Quantitative analysis and modeling probe polarity establishment in C. elegans embryos

Order from chaos: cellular asymmetries explained with modelling

Molecules inside cells are subject to physical forces and undergo biochemical interactions, continuously changing their physical properties and dynamics. Despite this, cells achieve highly ordered molecular patterns that are crucial to regulate various cellular functions and to specify cell fate. In the Caenorhabditis elegans one-cell embryo, protein asymmetries are established in the narrow time window of a cell division. What are the mechanisms that allow molecules to establish asymmetries, defying the randomness imposed by Brownian motion? Mathematical and computational models have paved the way to the understanding of protein dynamics up to the 'single-molecule level' when resolution represents an issue for precise experimental measurements. Here we review the models that interpret cortical and cytoplasmic asymmetries in the one-cell C. elegans embryo.

A balance between antagonizing PAR proteins specifies the pattern of asymmetric and symmetric divisions in C. elegans embryogenesis

Coordination between cell differentiation and proliferation during development requires the balance between asymmetric and symmetric modes of cell division. However, the cellular intrinsic cue underlying the choice between these two division modes remains elusive. Here, we show evidence in Caenorhabditis elegans that the invariable lineage of the division modes is specified by the balance between antagonizing complexes of partitioning-defective (PAR) proteins. By uncoupling unequal inheritance of PAR proteins from that of fate determinants during cell division, we demonstrate that changes in the balance between PAR-2 and PAR-6 can be sufficient to re-program the division modes from symmetric to asymmetric and vice versa in two daughter cells. The division mode adopted occurs independently of asymmetry in cytoplasmic fate determinants, cell-size asymmetry, and cell-cycle asynchrony between sister cells. We propose that the balance between PAR proteins represents an intrinsic self-organizing cue for the specification of the two division modes during development.

Describing the movement of molecules in reduced-dimension models

When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is restricted to the reduced dimension, changing the nature of molecular movement. This change in molecular movement can lead to quantitatively and even qualitatively different results in the full and reduced systems. Within this manuscript we discuss the condition under which restricted molecular movement in reduced-dimension models accurately approximates molecular movement in the full system. For those systems which do not satisfy the condition, we present a general method for approximating unrestricted molecular movement in reduced-dimension models. We will derive a mathematically robust, finite difference method for solving the 2D diffusion equation within a 1D reduced-dimension model. The methods described here can be used to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.

Stoichiometric interactions explain spindle dynamics and scaling across 100 million years of nematode evolution

The spindle shows remarkable diversity, and changes in an integrated fashion, as cells vary over evolution. Here, we provide a mechanistic explanation for variations in the first mitotic spindle in nematodes. We used a combination of quantitative genetics and biophysics to rule out broad classes of models of the regulation of spindle length and dynamics, and to establish the importance of a balance of cortical pulling forces acting in different directions. These experiments led us to construct a model of cortical pulling forces in which the stoichiometric interactions of microtubules and force generators (each force generator can bind only one microtubule), is key to explaining the dynamics of spindle positioning and elongation, and spindle final length and scaling with cell size. This model accounts for variations in all the spindle traits we studied here, both within species and across nematode species spanning over 100 million years of evolution.

Guiding self-organized pattern formation in cell polarity establishment

Spontaneous pattern formation in Turing systems relies on feedback. Patterns in cells and tissues however often do not form spontaneously, but are under control of upstream pathways that provide molecular guiding cues. The relationship between guiding cues and feedback in controlled biological pattern formation remains unclear. We explored this relationship during cell polarity establishment in the one-cell-stage C. elegans embryo. We quantified the strength of two feedback systems that operate during polarity establishment, feedback between polarity proteins and the actomyosin cortex, and mutual antagonism amongst polarity proteins. We characterized how these feedback systems are modulated by guiding cues from the centrosome. By coupling a mass-conserved Turing-like reaction-diffusion system for polarity proteins to an active gel description of the actomyosin cortex, we reveal a transition point beyond which feedback ensures self-organized polarization even when cues are removed. Notably, the baton is passed from a guide-dominated to a feedback-dominated regime significantly beyond this transition point, which ensures robustness. Together, this reveals a general criterion for controlling biological pattern forming systems: feedback remains subcritical to avoid unstable behaviour, and molecular guiding cues drive the system beyond a transition point for pattern formation.

Uncovering the balance of forces driving microtubule aster migration in C. elegans zygotes

Microtubule asters must be positioned precisely within cells. How forces generated by molecular motors such as dynein are integrated in space and time to enable such positioning remains unclear. In particular, whereas aster movements depend on the drag caused by cytoplasm viscosity, in vivo drag measurements are lacking, precluding a thorough understanding of the mechanisms governing aster positioning. Here, we investigate this fundamental question during the migration of asters and pronuclei in C. elegans zygotes, a process essential for the mixing of parental genomes. Detailed quantification of these movements using the female pronucleus as an in vivo probe establish that the drag coefficient of the male-asters complex is approximately five times that of the female pronucleus. Further analysis of embryos lacking cortical dynein, the connection between asters and male pronucleus, or the male pronucleus altogether, uncovers the balance of dynein-driven forces that accurately position microtubule asters in C. elegans zygotes.

Microtubule asters are positioned precisely within cells by forces generated by molecular motors, but it is unclear how these are integrated in space and time. Here the authors perform in vivo drag measurements and genetic manipulations to determine the balance of forces that position microtubule asters in C. elegans zygotes.

The PAR proteins: from molecular circuits to dynamic self-stabilizing cell polarity

PAR proteins constitute a highly conserved network of scaffolding proteins, adaptors and enzymes that form and stabilize cortical asymmetries in response to diverse inputs. They function throughout development and across the metazoa to regulate cell polarity. In recent years, traditional approaches to identifying and characterizing molecular players and interactions in the PAR network have begun to merge with biophysical, theoretical and computational efforts to understand the network as a pattern-forming biochemical circuit. Here, we summarize recent progress in the field, focusing on recent studies that have characterized the core molecular circuitry, circuit design and spatiotemporal dynamics. We also consider some of the ways in which the PAR network has evolved to polarize cells in different contexts and in response to different cues and functional constraints.

Self-organization and advective transport in the cell polarity formation for asymmetric cell division

Anterior-Posterior (AP) polarity formation of cell membrane proteins plays a crucial role in determining cell asymmetry, which depends not only on the several genetic process but also biochemical and biophysical interactions. The mechanism of AP formation of Caenorhabditis elegans embryo is characterized into the three processes: (i) membrane association and dissociation of posterior and anterior proteins, (ii) diffusion into the membrane and cytosol, and (iii) active cortical and cytoplasmic flows induced by the contraction of the acto-myosin cortex. We explored the mechanism of symmetry breaking and AP polarity formation using self-recruitment model of posterior proteins. We found that the AP polarity pattern is established over wide range in the total mass of polarity proteins and the diffusion ratio in the cytosol to the membrane. We also showed that the advective transport in both membrane and cytosol during the establishment phase affects optimal time interval of establishment and positioning of the posterior domain, and plays a role to increase the robustness in the AP polarity formation by reducing the number of posterior domains for the sensitivity of initial conditions. We also demonstrated that a proper ratio of the total mass to cell size robustly regulate the length scale of the posterior domain.

CAST: An automated segmentation and tracking tool for the analysis of transcriptional kinetics from single-cell time-lapse recordings

Fluorescence and bioluminescence time-lapse imaging allows to investigate a vast range of cellular processes at single-cell or even subcellular resolution. In particular, time-lapse imaging can provide uniquely detailed information on the fine kinetics of transcription, as well as on biological oscillations such as the circadian and cell cycles. However, we face a paucity of automated methods to quantify time-lapse imaging data with single-cell precision, notably throughout multiple cell cycles. We developed CAST (Cell Automated Segmentation and Tracking platform) to automatically and robustly detect the position and size of cells or nuclei, quantify the corresponding light signals, while taking into account both cell divisions (lineage tracking) and migration events. We present here how CAST analyzes bioluminescence data from a short-lived transcriptional luciferase reporter. However, our flexible and modular implementation makes it easily adaptable to a wide variety of time-lapse recordings. We exemplify how CAST efficiently quantifies single-cell gene expression over multiple cell cycles using mouse NIH3T3 culture cells with a luminescence expression driven by the Bmal1 promoter, a central gene of the circadian oscillator. We further illustrate how such data can be used to quantify transcriptional bursting in conditions of lengthened circadian period, revealing thereby remarkably similar bursting signature compared to the endogenous circadian condition despite marked period lengthening. In summary, we establish CAST as novel tool for the efficient segmentation, signal quantification, and tracking of time-lapse images from mammalian cell culture.