Biotopology: 3 rd July 2015
To understand the basic concepts of Topology from the viewpoint of Biology andTo focus on natural topological phenomena

Biomolecular Motors: Topology inBiology, Structural Integrationand Emergence of Functions

Arif Md. Rashedul KABIR
Faculty of Science, Hokkaido University

What is Topology?
SpaceThe study of geometric properties and spatial
relations unaffected by the continuous changeof shape or size of objects.

Topology and Nature
Topology in Biology
Structure

Function

Integrated EmergentStructure
Function

Topology in biology Offer divers functions

Levels of organization in nature

Topology inside cell
Biomolecular Motor Protein SystemActinMyosin
MicrotubuleKinesin
Cytoskeleton
Molecular Biology of The Cell, 5th Edition

Motor protein systems
in cellular activities
red : actin
green : bacteria

Phagocytosis

red : actin

Structural support

Cell movement

Muscle contraction

blue : actinorange : microtubules

Cytokinesis

Actin-Myosin: Cell locomotion

Cell shape regulation………

Microtubule-Kinesin:
Intracellular transport
Organelles regulation………

Topological Variation of Actin
Polymerization

Actin Polymerization: Cell Movement

Actin web: Cell Movement

Actin web: Cell Movement

Treelike web of polymerized ActinsMolecular Biology of The Cell, 5th Edition

Actin web: Cell MovementActin polymerization enables

cell motility.

Movement of Listeria monocytogenes:
use of polymerization force

kT[ A1 ]Fln
KC
F : Force generated by polymerization.
: Increase in length due to incorporation of one molecule.
KC: Critical concentration in the absence of an external force.
[AI]: Concentration of free molecules.

Linear motor proteins
Myosin: Actin associated motor

Molecular Biology of The Cell, 5th EditionLinear motor proteins
Kinesin and Dynein: Microtubule’s motor

KinesinDyneinDiffusion: How fast is it?

time (s)Diffusion speed depends on the size of body.
10410

310

210

1

100

2

t=𝑥2𝐷

D=kBT/6phrhkB-1

10-2

10

100

110

10

2

310

length (m)Diffusion time as a function of the length for a typical valueof the diffusion coefficient (D=100m2/s) of a protein in water.

How to communicate inside cell?
…………Active transport

Biomolecular motor driven transportation

Linear motor driven

bending motion
Slipper animalcule
CiliumDyneinMT
ref: Nikon

ref: Heuser et al. JCB,2009

Cilia and Flagella
Motile structures from Microtubules

Motion in sperm, protozoan etc.
Molecular Biology of The Cell, 5th Edition

Organelle transportation

by Kinesin and Dynein

Melanosome movement regulation
Change in skin color of fish

Transport of pigment granules inAfrican cichlid fish.

Myosin mediated muscle contraction

Molecular communication system
Broadcast of Information‘Natural Computing’-by Yasuhiro Suzuki, Masami Hagiya, Hiroshi Umeo, Andrew Adamatzky

Stress, deformation and topology
PhysicalImpact

Cargo

Microtubulefracture

Traumatic Brain Injury (TBI)

Mechanical stress↓
Microtubule Breakage↓Interrupted cellulartransport
Min. D., et al.,Exp. Neurol 2012, 233, 364

 Impaired cellular transport  10 million TBI’s per year world-wide 1
 1.7 million TBI’s per year in the U.S.
 Memory loss
-52,000 Deaths-275,000 Hospitalizations

Important to know……
What is mechanism of microtubule breakage on molecular level?
What fracture mode induces severe damage of microtubule?
1Faul M, Xu L, Wald MM, Coronado VG. Traumatic Brain Injury in the United States: Emergency Department Visits, Hospitalizations and Deaths

2002–2006. Atlanta (GA): Centers for Disease Control and Prevention, National Center for Injury Prevention and Control; 2010.
Finkelstein E, Corso P, Miller T and associates.

Different fracture modes
Mode Ⅰ:
Opening mode

Mode Ⅱ:
Shear mode

Mode Ⅲ:
Torsional mode?
Optical trap

MT breakage by optical tweezers
Young’s modulus
of MT: 0.29 MPa

MTBroken
Guo et al, Biophysical journal, 2006, 90, 2093

5 µm

What and how to do?
Microtubule

SubstrateI. Establish an experimental setup forstudying effect of shear stress on MTs.

II. Perform quantitative investigation on
the behavior of MTs under shear stress.

Stretch chamber
Verticalstepping motor

 OMEC-2BG (Sigma Koki)
 Output velocity:1.5-100µm/s

DCmotorPC N2DC motor

PDMS

PCLensKinesinanti-GFP
antibody

PDMS

MTCaseinStress direction

 Young’s modulus:
E=1.86 MPa

Stretch chamber
How it works?
Stretcher

ΔL
Strain,  (%) 100L∆L= Length change of PDMS
L= Initial length of PDMS

3 cm

Microtubule fragmentation
MicrotubuleElongation

Kinesin: 900 nM
Strain: 14%
Strain rate: 1.4 %/s
Before applying
stressFragmentation

10 µm

After applying
stressShear stress causes fragmentation of MTs.

Microtubule fragmentation

Kinesin changes rigidity ofMicrotubule

Kinesin (nM)
501002006009001300

Kinesin works as a softening agent for
Microtubule.

Buckling of MT by compression
Kinesin: 30 nM
Compression rate:
1.4 %/sCompression

Before compression
10 µm

After 14% compression

Compression causes buckling of MTs.

Role of Kinesin in compression
induced deformation of MTS
Kinesin (nM)
1030

50100
20010 µm

Structural integration of Actin
SaltActin

m
＝

KCl
10nm

5nm

pI=4.7

F-actin

E.D. 4e/nm
Lp 10um

F-Actin

Poly (L-lysine)

10μmPolycation

NH CH CO n
CH 2 4
NH 3+ Cl

Poly x, y-ionene

Actin bundle

PDMAPAA-Q
CH2 CHnCONH
CH2 3
H3C

N+ CH3
ClCH350nm
Biomacromol., 9, 537-542 (2008)

Bioconjugate Chem 14(6); 1185-1190 (2003)

Anisotropic growth of bundles
LDAnisotropic nucleation growth model
NucleusF-actins + polycation

D is determined by D*

D*  4 / 2g (G / D  0)

Di DL

L is determined by CA / CN(CN : nucleus concentration)

 LiΔgG  G  G  gV  Sbulksurfπ D2L
π D 2  2pDLg 
42Actin bundle : Surface energy per unit areag : Energy gain per unit volum e / g : Nucleus size

 (gD2 D)L   (gL) D2  (L)DBiochemistry, 45(34), 10313 (2006)

Active self-organization
Structural Integration of Microtubules
Kinesin＋ATP

Microtubule(MT）streptavidin(St)Biotin(Bt)Ref. Nano let.,2005

Biomacromolecules 9, 2277–2282 (2008)

Active Self-Organization

Parameters
・Cross-linker conc.
（St/Bt)・MT conc.

Polymorphism

SingleTub: 672nM
St/Bt: 1/100

Bundles+ATP 5mM~4h
Tub: 672nM
St/Bt: 1/16

Network+ATP 5mM~4h
Tub: 3360 nM
St/Bt: 1/8

+ATP 5mM~4h
Tub: 672nM
St/Bt: 1/1620μm（X100 speed）

20μm（X100 speed）

Phase diagram for MT assembly

NetworkRingBundle

SingleSoft matter 2011

Major Parameters20μm）
Langmuir 201032±2 x10-24 Nm2
62±9 x10-24 Nm2

Handedness of the rotation
C.C.W : C.W. =93:7(n=238)
Microtubule: 240nM
Kinesin: 63nM

Biomacromolecules 9, 2277–2282 (2008)

Supertwist in PFs arrangement

Scenario for preferential rotation
Right handed

CWCCW

Left handed

Increase in PFs of MT
TEM Image
Percentage of total MTs

5030min24h

40

Ref. J.mol.Biol.,2000

30

Right20
10Left01112

131415

Number of PFs

1617

Effect of PFs(n) on bending momentn12R2rCross-section

EI2 3p 4R, I  ( 2 n  n) rp4
M

M : bending moment [Nm]R : radius of curvature [m]EI : flexural rigidity [Nm2]
I : Second moments[m4]R15
 1.22
R14R24h 1.28
R30minTheoreticalExperimentalIncrease in Ring diameterwith Incubation time
Ave. 4.5μm、Mean 3.7μm

Ave. 5.8μm、Mean 4.8μm

251524 h

30min201524h
10R24h 1.28R30min1050

Events (number)

Events (number)

30 min02

468 10 12 14 16

Ring diameter (m)

→

500

2

468 10 12 14 16

Ring diameter (m)

Chirality shift in nature

T. Hashimoto et. al: PNAS 2007

R. Kuroda et. al: Current Biology 2004

Size distribution

10mImportant parameter forring formation

1.Bulk and Surface E

2.Bending E
3.Confrmational ESize variation of MT rings

10m

Bending rigidity  : bundle rigiditybDb   s ( b )4Ds

 s : filament rigidy
Db : bundle diameter
Ds : filament diameter

Thermodynamics of MT ring formation
ΔG~Bulk＋Surface＋bending＋Conformation＋Coulomb E＋Counter ion S

32/3
2 / 3
2/3
Gcoil    2 / 3  L  k BT  
2e2k BT 2 / 3 ln 
2/3
ls 3 : effective binding energy : effective surface energy : density of the polymer chaink : rigidity of the polymer chain
L : contour length
: dielectric constantls: Bjerrum length Soft-matter, 2012

Thermodynamics of MT ring formation

3
2/3
2 / 3
2/3
Gcoil    2 / 3  L  k BT  
2e2k BT 2 / 3 ln 
2/3
ls 3Soft-matterMT ring formation at Air/buffer interface

Yield >90% (previsou~0.4%)

Soft matter(2012)
Front cover

Conclusions:
1. Topological variance is a very common

phenomenon observed in nature.

2. Diverse structural variation is the key
to highly complex and versatile activities

of natural bodies.