Physics of Multicellularity
Raymond E Goldstein
Department of Applied
Mathematics and
Theoretical Physics
University of Cambridge
The Size-Complexity Relation
Amoebas, Ciliates, Brown Seaweeds
Green Algae and Plants
Red Seaweeds
Fungi
Animals
?
Bell & Mooers (1997)
Bonner (2004)
The Recent Literature
Phil. Trans. 22,
509-518 (1700)
(1758)
Volvox In Its Own Frame
Tracking microscope
in vertical orientation
Laser sheet illumination
of microspheres
Drescher, Goldstein, Michel, Polin, and Tuval, PRL 105, 168101 (2010)
Rushkin, Kantsler, Goldstein, PRL 105, 188101 (2010)
A Family Portrait
Chlamydomonas
reinhardtii
Pleodorina
californica
Gonium pectorale
Volvox carteri
Germ-soma differentiation
Eudorina elegans
Volvox aureus
daughter colonies
Altruism, apoptosis
somatic cells
Huygens’ Clock Synchronization (1665)
Pendulum clocks hung on a common
wall synchronize out of phase!
Modern version of experiment confirms
that vibrations in the wall cause the
synchronization.
Schatz, et al. (Georgia Tech)
Coupled Metronomes (Lancaster University)
Microscopy & Micromanipulation
micromanipulator
micromanipulator
Quantifying Synchronization
strokes of
flagella
S1 (t ) = A1 cos[θ1 (t )]
Frame-subtraction
S 2 (t ) = A 2 cos[θ 2 (t )]
amplitudes
dθ1
= ω1 + ⋅ ⋅ ⋅
dt
dθ 2
= ω2 + ⋅ ⋅ ⋅
dt
“phases”
or angles
natural
frequencies
θ1 − θ 2
∆≡
= (ν 1 −ν 2 ) t + ⋅ ⋅ ⋅
2π
Cell body
Micropipette
Polin, Tuval, Drescher, Gollub, Goldstein, Science 325, 487 (2009)
A Phase Slip
Goldstein, Polin, Tuval, Phys. Rev. Lett. 103, 168103 (2009)
Model for Phase Evolution
stochastic Adler equation:
∆ = δν − 2πε sin( 2π∆) + ξ (t )
diffusion
Veff(Δ)
Slips
Δ
Synchrony
𝑝+
= 𝑒 𝛿𝛿/𝑇𝑒𝑒𝑒
𝑝−
𝑅 𝑡 = 𝜏𝑇𝑒𝑒𝑒 𝑒 −𝑡/𝜏
τ=
2𝜋
2𝜋𝜋
2 −(𝛿𝛿)2
−1
Beating Dynamics of the
Flagellar Dominance Mutant ptx1
Wild type (in-phase)
ptx1 (anti-phase)
K.C. Leptos, K.Y. Wan, et al., sub judice (2013)
Phototaxis
Adaptive Flagellar Dynamics and the Fidelity
of Multicellular Phototaxis
Drescher, Goldstein, Tuval, PNAS 107, 11171 (2010)
The Mathematics of Turning
angular
velocity
direction
of gravity
Ω(t ) =
1
τ bh
axis
direction
gˆ × kˆ −
bottom-heaviness
relaxation time
In the Volvox frame of
reference, light direction
evolves according to:
surface
normal
surface
fluid velocity
3
ˆ
n
× u(θ , φ , t )dS
3 ∫
8π R
Based on Reciprocal Theorem
(Stone & Samuel)
d Iˆ
= −Ω × Iˆ
dt
Dynamic PIV Measurements – Step Response
Adaptive, two-variable model
p =
( s − h) − p
τr
s−h

h=
τa
p=“photoresponse” amplitude
h=“hidden” biochemistry
Adaptive dynamics also play
a role in sperm chemotaxis:
Friedrich and Jülicher (2007,09)
u = u0 (1 − β p )
Simple modulation of flow
Frequency-Dependent Response
Two-variable model
Data
R(ω ) =
ωτ a
[(1 + ω τ )(1 + ω τ )]
2 2
r
2 2
a
1/ 2
Peak of frequency-response
coincides accurately with the
range of rotational frequencies
within which accurate phototaxis
occurs: TUNING
Multicellular Phototaxis as Dynamic Phototropism
Reduced model
Light direction
Collaborators
Postdocs:
Marco Polin (to Warwick)
Idan Tuval (now Mallorca)
Kyriacos Leptos
Vasily Kantsler (to Warwick)
Jorn Dunkel (to MIT)
Ph.D. students:
Sujoy Ganguly (now Dresden)
Knut Drescher (now Princeton)
Kirsty Wan
Visiting students:
Nicholas Michel (Ecole Poly.)
Silvano Furlan (Pisa)
Faculty:
Cristian Solari – U. Buenos Aires
Adriana I. Pesci – DAMTP
Timothy J. Pedley - DAMTP
John O. Kessler – Arizona
Richard Michod – Arizona
Jerry P. Gollub – Haverford/Cambridge
Jeffrey S. Guasto – Haverford/MIT
Staff:
David Page-Croft G.K. Batchelor
Colin Hitch
Lab (DAMTP)
John Milton