization and membrane protrusion.This article is part of the theme issue 'Self-organization in cell biology'.

Image-based spatiotemporal causality inference for protein signaling networks

Motivation

Efforts to model how signaling and regulatory networks work in cells have largely either not considered spatial organization or have used compartmental models with minimal spatial resolution. Fluorescence microscopy provides the ability to monitor the spatiotemporal distribution of many molecules during signaling events, but as of yet no methods have been described for large scale image analysis to learn a complex protein regulatory network. Here we present and evaluate methods for identifying how changes in concentration in one cell region influence concentration of other proteins in other regions.

Results

Using 3D confocal microscope movies of GFP-tagged T cells undergoing costimulation, we learned models containing putative causal relationships among 12 proteins involved in T cell signaling. The models included both relationships consistent with current knowledge and novel predictions deserving further exploration. Further, when these models were applied to the initial frames of movies of T cells that had been only partially stimulated, they predicted the localization of proteins at later times with statistically significant accuracy. The methods, consisting of spatiotemporal alignment, automated region identification, and causal inference, are anticipated to be applicable to a number of biological systems.

Availability and implementation

The source code and data are available as a Reproducible Research Archive at http://murphylab.cbd.cmu.edu/software/2017_TcellCausalModels/

Exploiting Bioprocessing Fluctuations to Elicit the Mechanistics of De Novo Lipogenesis in Yarrowia lipolytica

Despite substantial achievements in elucidating the metabolic pathways of lipogenesis, a mechanistic representation of lipid accumulation and degradation has not been fully attained to-date. Recent evidence suggests that lipid accumulation can occur through increases of either the cytosolic copy-number of lipid droplets (LDs), or the LDs size. However, the prevailing phenotype, or how such mechanisms pertain to lipid degradation remain poorly understood. To address this shortcoming, we employed the-recently discovered-innate bioprocessing fluctuations in Yarrowia lipolytica, and performed single-cell fluctuation analysis using optical microscopy and microfluidics that generate a quasi-time invariant microenvironment. We report that lipid accumulation at early stationary phase in rich medium is substantially more likely to occur through variations in the LDs copy-number, rather than the LDs size. Critically, these mechanistics are also preserved during lipid degradation, as well as upon exposure to a protein translation inhibitor. The latter condition additionally induced a lipid accumulation phase, accompanied by the downregulation of lipid catabolism. Our results enable an in-depth mechanistic understanding of lipid biogenesis, and expand longitudinal single-cell fluctuation analyses from gene regulation to metabolism.

Diagonally Scanned Light-Sheet Microscopy for Fast Volumetric Imaging of Adherent Cells

In subcellular light-sheet fluorescence microscopy (LSFM) of adherent cells, glass substrates are advantageously rotated relative to the excitation and emission light paths to avoid glass-induced optical aberrations. Because cells are spread across the sample volume, three-dimensional imaging requires a light-sheet with a long propagation length, or rapid sample scanning. However, the former degrades axial resolution and/or optical sectioning, while the latter mechanically perturbs sensitive biological specimens on pliant biomimetic substrates (e.g., collagen and basement membrane). Here, we use aberration-free remote focusing to diagonally sweep a narrow light-sheet along the sample surface, enabling multicolor imaging with high spatiotemporal resolution. Further, we implement a dithered Gaussian lattice to minimize sample-induced illumination heterogeneities, significantly improving signal uniformity. Compared with mechanical sample scanning, we drastically reduce sample oscillations, allowing us to achieve volumetric imaging at speeds of up to 3.5 Hz for thousands of Z-stacks. We demonstrate the optical performance with live-cell imaging of microtubule and actin cytoskeletal dynamics, phosphoinositide signaling, clathrin-mediated endocytosis, polarized blebbing, and endocytic vesicle sorting. We achieve three-dimensional particle tracking of clathrin-associated structures with velocities up to 4.5 μm/s in a dense intracellular environment, and show that such dynamics cannot be recovered reliably at lower volumetric image acquisition rates using experimental data, numerical simulations, and theoretical modeling.

Quantitative Multiscale Cell Imaging in Controlled 3D Microenvironments

The microenvironment determines cell behavior, but the underlying molecular mechanisms are poorly understood because quantitative studies of cell signaling and behavior have been challenging due to insufficient spatial and/or temporal resolution and limitations on microenvironmental control. Here we introduce microenvironmental selective plane illumination microscopy (meSPIM) for imaging and quantification of intracellular signaling and submicrometer cellular structures as well as large-scale cell morphological and environmental features. We demonstrate the utility of this approach by showing that the mechanical properties of the microenvironment regulate the transition of melanoma cells from actin-driven protrusion to blebbing, and we present tools to quantify how cells manipulate individual collagen fibers. We leverage the nearly isotropic resolution of meSPIM to quantify the local concentration of actin and phosphatidylinositol 3-kinase signaling on the surfaces of cells deep within 3D collagen matrices and track the many small membrane protrusions that appear in these more physiologically relevant environments.

Deconvolution-free Subcellular Imaging with Axially Swept Light Sheet Microscopy

The use of propagation invariant Bessel beams has enabled high-resolution subcellular light sheet fluorescence microscopy. However, the energy within the concentric side lobe structure of Bessel beams increases significantly with propagation length, generating unwanted out-of-focus fluorescence that enforces practical limits on the imaging field of view size. Here, we present a light sheet fluorescence microscope that achieves 390 nm isotropic resolution and high optical sectioning strength (i.e., out-of-focus blur is strongly suppressed) over large field of views, without the need for structured illumination or deconvolution-based postprocessing. We demonstrate simultaneous dual-color, high-contrast, and high-dynamic-range time-lapse imaging of migrating cells in complex three-dimensional microenvironments, three-dimensional tracking of clathrin-coated pits, and long-term imaging spanning >10 h and encompassing >2600 time points.