Review of “Emergent

Morphogenesis: elastic mechanics of

a self-deforming tissue”.

Davidson et.al Journal of

Biomechanics, 43, 63–70 (2010).

Bradly Alicea

http://www.msu.edu/~aliceabr

COURTESY: Pharyngula Blog, How to build a tadpole.

Why is this paper relevant?

Q: how are tissues self-assembled (from a

blastula to an embryo)?

Q: how do cells collectively form

structures in development/regeneration?

Q: how do physical processes affect the

nature and composition of cell populations?

Can we apply what we learn to:

* regenerative medicine (growth of tissues

on a scaffold)?

* selective phenotypic respecification,

selective differentiation?

Cell Biology Development

Emergent Morphogenesis

Mathematics,Physics,

Computer Science

Biomechanics

Tissue Engineering

Main HypothesisH: developmental processes can be modeled

and better understood using computational

geometry.

Gastrulation = geometric transformation.

* from sphere (A, left) to torus (A, middle)

to tube (A, right).

Gastrulation + elongation = deformation of

sphere along anterior-posterior axis (B).

Convergent extension = cell rearrangement

(C).

a) tissue deforms along anterior-posterior

axis.

b) oval with dot pushes itself in between the

other two ovals.

Previous Approaches to

MorphogenesisD‟Arcy Thompson (1900): “On Growth and Form”

* mathematical rules govern developmental program

(relative position of cells in a structure).

* example: geometrical transformations determine species differences.

Alan Turing (1952): diffusion-based model.

* molecular interactions govern pattern-formation

(chemical diffusion).

* example: striping in Drosophila embryo.

Modern approaches (see Curr. Opin. Genetics and Development, 14(4), 399–406):

* diffusion-advection models, refinement of Turing model.

* example: diffusion-limited aggregation model.

Nature, 406,131 (2000).

Goals of Computational Modeling

Computational Model: abstraction/representation and approximation.

Abstraction/representation: represent only the most “important” attributes of a

phenomenon.

CAVEAT: we may not know what the most important parts are a priori.

Approximation: behavior of model is close to behavior of natural phenomenon.

CAVEAT: is behavior similar (mimicked only in certain situations), or is internal

mechanism?

Excitable brain

tissues as neural

network.

Definition of TermsViscoelasticity: materials that exhibit both viscous and elastic properties when

deformed.

Convergent extension (CE): part of gastrulation, moves cells from three germ layers

into prospective positions (convergence + extension).

* brings prospective dorsal tissues from a broad area

of the early embryo and organizes them into a compact

column that runs from head to tail.

Intercalation : a reversible or irreversible inclusion of a cell between two other cells.

Xenopus spina bifida due

to KO in gastrulation.

COURTESY: http://www.

nibb.ac.jp/annual_report/

2002/html/02ann203.html

* mediolateral cell intercalation = cells

intercalate between adjacent neighbors, driving

them apart along AP axis. Several rounds

required to elongate embryo.

* fibronectin and fibrils at tissue interfaces

provide cues, keep all three cells in same

geometric plane.

Position and Mechanics as

InformationMechanotransduction: the sensing by a living entity of mechanical cues that

result in an electric or chemical set of responses.

a) Nervous system: moving arm through a liquid, swinging a baseball bat.

* difference in mechanical forces, representation in nervous system (brain, spinal cord) of this information

(time-differencing + feedback = intelligent behavior).

* mechanisms: proprioceptors, joint receptors,

nociceptors.

b) Single cells: cells move across a surface

of specific hardness (motility), experience

pressure cues.

* difference in mechanical forces, changes in gene

expression, motile behavior, and cellular memory.

* mechanisms: cytoskeleton, focal adhesions, kinesins

(ECM).Science, 315, 370-373, (2007)

Molecular-mechanical processesMolecular-mechanical processes underlying morphogenesis are crucial to

understanding:

1) source of birth defects.

2) formation of tumors and progression

of cancer (see 1-7).

3) principles of tissue engineering.

Roles of mechanics in development:

1) Multicellular integration. Mechanical integration (tissue level) coordinates force

production, material properties of tissues, tissue movements (morphogenesis).

2) Intracellular cell integration. Mechanical integration of intracellular force generation with

local environment, direct molecular-mechanical processes (cell behavior).

(3) Intracellular gene integration. Mechanical integration of the cell, local environment, and

gene regulatory networks (direct cell differentiation).

Courtesy: Nature

Cell Biology, 9(9),

1010-1015 (2007).

Carbon Nanotube

tissue scaffold

1

2

3

4

5

6

7

Molecular-mechanical processes

(con’t)Interactions between cell mechanics and

molecular /cell biology (examples):

1) coordinated movements of epithelial cells

during morphogenesis.

* build grooves, elongate tissues, and enclose

the embryo.

2) forces exerted by bone deformation trigger

signalling pathways.

*cells secrete extracellular matrix, nucleation

sites for minerals.

3) stromal cells react to external mechanical

loads by generating counteracting forces.

* exogenous (external) stresses and endogenous

(internal) tension.

Intercalation: “rules” and models

Intercalation drives convergent extention using

four “rules”:

1) Planar polarity. Intercalating cell moves in

mediolateral direction, separates neighboring cells

along anterior–posterior axis (A).

2) Remain in-the-plane. Intercalating cell stays in

same plane as the two neighbors (B).

3) Irreversibility. Intercalating cell does not reverse

direction and pop back out of plane (C).

4) Cell shape constraint. Intercalating cell and

neighboring cells maintain their shapes, do not re-

organize within the same volume (D).

Intercalation: “rules” and modelsIn silico models simulate cellular tissues via cell–cell

adhesion, cell protrusive or traction forces, and cell

rearrangement.:

* make sense of the complex cell intercalation movements

* account for the rates of cell rearrangement and cell shape changes that

have been quantified during Xenopus and zebrafish convergent

extention.

Model parameters based on empirical observations:1) increase in mediolateral cell elongation length: width ratio

2) incidence of cell–cell neighbor change (does a cell change neighbors

during intercalation).

3) rate of cell neighbor change (probability that a cell contacts a new

neighbor during intercalation).

Xenopus Zebrafish

Beginning of gastrulation 1.5 1.5

Beginning of neurulation 2.2 > 3.0

Vertex

Cellular

Potts

FE

#1: Vertex Model

“Agent-based” model: autonomous agents use a ruleset to interact with each other and

form emergent patterns.

H: agent-based models can replace equation-based (deterministic) models. Emergence

= more than the sum of all parts (super-additive).

Vertex model: 2-D cell array, shared

boundaries between cells.

* boundary of each cell = Newtonian spring.

* stiffness, resting length parameters, uniform for

each cell.

Spring

Autonomous Agent

Driven by stochastic processes (intrinsic randomness).

#2: Cellular Potts Model

Cellular Potts models (CP, CPM): Agent-based model, simulate foam, biological

tissues (especially cell sorting – Nat. Rev. Genetics 10, 517-530, 2009), fluid flow.

* an array of “generalized” units: may be a single soap bubble, an entire biological cell, part of

a biological cell, or even a region of fluid.

CPM evolves by updating array

serially based on probabilistic rules.

* extended 2D model of convergent extension,

discrete packets of cytoplasm delimit contents

of each unit.

* cell sorting driven by adhesion/contractility.

Cellular Potts model for convergent extension:* individual units, contiguous block within grid.

* cell-cell interactions governed by energy function

(heuristic measurement).

Additional rules maintain cell size, retard

shape changes (stiffness, energy penalty):

Inhibited: changes from pre-defined standards.

Encouraged: restoration of previous properties.

#3: Finite Element (FE) Model

Finite Element (FE) Model: a tool commonly used in Mechanical Engineering.

* can be used to study the biomechanics of early development.

* cellular representation: divide each cell into a mesh

(tiling of triangles, etc). Mesh discretizes continuous

surface.

Use an energy function and deformations of the

structure to minimize potential energy.

* entire tissue structure is deformed in FE models

(global effect), energy minimized locally.

Convergence and extension represented in two ways:

1) contractile rods representing traction forces along mediolateral axis can occur at random

locations, triggered using stochastic mechanism.

2) algorithms track cell-cell boundaries and cell rearrangement within the FE mesh.

FE Lung

FE Eye

FE Head/Neck

Meshed cell

Autonomous Agent

Production of Four Rules in Vertex,

CP, and FE models1) each model type modeled a different aspect of convergent extension (tissue

self-organization), but all established mediolateral cell intercalation:

a) Vertex model = elastically coupled cells.

b) CP model = differential adhesion.

c) FE model = mediolaterally-directed traction forces.

2) each model incorporated an approximation of cell stiffness.

Vertex (V) Cellular Potts (CP) Finite Element (FE)

Planar Polarity YES YES NO

Remain in-plane NO NO NO

Irreversibility YES NO NO

Shape-Size Constraints NO YES NO

b) COURTESY:

Nature Cell Biology,

5, 948 - 949 (2003)

c) centripedal traction

forces, mesenchymal

stem cell.

Production of Four Rules in Vertex,

CP, and FE models (con’t)

Cell and tissue mechanics play an integral role in the emergence of convergent

extension.

* in particular, cell and tissue stiffness are critical for correct convergent extension.

Planar polarity: present in V and CP (but not FE) models, an outcome of local

feedback without initial bias.

* lack of bias is the criterion for convergent extension to be an emergent property.

Remain-in-plane: behavior is not reproduced by any model.

Irreversibility: reproduced only in V as a consequence of contact inhibition.

Cell shape and size constraints: not imposed in V nor FE models. May be a crude

approximation of shear and bulk stiffness.

“Wedge” Model

Simple equation rather than agent-based model (describe intercalation):

Ftraction (traction forces) overcomes friction (μ) and Felastic resistance (elastic resistance)

of neighboring cells

Length (L) and width (W) of intercalating cell determine intercalation angle (α),

where α = arctan (W/L).

Wedge phenomenon:

* intercalating cell acts as

wedge moving in between

two stationary cells.

* shape of cell determines success or failure of individual cell, how it fits into the

emerging monolayer, tissue structure.

Ftraction > Felastic resistance (μs + μs cosα + sinα)Traction of intercalating cell

must always be greater than

geometric constraints.

“Wedge” Model (con’t)

A simple, semi-quantitative

alternative to the three prevailing

in silico approaches:

* forces required for intercalation

reduced for a more elongate cell

regardless of friction (B).

* if cell and environment

modeled as viscoelastic, cells

progressively elongate as they

intercalate.

* as the intercalating cell

„wedges‟ between its neighbors,

compressed along with

intercalating cell (C).

“Wedge” Model (con’t)

Behavior of artificial embryo in Wedge model:

* minimal amounts of resistance to elongation at anterior and posterior ends of (i.e.

boundary conditions) compress the cell in the AP direction.

* strain in response to wedging, resistance of the material to volume (e.g. Poisson

ratio), and compression along AP direction -- elongates cell in ML direction.

* these conclusions do not rely on specific shape of wedge but are general

properties of wedge model.

Behavior of the wedge model suggests feedback between intercalation, a reduction

in forces required for intercalation, and cell elongation occur in natural systems.

“Wedge” Model: broader

implicationsWedge model = simple machine that reproduce mediolateral cell elongation, take

into account cell shape and mechanical properties such (tissue stiffness, boundary

conditions).

* reveal universal mechanical principles that allow the broader fields of cell and developmental biology to

understand the complexities of morphogenesis.

Successful simulated models of CE:

* must produce correct shapes under conditions of stiffness, force production observed in real embryos.

Predictions of three models suggest a series of experimental tests:

1) do notochord cells elongate autonomously when dissociated or transplanted to other sites, or require

surrounding tissues (prediction of FE and vertex models)?

2) does cell elongation vary between embryo, free explants, or explants cultured on glass?

3) does the length-to-width ratio of cells match FE and Vertex models with their required boundary

conditions?

Conclusions and Applications

Future CE models should simulate the conditions in a more transparent,

biologically relevant manner.

* integrate signaling networks (e.g. non-canonical Wnt pathway).

Complex mechanisms that self-organize planar polarity without boundary

conditions, remain-in- plane, irreversibility, and cell shape constraint, future

models will need to:

1) autonomously generate subcellular polarization that can direct mediolateral cell protrusions.

2) represent multiple cell layers or even full 3D cells.

3) autonomously generate persistent cell intercalation behaviors.

4) represent more realistic material properties of both intercalating cells and the tissues they form.

Also need flexibility to include specialized adaptations for different organisms

(mouse, chick, and zebrafish) and organ formation.

Conclusions and Applications

Microenvironments for stem cell niche:

Biophysical, geometric aspects of ECM,

affect retained self-renewal capacity

(Keung et.al, WIREs Sys. Bio. Medicine,

2, 49-64, 2010).

* effect of variables such as

dimensionality, linear elastic modulus,

stiffness?Tissue engineering at small scales:

* how can we have greater control over

stochastic mechanisms?

* how can we produce features of a

specific, characteristic size?

* can we use simulation, experiment to

predict by-products of emergent

properties?