New methods to study motile phenomena

A progress report

Topics

The challenge of understanding cell migration

Use of photoactivation & CALI to perturb cell migration

CMAP, a systems biology tool

How do we approach a quantitativeHow do we approach a quantitativeunderstanding of cell movement?understanding of cell movement?

Build up from Build up from molecularmolecular

mechanisms mechanisms

Top down modeling ofTop down modeling ofintegration of collectiveintegration of collectivemolecular mechanisms molecular mechanisms

e.g. protrusion, contraction etc.e.g. protrusion, contraction etc.

“Up close the paintings of Renoir & Monet look like ‘daubs of paint’, nothing more. Yet when we step back from the canvases, we see

fields of flowers”

From Davidson’s review of A Different Universe by Robert Laughlin-NYTimes 6/19/05

Philosophy of quantitative modeling

• Use model to simulate behavior & compare to experiment

• Revise model until concrete insight gained into key factors determining migration

• Test alternate models• Overarching goal: Quantitatively organize

information & ideas on migration mechanisms

Advantages of Simple-shaped Cells for Biophysical Studies

• Amenable to modeling

• Simple shape & migratory pattern: easy to see results of perturbation

• Simple, symmetric net traction stress pattern

Gliding Fish Keratocyte

In the keratocyte, protrusion & retraction smoothly coordinated

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Keratocyte Doing the LimboKeratocyte Doing the Limbo

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Magnitudes of cell forces

Type of force Force (pN)

Single actomyosin interaction ~ 1

Estimated actin polymerization force

per filament

~ 4

Tension on neurite during growth

cone advance

< 6000

Stall force for keratocyte ~ 50,000

Estimated maximum traction force

exerted by fibroblasts

~200,000

Gliding Fish Keratocyte

In the keratocyte, protrusion & retraction smoothly coordinated

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MyosinII F-actin

Dynamic Network Contraction

Rxn-diffusion sub-model (simplified)

polymn

depolyncofilin PF-ADPactin

PF-ATPactin TB4-ATPactin

A virtual keratocyte--A. Mogilner et al, UC-Davis[Front-dendritic nucleation; rear-dynamic network contraction]

Density of f-actin plotted

Rubenstein et al SIAM J. 3:413 (2005)

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Test robustness of in silico models of Test robustness of in silico models of migration i.e. do we have the rules of migration i.e. do we have the rules of

integration of protrusion, retraction and integration of protrusion, retraction and adhesion correct?adhesion correct?

Use light-directed methods to perturb molecular activities in single migrating cells in a spatially & temporally defined way--complement to genetic perturbations

Concentration of players as numerical input to

Mogilner model

G, F-actin, T4, profilin etc.

1 3

2

Release or inactivate at

different points in cell

Provide simultaneous traction & network

dynamics maps with photoactivation/CALI

operation

Photoactivate or laser inactivate different ABP

polymn PF-ATPactin TB4-ATPactin

capping protein

Experimental Perturbation

Local ACTIVATIONof molecule:

photoactivation

Local INACTIVATIONof molecule:CALI, photoactivation

Thymosin -4

Cofilin

FAK peptides

-actininConnexinsAurora B kinaseMenaCapping Capping proteinprotein

CALI: Chromophore Assisted Laser Inactivation

[Dan Jay]

Chromophore Assisted Laser Inactivation (CALI)

High spatial resolution – Subcellular inactivation– High selectivity

High temporal resolution– Instantaneous inactivation– Eliminates genetic/molecular compensation

Light-mediated loss-of-function tool

CALI Mechanism

Cell

proteinChr

Laser

Protein damage

x-x-

Reactive oxygen species

Loss of function

• Chromophore excitation leads to production of free radicals• Free radicals are highly destructive, causing protein damage - short half-life (nm destruction radius)• Potential for local, instantaneous inactivation of adjacent protein

EGFP as a CALI Chromophore

• Advantages– Genetically encoded– Covalent linkage to protein of

interest insures specificity– Widely used

• Disadvantages– Photostable

Ineffective ROS generator– 200-1000X less efficient than

other dyes

Photostability may also be an advantage in that there are separate regimes for imaging and inactivation

EGFP

CALI of EGFP-Capping Protein

Eric Vitriol, Andrea Utrecht & Jim Bear

Mena, Capping Protein, and the Regulation of Actin Structure

Mejillano et al. 2004

CPß Knockdown exhibits more filopodia: can CALI reproduce this

phenotype?

Mejillano et al. 2004

Control

CPß KD

LENTIVIRUS KD / RESCUE CONSTRUCT TO REPLACE ENDOGENOUS CP WITH EGFP-CP

5.0EGFP5’ LTR PromoterU6 Promoter Capping

Protein

Jim Bear + Andrea Utrecht

-select clones for good KD& rescue to physiological levels

DIC (left panels) and fluorescence of EGFP-CP (right panels) before (above) and after CALI (below)

CALI of EGFP-CPß

<--Large CALIRegion

1. DIC-pre

2. Pre-flour.

3. Post-fluor

4. Post-DIC

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F-actin & barbed end increase after CALI-induced dissociation of EGFP-CP from barbed ends of actin filaments

Phalloidin stainfor f-actin

Barbed end assay

CMAP: The Causal MapCan the cell biologist’s scheme, which organizes

elements, be transformed to a graphical model to check whether it semi-quantitatively predicts

observed behavior?

Gabriel Weinreb, Maryna Kapustina, Nancy Costigliola& Tim Elston

Cell oscillations induced by depolymerizing MT during cell spreading

depend on elevated Rho activity and cyclic Cai

2+

Pletjushkina et al, Cell Mot. & Cytoskeleton, 48 (4): 235-244 (2001).

Spreading mouse fibroblasts with depolymerized MTs

See also Paluch et al, BJ 89: 724 (2005) &Salbreux et al, Phys Biol 4:268(2007)

Note blebbing-> QuickTime™ and a

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Quantitation of oscillatory behavior

Inactivation ofROCK [arrow] byY27632blocks oscillations

Control cellspreading

Ca2+ also oscillates with similar period as morphological oscillations

normal spreading

increment due MT depolymerization

periodic increment due to [Ca2+]i variations

time

contractility

B.

How Rho and Ca2+ may be involved in regulating oscillations

MICROTUBULE DEPOLYMERIZATION

MORPHOLOGICAL OSCILLATIONS

Substrate stiffness

External[Ca2+]

Adhesion strength

MLC-phosphataseP

MLC- ↑P

CONTRACTILITY↑

GEF

Rho↑

ROCK↑

CICR

Activate SAC

Cai2+ ↑

MLCK↑

CaM

[Ca2+]↓ byretrieval

Functional map for cell oscillations depicting necessary elements and connections between them.

A systems biology test bed:

Experimental readout:% Cells Oscillating, Amplitude, and Period

of oscillations

CMAP(semi-quantitative)

Differential Equation model(quantitative)

Fine-grained models Coarse grained models

CMAP

Complexity

Cognitive networks

Boolean networks

Petri networks●●●●●

Complexity

ODE, PDE &Stochastic Models

Causal Mapping [CMAP]

• Concepts (elements) are enclosed in boxes and embody chemicals and/or mechanics

• Causal influences are edges and enable propagation of causality

• Concepts & influences are given numerical or linguistic weights based on data and/or expert opinion

A BW AB

W BA

•A,B are elements of the map, called ‘concepts’.

•Wij are the weights (magnitudes) of causal influence of one concept on the other;[weights are in terms of lingustic variables I.e. very strong….weak that are translated to numerical intervals between -1 to 1]

•Positive weight leads to increase of the concept it is directed to (activation)

•Negative weight leads to decrease of the concept it is directed to (inhibition).

•Time evolution described by simple “transfer” functions that connect concepts &incorporate weights from one or more input concepts

Development of a CMAP for cell oscillations

Biological background:

CMAPWeinreb, Elston, and Jacobson. 2006

•Actomyosin based contractility

•Volume oscillations

•Ca2+ oscillates

•Rho pathway involved.

Microtubule depolymerization

RhoA pathway

time, sec

concept, a.u.

0.0

0.2

0.4

0.6

0.8

1.0

time, sec

0 100 200 300

concept, a.u.

0.0

0.2

0.4

0.6

0.8

1.0

A

B

MT depolym

MT depolym+ROCK inhibition

red=contractility

blue=[Ca2+]i

CMAP simulation results

Using the CMAP for hypothesis generation: how do we determine the most likely CMAPs for the phenomenon?

Weinreb et al, in preparation

What system configurations provide viable hypotheses?

W AB

A BW BA

Configuration 1:

inactivation

activation

>0

<0

A BW AB

W BA

Configuration 2:

inactivation

inactivation

<0

<0

A BW AB

W BA

Configuration 3:

inactivation

no influence

=0

<0

MLC-P

SAC

Cai2+

MLCK

CONTRACTILITY*

Membrane

Ca-CaM

Ca-pump

MLC-P-ase

MLC-P

SAC

Cai2+

MLCK

CONTRACTILITY*

Membrane

Ca-CaM

Ca-pump

MLC-P-ase

Two distinct configurations

- feedback + feedback

• Define experimentally observable criteria that characterize the phenotype:

-oscillatory behavior in [Ca] and contractility-increasing myosin light chain phosphatase damps

oscillations• Determine all possible configurations of the network, i.e. all

combinations of possible connections between the elements

• For a each configuration, use all possible combinations of weights, Ntotal, [Monte Carlo] and count those that satisfy the criteria, Ni.

• Calculate the fitness index as a ratio fi=Ni/Ntotal in order to rank hypotheses [a zero fitness configuation is not a viable hypothesis]

Algorithm for hypotheses generation

MLC-P

SAC

Cai2+

MLCK

CONTRACTILITY*

Membrane

Ca-CaM

Ca-pump

MLC-P-ase

MLC-P

SAC

Cai2+

MLCK

CONTRACTILITY*

Membrane

Ca-CaM

Ca-pump

MLC-P-ase

HI FITNESS ZERO FITNESS

How can the competing, high fitness hypotheses be

experimentally distinguished?

• Identify on the CMAP a causal influence (weight) which can be experimentally manipulated. e.g. titration of an inhibitor .

• Vary the CMAP weight corresponding to the experimental manipulation keeping all other weights in the ensemble of hypotheses (Ni) unchanged.

• Examine how system responds to varying the weight of interest.

• Compare experimental outcome to prediction of CMAP for different hypotheses. Look for major qualitative differences.

Protocol (under development)

MLC- P

SAC

Cai2+

MLCK

CONTRACTILITY

Membrane tension

Ca-CaM

Ca-pump

MLC-phosphatase

A CMAP for cell oscillations

no buffering0.3 uM Kd buffer

Hypothesis 5Hypothesis 4

mean=4124

0

5000

10000

15000

20000

25000

30000

Period, a.u.

0 2000 4000 6000 8000 10000

counts

0

5000

10000

15000

20000

25000

30000

mean=4125

Experiment

mean=1517

0

200

400

600

800

1000

1200

1400

1600

1800

Period, a.u.

0 1000 2000 3000 4000 5000

counts

0

200

400

600

800

1000

1200

1400

1600

1800

mean=1800

Comparison of experiment & CMAP predictions

Single cell behaviorin both experiment &CMAP predictions canalso be compared

An ODE model for cell oscillations based on a likely

CMAP produces cell oscillations

Kapustina et al BJ, in press (2008)

Evidence for a linear oscillation mode

SEM (3700x) of spreading cell with colcemid

50s 70s 90s 120s

180s150s 200s220s

40s

Frames from video record

ODE model using literature parameters describes linear oscillation mode

Ca2+

contraction

Ca2+

contraction

Volume equilibration

cyt mem contract

dRF F F

dtγ = − −

R

Fcyt Fcontract

Fmem

1

2

Kapustina et al BJ epub (2008); see also Salbreux et al, Phys Biol 4:268(2007)

Fmem = force resulting from

elasticity of membrane

Fcyt = constant force generated

by pressure inside cell

Fcontract= actomyosin generated

contractile force

R

Assume contractile force is proportional to p-MLC-->kinetic model of calcium dynamics as it relates to MLCK activation

200 300 400 5000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0

10

20

30

40

50

60

[Ca],

μM

time, s

[ _ ] ( )MLC P contractility

Oscillations of [Ca2+] and [MLC_P]

CONCLUSIONS

Model reproduces the experimentally observed cortical oscillations with only 2 free parameters out of a total of 34 [proportionality constants between p-MLC and contractility and that characterizing cytoplasmic pressure].

Mechanism responsible for the oscillations is a negative feedback loop from contractility to stretch activated channels.

Oscillations only result when the level of myosin light chain phosphatase falls within a certain range

Model predicts that buffering intracellular calcium increases the period and decreases the amplitude of cortical oscillations (preliminary data supports this)

References:1. Pletjushkina O, Rajfur Z, Pomorski , Oliver T, Vasiliev J, Jacobson K. 2001. Induction of cortical oscillations in

spreading cells by depolymerization of microtubules. Cell Motility&Cytoskeleton 48:235–2442. Weinreb G, Elston T, Jacobson K. Causal Mapping as a Tool to Mechanistically Interpret Phenomena in

Cell Motility: Application to Cortical Oscillations in Spreading Cells. Cell Motility& Cytoskeleton Sep;63(9):523-32

3. Kapustina M, Weinreb G, Costigliola N, Rajfur Z, Jacobson K, Elston T. Mechanical and biochemical modeling of cortical oscillations in spreading cells. Biophysical Journal, in press..

Conclusions• CMAPs have potential value as a check of a cell biological mechanism;

does the scheme actually do what it is supposed to?

• CMAPs permit incorporation [without having exact knowledge their values] of different elements (mechanical, chemical); they can point to missing elements or superfluous ones.

• Hypotheses generated using the CMAP approach can be qualitatively checked for consistency with experiment.

• The coarse-grained CMAP prescription leads to successful ODE mechanochemical model; such differential equation models generate quantitative predictions that can be experimentally tested.

Acknowledgements- NIH Cell Migration Consortium

Photomanipulation

Partha Roy, now at Univ. of Pittsburgh 

Zenon RajfurDave Humphrey, now at US Patent Office

Barbara Imperiali, MIT

Eric Vitrol &Andrea Utrecht

Jim Bear, UNC

Gerard Marriott-UW

Alex Mogilner-UC-Davis & CMC

CMAP-- all at UNC

Gabriel Weinreb

Tim Elston

Maryna Kapustina

Nancy Costigliola

Traction Experiments & Analysis

Zenon Rajfur

Micah Dembo-Boston Univ.

Xavier Trepat-HMS