Extending Physics through the Exotic Events in Life:
Simple Theory and Real-World Modeling
K. Yoshikawa (Doshisha Univ.)
Scale
Free Energy (local equilibrium)
Protein
RNA
DNA
Microscopic Master Eq.
Single Cell
Mesoscopic Langevin
Cell-Cell Commun.
Development
Macroscopic PDE
Short DNA is
a stiff rod.
All of the genomic DNAs are
giant (above 1 mm).
0.8 Mbp DNA;
Full length 300mm
Persistence
Length; 50 nm
(170 base pairs)
Giant DNA is a flexible rope.
AFM
1 mm
Current Picture on Folding Transition of a Polymer Chain
Good Solvent
Θ－Solvent
Poor Solvent
Flory-Huggins Theory
http://rkt.chem.ox.ac.uk
Mean-Field Theory on Single Chain
Majority of theoretical studies had adapted the picture of
continuous transition, expect some (Grosberg & Khoklov), on
the coil-globule transition of single chain, until a decade ago.
JCP,102,6595(’95); PRL, 76,3029(’96); JPCB, 101, 9396 (‘97).
Flexible: Continuous
Coil
Globule
Semi-flexible:
Discrete
Contour length: 57 mm
Ｔ4 ＤＮＡ
（166ｋｂｐ）
Cationic surfactant
Ｇ
Full length 57mm
Electron Micrograms
Bar: 0.1 mm
Surviving Charge Decides the
Characteristic Scale of Segregation
F ( N )  N  N
F(N)
ー
ー
ー
ー
ー
ー
ー
ー
ー
ー
2/3
Q /r
2
ー
ー
ー ー
ー
ー
ー
ーQ
ー
N
ー
ー
ー
ー
ー ー
ー
ー
ー
Number of
Segments
If Q∝N ,
F ( N )  N  N
2/3
 kN
5/3
Elongation of Genomic DNA
of E-Coli by Laser
Shindo, et al.J. Biotech.(2008).
Change in DNA length after g-ray irradiation
Irradiation on elongated DNA
Irradiation on compact DNA
60Co
1.2
1.2
0 mM spd
0.3 mM spd
0.8 mM spd
L / Lo
1.0
0.8
0.8
0.6
0.4
0.4
0.2
0.2
0
500
1000
1500
2000
0 mM spd
0.3 mM spd
0.8 mM spd
1.0
0.6
0
60Co
0
0
Radiation dose D (Gy)
The fitting curves are based on the Eq.
Y. Yoshikawa, KY, et al. Chem. Phys. Lett. (2008)
500
1000
1500
Radiation dose D (Gy)
L / L0  1 / ( kD 1)
2000
0.020
Irradiation on elongated DNA
Irradiation on compact DNA
L / L0  1 / ( kD 1)
k (Gy-1)
0.015
0.010
Relative ratio:
0.04
0.005
0
0
0.2
0.4
0.6
[SPD] (mM)
0.8
1.0
The breaking efficiency k of g-ray-induced breakage for compact
DNA was 25 times smaller than that for elongated DNA.
Y. Yoshikawa, KY, et al. Chem. Phys. Lett. (2008)
Takata, Maezima, KY, et al, Plos One (2013)
Reactive Oxygen
g-Ray
quadratic
linear
Y. Yoshikawa, KY, et al., FEBS Lett. (2004)
Threshold
Ultrasound
Shimobayashi, KY, et al., JCP, 2013.
Yoshida, KY, et al., Appl. Phys. Lett., 2013.
Extending Physics through the Exotic Events in Life:
Simple Theory and Real-World Modeling
K. Yoshikawa (Doshisha Univ.)
Scale
Free Energy (local equilibrium)
Protein
RNA
DNA
Microscopic Master Eq.
Single Cell
Mesoscopic Langevin
Cell-Cell Commun.
Development
Macroscopic PDE
Experiments under 2-D confinement
10mm
Collaboration with
Prof. C-Y. Shew
NY City Univ.
Oda, Shew, Kubo, KY (2015)
Cell-sized sphere with actin & DNA
0.6mg/ml
0.3mg/ml
Negishi, et al., Phys. Rev. E, 2010
Gene expression is promoted in smaller confinement
DNA mRNA Protein
• GFP-intensity is inversely proportional to the droplet size.（DOPG, 3hr）
Cell-free gene expression system:
TNT rabbit coupled reticulocyte
lysate
system
(Promega,
Madison, WI)
10～100µm
Kato, et al., Sci. Rep.2012
Who manages the expression of 20,000 genes?
Current network hypothesis gives the
answer:
Hypothesis of Jacob & Monod
Hypothesis of Jacob & Monod
(1961)
(1961)
Jacob-Monod
a  b 1
    0.1
g 1
Fluctuation Destroys the
Stability of Fixed Points
Bifurcation
Stable Fixed Point
Unstable Fixed Point
Stable Fixed Point

 dx1
 dt    y   gx1
2

 dx2

 gx2
 dt 

  y1



 dy
 1  ax1  by1
 dt
 dy2
 ax2  by2

 dt
[Oper ]  Y
[Oper ]  Y

Without higher order nonlinearity,
the stable fixed points are fragile.
In actual biochemical interactions, large
nonlinearity is unrealistic because of the
existence of intermediate states.
Network: Fluctuating pairs of key-locks
Environment: Robust owe to large number
Metabolic Network
Expression
Genetic Regulators
Unfolded DNA
Transcription
Intra-cellular
Network
Nuclear
Environment
Loose Packing
Tight Packing
Outer
Environment
Folder of genes
Life is a hybrid system between
network and environment.
Extending Physics through the Exotic Events in Life:
Simple Theory and Real-World Modeling
K. Yoshikawa (Doshisha Univ.)
Scale
Free Energy (local equilibrium)
Protein
RNA
DNA
Microscopic Master Eq.
Single Cell
Mesoscopic Langevin
Cell-Cell Commun.
Development
Macroscopic PDE
Current Hypothesis on Morphogenesis:
Turing Pattern (1952)
Reaction Diffusion System
The Necessary Condition
Du  Dv u : activator,
v ：inhibitor
Criticisms： Long-range diffusion of morphogens (inhibitor)
would not be common in biology.(Goodwin 2001)
Somitogenesis（体節形成）
Mouse Embryo
1234
5
6
Traveling wave of Gene
Expression (Hes1 / Hes7)
Head
Tail
Tail
0.5mm
2 h / period
0.5mm
Masamizu, Kageyama, KY, et al., PNAS 2006
Y. Saga, H. Takeda Nature Reviews 2, 835, (2001).
Activator-Inhibitor Model
u:activator,
v:inhibitor,
f, g: local kinetics of u, v
t1,t2: timescales of local (intra
cellular) kinetics
“Turing Pattern” never occurs.
Laplace Operator; From continuous into Discrete
Somite Segmentation is Generated through Traveling Waves
Numerical
Experiment
Nagahara, KY, etc “Phys. Rev. E, (2009)
Difference from the Turing model
Present scenario
• Discrete medium
• Stationary but Critically
Dependent on history
and boundary .
Oscillatory
Bistable
Extending Physics through the Exotic Events in Life:
Simple Theory and Real-World Modeling
K. Yoshikawa (Doshisha Univ.)
Scale
Protein
RNA
First-Order Phase Transition in
a Polymer Chain Free Energy
DNA
Single Cell
Confinement of Mesoscopic System
Cell-Cell Commun.
Development
Spatial Discreteness Create SelfOrganized Pattern