Reverse engineering of mitotic spindle

Roy WollmanRoy WollmanJon Scholey and Gul Civelekoglu (Davis)

Mitosis (segregation of chromosomes before cell division) in Drosophila Embryo

Tram et al., Encyclopedia of Life Sciences,2002

After prophase the dance isthe dance is very complex

Astral MicrotubulesKinetochore Microtubuless a c o ubu es Microtubules

Inter-polar MicrotubulesChromosomal Microtubules

Inter polar Microtubules

Quantitative measure of mitotic progression

Pole Pole –– Pole distance Pole distance ss over timeover timeSS

Biochemicalregulationg

SwitchesSwitches

Mechanics

Phenotype

Defining the puzzle: Find activation sequence and mechanical characteristics of motors that explains the data

f Force velocity relationff Force velocity relationf

mFForce velocity relation

vf

f

mF

f

mFForce velocity relation

vf vf, , , - ?off on m mt t F V⎡ ⎤⎣ ⎦

Motor activation profiles vmV

1mm

vf FV

⎛ ⎞= −⎜ ⎟

⎝ ⎠v

mV vmV

1mm

vf FV

⎛ ⎞= −⎜ ⎟

⎝ ⎠

All phenotypes

ontofft

All phenotypes

onoff

Building the model (example of chrMTs) chrVpoleV

, ,, ,

1 1chrkchrk

MT poleMT chrchrk mx dep mx

chrk mx dep mx

V VV VF FV V

⎛ ⎞⎛ ⎞ −−− − = −⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

chrkMTV

chrV

, , , ,, ,

1 1pole chrdep mx chrk mx dep mx chrk mx

dep mx chrk mxchrkMT

V VF F V VV V

VV F V F

⎛ ⎞⎛ ⎞ ⎛ ⎞+ + +⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠=

+ chrkV V⎛ ⎞−

2 ,,

1 pole chrchrk mx

chrk mx

V VF F

V⎛ ⎞−

= −⎜ ⎟⎜ ⎟⎝ ⎠

, , , ,dep mx chrk mx chrk mx dep mxV F V F+3 ,

,

1 MT poledep mx

dep mx

V VF F

V⎛ ⎞−

= − −⎜ ⎟⎜ ⎟⎝ ⎠

3. Forces on microtubule populationp p

( )( )( )2 32 1chrk chr

chrk chrk dep depN AF P P F P FS D

= − +−( )

R l t it h Si l Mi t b lN b fRegulatory switch Single Microtubuleequations

Number ofmicrotubules

⎩⎨⎧

=activeinactive

Pchrk 10

4 types of microtubule populations

Forces on the spindle and dynamic equations

( )2 ip chrk aster ktF F F FdS + + −=

poledt μ=

( )2 kt chrk cohesion

chr

F F FdDdt μ

− −=

1l

dSV = 1h

dDV =

( )( )2 2 1ip ipploy dep pole dep MT

dL V P V P Vdt

= − − +

2poleVdt 2chrV

dt

Numerical solution of the model equations (stiff ODE solver)

Solve for single microtubule (v f)

Score

Integrate forIntegrate for microtubule

population (f F)

Integrate for entire spindle (F v)

Impossibility of systematic scanning of the parameter space(~ 50 parameters)

So: genetic algorithm based optimizationg g p

1. Start with random population of solutions

Subpopulation I Subpopulation II

population of solutions

2 Evaluate goodness of35

42

score (less=better)

2. Evaluate goodness of solutions.

218

239

3. ‘Survival of the fittest’3

223

2004. Mutation

x 200

5. Recombination

Examples of good models( )2 ip chrk aster ktF F F FdS

dt μ

+ + +=

poledt μ

We have 10,000+ more examples…p

Bewildering variety of the ‘perfect’ models: switches

Bewildering variety of the ‘perfect’ models: forcesrc

e [p

N]

For

Outwards: Inwards: Kinesin-13Dynein, Chr-Arms

Kinesin-5

Outwards: Inwards: Kinesin-13Dynein, Chr-Arms

Kinesin-5Chr-Arms

Outwards: Inwards: Kinesin-13Kinesin-5Chr-Arms

Kinesin-13, KT-dep

Kinesin-13, KT-depOutwards: Inwards:Kinesin-5Chr-Arms

Kinesin-14

Kinesin-13, KT-depOutwards: Inwards:Kinesin-5Chr-Arms

Kinesin-14

Kinesin-13, KT-depOutwards: Inwards:Kinesin-5Chr-Arms

Kinesin-14KT-dep

Outwards: Inwards:Kinesin-5Chr-Arms

Kinesin-14KT-dep

Final Model

Model prediction: estimates of the mechanical parameters

Kinetic / mechanic properties of participating motorsIn agreement withIn agreement with in vitro biochemical study:

+KF NF

v +-

k n

∑= FdS 2μ

Design principle: Balance of large forces

∑

∑

=

=

Chchr

Polepole

FdtdD

Fdt

2

2

μ

μ

Chrdt

Typical drag ~ 100 [pN sec/μm]

dS [ ] [ ]~ 0.03 / sec ~ 1 10Pole

dS m F pNdt

μ ⇒ −∑

onse

Outward Force

Res

po

Inward Force

Total Force

Perturbation / Noise

Total Force