Calling heads from tails: the role of mathematical modeling in understanding cell polarization

doi:10.1016/j.ceb.2009.01.001

Current Opinion in Cell Biology

Volume 21, Issue 1, February 2009, Pages 74-81

https://doi.org/10.1016/j.ceb.2009.01.001 Get rights and content

Theorists have long speculated on the mechanisms driving directed and spontaneous cell polarization. Recently, experimentalists have uncovered many of the mechanisms underlying polarization, enabling these models to be directly tested. In the process, they have demonstrated the explanatory and predictive value of these models and, at the same time, uncovered additional complexities not currently explained by them. In this review, we discuss some of main theories regarding cell polarization and highlight how the intersection of mathematical and experimental biology has yielded new insights into these mechanisms in the case of budding yeast and eukaryotic chemotaxis.

Introduction

Cells are not static entities but rather dynamically reorganize in response to internal and external cues. The ability to spontaneously form specialized domains of regulatory and structural elements is crucial to the function of many cellular processes including differentiation, communication, and directed migration [1]. While cell polarization has been well documented, the driving mechanism has proved challenging to understand. Namely, how does a cell transition from homogeneous state to a heterogeneous, asymmetric one? And, as one author elegantly put it “how are heads made different from tails and everything in between?” [2]. Theorists have long puzzled over this question and proposed a number of potential models to address it. In the past decade, substantial progress has been made toward understanding the mechanisms involved in different polarization processes. These results have enabled various mathematical models to be tested and also uncovered new phenomena lacking in them. The aim of this review is to briefly highlight some of these theories and illustrate how the intersection between mathematical modeling and experimentation has led to new insights into the mechanisms behind cell polarization.

Section snippets

Theoretical foundations

Theorists employ at least two approaches when constructing models of biological processes. In the bottom-up approach, modeling has been used to test whether a proposed set of biochemical reactions is capable of generating a specific response, such as polarization; if not, then this approach can be used to explore what reactions are possibly missing. Alternatively, in a top-down approach, a general mechanism is proposed and then various molecules and reactions are assigned roles within this

Polarization in budding yeast

A classic model for polarization is the budding yeast Saccharomyces cerevisiae [9]. During the cell cycle, yeast transitions from uniform to polarized growth in order to build a bud. A key step in initiating polarization involves the clustering of active, GTP-bound Cdc42 to the membrane [10]. Cdc42 then directs the nucleation of actin cables, which serve as conduits for delivering the necessary components for bud formation [11, 12]. The transition to and maintenance of the polarized state is

Polarization and gradient sensing

Many kinds of cells are able to migrate in response to external cues [21, 22]. For example, neutrophils and the slime mold Dictyostelium discoideum are able to detect shallow gradients of chemoattractants and crawl toward the source of these chemicals [23]. Before stimulation with chemoattractant, these cells exist in an unpolarized, non-motile state. When stimulated, they migrate by extending pseudopods at their front and contracting at their rear. This transition, from an unpolarized state to

Conclusions

We are now in a position to experimentally test many competing models of directed and spontaneous cell polarization. For theorists, the experimental results so far have been very encouraging, as they have validated many key predictions from their models. At the same time, these results have uncovered new behaviors and mechanisms, requiring new concepts and models that will keep theorists busy for the foreseeable future. For experimentalists, mathematical models offer a systematic framework for

References and recommended reading

Papers of particular interest, published within the period of review, have been highlighted as:

• of special interest
•• of outstanding interest

Acknowledgements

We thank members of the Merrimack Pharmaceuticals and the Rao lab for helpful comments. CVR is supported by the National Institutes of Health grant GM083601.

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2021, Encyclopedia of Biological Chemistry: Third Edition
Chemotaxis is the migration of a cell toward a chemical signal. Ameboid cell motion is characterized by high speeds, low adhesion to substrates, and large deformability in cell shape. Here we focus on the biochemical signaling pathways and motion of two heavily studied ameboid cell systems: Dictyostelium discoideum and neutrophils. In order to migrate toward a chemical signal, these cells must be able to accurately sense small chemical gradients across their periphery and organize a polarized cytoskeletal response. This process begins by a chemoattractant binding to a transmembrane receptor, initiating a signaling cascade that localizes specific gradient-sensing molecules to the up- and down-gradient ends of the cell. In the most well-characterized pathway, the cell localizes Ras and phosphatidylinositol 3 kinase at the up-gradient end, leading to conversion of phosphatidylinositol-4,5-biphosphate (PIP₂) into phosphatidylinositol-3,4,5-triphosphate (PIP₃). PIP₃ then recruits various effectors, causing localized actin polymerization and pseudopod protrusion. Likewise, at the down-gradient end of the cell, PTEN is recruited, recycling PIP₃ back to PIP₂, and suppressing lateral pseudopod formation. In addition, actomyosin contraction leads to retraction at the cell back. Understanding the dynamics of the gradient-sensing and polarization process is aided by the use of several classes of mathematical models, which determine whether experimentally observed cell behaviors can be entirely understood using known molecules and their spatiotemporal dynamics.
Global existence for a bulk/surface model for active-transport-induced polarisation in biological cells
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Citation Excerpt :
A distinct and well-documented mechanism [34,35,19] is a positive feedback between membrane-recruited signalling proteins and the cytoskeleton. The latter is built from actin monomers that polymerise to form long filaments: activated Cdc42 directs actin polymerisation at the membrane, and, in turn, Cdc42 is actively transported along the cytoskeleton filaments towards the membrane, leading to a positive feedback loop [25]. Such active transport relies on a permanent energy input from ATP hydrolysis, and hence constitutes an example of an out-of-equilibrium system.
We consider a coupled bulk/surface model for advection and diffusion of interacting chemical species in biological cells. Specifically, we consider a signalling protein that can exist in both a cytosolic and a membrane-bound state, along with a variable that gives a coarse-grained description of the cytoskeleton. The main focus of our work is on the well-posedness of the model, whereby the coupling at the boundary is the main source of analytical difficulty. A priori $L^{p}$ -estimates, together with classical Schauder theory, deliver global existence of classical solutions for small data on bounded, Lipschitz domains. For two physically reasonable regularised versions of the boundary coupling, we are able to prove global existence of solutions for arbitrary data. In addition, we prove the existence of a family of steady-state solutions of the main model which are parametrised by the total mass of the membrane-bound signal molecule.
Mechanochemical Interplay Drives Polarization in Cellular and Developmental Systems
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Stochastic mechano-chemical kinetics of molecular motors: A multidisciplinary enterprise from a physicist's perspective
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Polarization leads to the formation of cell protrusions which are used by a wide variety of cells for their motility. The “universal” features of polarized cells (i.e., features shared by most of the polarized cells) have been listed recently [995]. Establishment, as well as the subsequent maintenance, of cell polarity depend, at least partly, on the dynamic assembly of the cytoskeletal filaments and the motor-driven transport that they support [997–1000].
A molecular motor is made of either a single macromolecule or a macromolecular complex. Just like their macroscopic counterparts, molecular motors “transduce” input energy into mechanical work. All the nano-motors considered here operate under isothermal conditions far from equilibrium. Moreover, one of the possible mechanisms of energy transduction, called Brownian ratchet, does not even have any macroscopic counterpart. But, molecular motor is not synonymous with Brownian ratchet; a large number of molecular motors execute a noisy power stroke, rather than operating as Brownian ratchet. We review not only the structural design and stochastic kinetics of individual single motors, but also their coordination, cooperation and competition as well as the assembly of multi-module motors in various intracellular kinetic processes. Although all the motors considered here execute mechanical movements, efficiency and power output are not necessarily good measures of performance of some motors. Among the intracellular nano-motors, we consider the porters, sliders and rowers, pistons and hooks, exporters, importers, packers and movers as well as those that also synthesize, manipulate and degrade “macromolecules of life”. We review mostly the quantitative models for the kinetics of these motors. We also describe several of those motor-driven intracellular stochastic processes for which quantitative models are yet to be developed. In part I, we discuss mainly the methodology and the generic models of various important classes of molecular motors. In part II, we review many specific examples emphasizing the unity of the basic mechanisms as well as diversity of operations arising from the differences in their detailed structure and kinetics. Multi-disciplinary research is presented here from the perspective of physicists.
Eukaryotic Chemotaxis
2013, Encyclopedia of Biological Chemistry: Second Edition
Chemotaxis is the migration of a cell toward a chemical signal. Amoeboid cell motion is characterized by high speeds, low adhesion to substrates, and large deformability in cell shape. Here we focus on the biochemical signaling pathways and motion of two heavily studied amoeboid cell systems: Dictyostelium discoideum and neutrophils. In order to migrate toward a chemical signal, these cells must be able to accurately sense small chemical gradients across their periphery and organize a polarized cytoskeletal response. This process begins by a chemoattractant binding to a transmembrane receptor, initiating a signaling cascade that localizes specific gradient-sensing molecules to the up- and down-gradient ends of the cell. In the most well-characterized pathway, the cell localizes Ras and phosphatidylinositol 3 kinase at the up-gradient end, leading to conversion of phosphatidylinositol-4,5-biphosphate (PIP₂) into phosphatidylinositol-3,4,5-triphosphate (PIP₃). PIP₃ then recruits various effectors, causing localized actin polymerization and pseudopod protrusion. Likewise, at the down-gradient end of the cell, PTEN is recruited, recycling PIP₃ back to PIP₂, and suppressing lateral pseudopod formation. In addition, actomyosin contraction leads to retraction at the cell back. Understanding the dynamics of the gradient-sensing and polarization process is aided by the use of several classes of mathematical models, which determine whether experimentally observed cell behaviors can be entirely understood using known molecules and their spatiotemporal dynamics.
PIP3 waves and PTEN dynamics in the emergence of cell polarity
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Citation Excerpt :
The different pathways of front to tail and tail to front transitions described here provide a framework for the analysis and modeling of mechanisms that are implicated in normal and aberrant cell motility and in changes of polarity induced by external factors such as chemoattractants (30–33).
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View full text

Calling heads from tails: the role of mathematical modeling in understanding cell polarization

Introduction

Section snippets

Theoretical foundations

Polarization in budding yeast

Polarization and gradient sensing

Conclusions

References and recommended reading

Acknowledgements

Curr Opin Microbiol

Science

EMBO J

Annu Rev Cell Dev Biol

Nat Rev Mol Cell Biol

Nat Rev Mol Cell Biol

Proc Natl Acad Sci U S A

Biophys J

PLoS Comput Biol

Cell

J Cell Biol

Dev Cell

Nat Cell Biol

Adaptation of core mechanisms to generate cell polarity

Nature

Anterior-posterior polarity in C. elegans and Drosophila—parallels and differences

Science

The chemical basis of morphogenesis

Phil Trans Roy Soc B

A theory of biological pattern formation

Kybernetik

Orientation of chemotactic cells and growth cones: models and mechanisms

J Cell Sci

Applications of a theory of biological pattern formation based on lateral inhibition

J Cell Sci

On the spontaneous emergence of cell polarity

Nature

Wave-pinning and cell polarity from a bistable reaction-diffusion system

Biophys J

Central roles of small GTPases in the development of cell polarity in yeast and beyond

Microbiol Mol Biol Rev

Polarization of cell growth in yeast

J Cell Sci