Cell Movement - Zooming In

Cell Movement - Zooming In

Single Cell Movement

Understanding the Lamellipodium

Cell Movement

Zooming In

A. M., D. Oelz, C. Schmeiser , N. Sfakianakis, An extended Filament Based Lamellipodium Model produces various moving cell shapes in the presence of chemotactic signals.

Journal of Theoretical Biology, 382 (2015), pp. 244-258

A. M., D. Oelz, C. Schmeiser, N. Sfakianakis, Numerical treatment of the Filament Based Lamellipodium Model, Modeling Cellular Systems, Springer, (2016)

Angelika Manhart

Courant Institute, New York University

A.M. and C. Schmeiser, Decay to equilibrium of the filament end density along the leading edge of the lamellipodium, Journal of Mathematical Biology (2016), online first

The Filament Based Lamellipodium Model

Joint work with: C. Schmeiser, N. Sfakianakis, D. Ölz and S. Hirsch

S. Hirsch, A. M., C. Schmeiser, Mathematical modeling of myosin induced bistability of lamellipodial fragments, Journal of Mathematical Biology (2016), online first.

New York, 23. March, 2017

Michael Sixt, Vic Small

Jan Müller, Maria Nemethova

Biological Collaborators:

(IST, IMBA)

Original Model

Components

Actin filaments are polar with a fast polymerizing (plus) end

Filament Properties

I'm a fish cell

Polymeric Actin Filaments

Resistance to bending

Filaments are inextensible

Cross-linkers (e.g. FILAMIN) give stability

Adhesions (containing e.g. INTEGRINS) connect the network to the ground

Filament Interactions

What to include?

The Mathematical Model

Thin, sheet-like structure called LAMELLIPODIUM

New Model Components

What does the model do?

Analysis and Simulation

Branching

Capping and severing

Pressure

Pressure between

neighboring filaments

Filament number and

length regulation

Recycling Arp2/3

Regulating the Network

Myosin filaments can pull actin filaments

towards each other

Contraction

CONTRACTILE BUNDLE

Main Modeling

Assumptions

The FBLM (Filament Based Lamellipodium Model) is a...

D. Ölz, C. Schmeiser, How do cells move? Mathematical modeling of cytoskeleton dynamics and cell migration, in Cell mechanics: from single scale-based models to multiscale modelling, Chapman and Hall, (2010)

NUCLEUS

x

Submodel

Asymptotic

Full Model

Simulation

Full Cell Simulation

The model can reproduce complex situations

Results I

Chemotaxis

How do cells move?

The Biology

Cell shapes

Results II

Selective Adhesion Patterns

Monomer displacement

Wilson et al, Nature, 2003

A. M., D. Oelz, C. Schmeiser , N. Sfakianakis, An extended Filament Based Lamellipodium Model produces various moving cell shapes in the presence of chemotactic signals.

Journal of Theoretical Biology, 382 (2015), pp. 244-258

Biological Correspondence

Csuc et al, Cytoskeleton, 2007

Selective Adhesion Patterns

Different ratios

A. M., D. Oelz, C. Schmeiser, N. Sfakianakis, Numerical Treatment of the Filament Based Lamellipodium Model, Modeling Cellular Systems, Springer

Regime

What kind of cells are we looking at?

A moving keratocyte

Cell-Cell Interactions

Leukocytes

polymerization rate

(force dependent)

D. Peurichard & N. Sfakianakis

David Rogers, Vanderbilt University, 1950s

Looking at an Asymptotic Regime

Explaining the bistability of keratocytes

Theoretical Results & Biological Relevance

Results

Stability analysis of the model reveals several stable steady states

Theoretical Results

Analyzing a Submodel

Results are qualitatively reproduced in full FBLM

Existence of unique, global, mild solutions

Bistable behavior can be explained by

• Competition between cross-links and myosin

Positivity of solutions

• Myosin activity depends on the angle between filaments

S. Hirsch, A. M., C. Schmeiser, Mathematical modeling of myosin induced bistability of Lamellipodial Fragments, Journal of Mathematical Biology (2016), online first.

Filament End Density Evolution

A.M. and C. Schmeiser, Decay to equilibrium of the filament end density along the leading edge of the lamellipodium, Journal of Mathematical Biology (2016), online first

Model

x

Keratocytes

Main Aspects

Straight geometry

Stiff filaments

Boundary Conditions

Periodic BC

MAIN EQUATION

single filament

cross-links

pressure

myosin

+ ADDITIONAL MODELS

Yam et al, J. Cell. Biol., 2007

filament end density

Myosin activity angle dependent

shortening of filaments

polymerization rate v

+ BOUNDARY CONDITIONS

Dirichlet BC

S. Hirsch, A. M., C. Schmeiser, Mathematical modeling of myosin induced bistability of Lamellipodial Fragments, Journal of Mathematical Biology (2016), online first.

Angelika Manhart (http://cims.nyu.edu/~amanhart/)