Modeling cellular deformations using the level set formalism

Yang, Liu; Effler, Janet C.; Kutscher, Brett; Sullivan, Sarah E.; Robinson, Douglas N.; Iglesias, Pablo A.

doi:10.1186/1752-0509-2-68

Cited by 85 publications

(87 citation statements)

References 52 publications

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“…If we normalize the friction coefficient between the cell and its substrate to 1, then the following level set equation describes the dynamics of the cell boundary [31]:…”

Section: Example: Cell Polarization Via An Actin-myosion Systemmentioning

confidence: 99%

“…More precisely, the surface can be represented by the zero level set of the solution to the level set equation. Several level set equation-based models that describe surface motions are used in computer vision [19], computer graphics [11], multi-phase physics [23] and spatial systems biology [31]. One of the most important basic level set equation models is a Hamilton-Jacobi equation that describes the evolution of the surface in the normal direction of its boundary with the speed profile distributed over the boundary [25,22]: it models, for example, the balance between the adhesion and the normal protrusion (or contraction) forces in a biological cell boundary [31,26].…”

Section: Introductionmentioning

confidence: 99%

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Regularization-based identification for level set equations

Yang

Tomlin

2013

52nd IEEE Conference on Decision and Control

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An optimization-based method for identifying the speed profile of a moving surface from image data is studied. If the dynamic surface motion is modeled by a level set equation, the identification problem can be formulated as an optimization problem constrained with the level set equation whose (viscosity) solution, in general, has kinks. The non-differentiable solution prevents us from having a bounded gradient of the cost function of the optimization problem. To overcome this difficulty, we develop a novel identification approach using a regularized level set equation. The regularization guarantees the differentiability of the cost function and the boundedness of the gradient. Using numerical optimization techniques with the adjoint-based gradient, we solve the identification problem. We perform a numerical test to validate that the solution of an optimization problem with a regularized level set equation converges to the solution of the same optimization problem with an unregularized level set equation as the regularization factor tends to zero. The performance and usefulness of the method are demonstrated by a biological example in which we estimate the forces (per density) of actin and myosin in cell polarization.

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“…If we normalize the friction coefficient between the cell and its substrate to 1, then the following level set equation describes the dynamics of the cell boundary [31]:…”

Section: Example: Cell Polarization Via An Actin-myosion Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regularization-based identification for level set equations

Yang

Tomlin

2013

52nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

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“…1 B) (17). Upon application of a fixed pressure by micropipette aspiration, the cell will deform and protrude a certain length, L p , into the pipette (Fig.…”

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confidence: 99%

“…Upon application of a fixed pressure by micropipette aspiration, the cell will deform and protrude a certain length, L p , into the pipette (Fig. 1 B) (17). In wild-type and filaminnull Dictyostelium, damper g b approaches zero, so the initial deformation is largely elastic and happens in <1 s (Fig.…”

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confidence: 99%

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Mechanochemical Signaling Directs Cell-Shape Change

Schiffhauer

Robinson

2017

Biophysical Journal

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For specialized cell function, as well as active cell behaviors such as division, migration, and tissue development, cells must undergo dynamic changes in shape. To complete these processes, cells integrate chemical and mechanical signals to direct force production. This mechanochemical integration allows for the rapid production and adaptation of leading-edge machinery in migrating cells, the invasion of one cell into another during cell-cell fusion, and the force-feedback loops that ensure robust cytokinesis. A quantitative understanding of cell mechanics coupled with protein dynamics has allowed us to account for furrow ingression during cytokinesis, a model cell-shape-change process. At the core of cell-shape changes is the ability of the cell's machinery to sense mechanical forces and tune the force-generating machinery as needed. Force-sensitive cytoskeletal proteins, including myosin II motors and actin cross-linkers such as a-actinin and filamin, accumulate in response to internally generated and externally imposed mechanical stresses, endowing the cell with the ability to discern and respond to mechanical cues. The physical theory behind how these proteins display mechanosensitive accumulation has allowed us to predict paralogspecific behaviors of different cross-linking proteins and identify a zone of optimal actin-binding affinity that allows for mechanical stress-induced protein accumulation. These molecular mechanisms coupled with the mechanical feedback systems ensure robust shape changes, but if they go awry, they are poised to promote disease states such as cancer cell metastasis and loss of tissue integrity.The concept ''form begets function begets form'' provides an excellent foundation for understanding the behavior of biological systems. Even specialized cells, the smallest unit of complex living systems, perform all of the necessary functions of an organism by assuming distinct shapes, mechanical properties, and physical behaviors. Different cell types use a common set of cytoskeletal elements to provide precise physical support for their distinct functions. For example, red blood cells and neurons have very different shapes that allow them to perform their specific roles. However, they both utilize alternating patterns of actin and spectrin to form cortices with appropriate viscous and elastic properties, albeit in different structural arrangements. Perturbations to this structural network cause a breakdown in the mechanical properties, or the form, of these cells, which inhibits cell function (1,2).Fascinatingly, the physical properties of cells are both determined and acted upon by the cytoskeletal apparatus. Cells are capable of modifying their own physical properties and driving changes in cell shape in response to internal and external chemical and mechanical stimuli. These modifications occur through the remodeling of the cell cortex, the network of cytoskeletal proteins directly under the plasma membrane. Much progress has been made recently in deciphering how chemical signa...

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A review of models of fluctuating protrusion and retraction patterns at the leading edge of motile cells

2012

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A characteristic feature of motile cells as they undergo a change in motile behavior is the development of fluctuating exploratory motions of the leading edge, driven by actin polymerization. We review quantitative models of these protrusion and retraction phenomena. Theoretical studies have been motivated by advances in experimental and computational methods that allow controlled perturbations, single molecule imaging, and analysis of spatiotemporal correlations in microscopic images. To explain oscillations and waves of the leading edge, most theoretical models propose nonlinear interactions and feedback mechanisms among different components of the actin cytoskeleton system. These mechanisms include curvature-sensing membrane proteins, myosin contraction, and autocatalytic biochemical reaction kinetics. We discuss how the combination of experimental studies with modeling promises to quantify the relative importance of these biochemical and biophysical processes at the leading edge and to evaluate their generality across cell types and extracellular environments. V C 2012 Wiley Periodicals, Inc Key Words: actin, cell motility, lamellipodium dynamics, mathematical modeling, single molecule microscopy Introduction E ukaryotic cell motility is driven by actin protrusions at the leading edge, formation of adhesions, and myosin-driven contraction at the trailing edge. Understanding the function of these three motility components has inspired a huge body of biological, biochemical, and modeling work [Mogilner and Keren, 2009;Pollard and Cooper, 2009;Carlsson, 2010a;Watanabe, 2010]. Prior work has addressed many of the underlying molecular mechanisms of protrusion, adhesion, and retraction, as well as their combined influence in determining cell shape and motion. Many works have also examined the mechanisms of control of cell motility: how cells respond to stimuli in order to reorganize their cytoskeleton and move along a preferred direction [Jilkine and Edelstein-Keshet, 2010].In this review, we focus on a dynamical pattern of motile cells that involves cycles of protrusion-and-retraction (CPAR) of the leading edge. This type of motion consists of back and forth movements of the leading edge over a few microns over a few minutes. It is usually more pronounced as cells change polarization states, for example, during cell spreading or cell stimulation (Fig. 1). CPAR dynamics occur reproducibly in experiments and are easy to quantify as compared to other more complex features of cell shape. Statistical analysis of these repeated motions can provide insight into the regulatory mechanisms of motility. For this reason, in addition to novel experimental work, they have motivated mathematical and computational modeling studies and development of image analysis methods. We discuss some of the conceptual contributions of these quantitative studies to cell motility research and challenges for future feedback between experiment and theory.One of the best examples of CPAR occurs during cell spreading [Dobereiner et al., , 2006Du...

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Modeling cellular deformations using the level set formalism

Cited by 85 publications

References 52 publications

Regularization-based identification for level set equations

Regularization-based identification for level set equations

Mechanochemical Signaling Directs Cell-Shape Change

A review of models of fluctuating protrusion and retraction patterns at the leading edge of motile cells

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