Summer 2008
Syllabus
Biophysics II
Cell Biophysics
English: RM224, 15:15-18:30
Lecture notes with the according references will be published in the www.
1. Basic Cell Biology
2. Membrane Biophysics
3.
4.
5.
6.
Intracellular Transport
Active and Passive Physics of the Cytoskeleton
Neurophysics
Photosynthesis
(parts are courtesy of Monika Möddel, rest collected by Carsten Selle )
Diffusion – Brownian motion
Botanist Robert Brown noticed in 1828 that pollen grains (~ 1 µm) suspended in water do a peculiar „dance“ visible with his
microscope. He assumed that he was observing some life process. But the pollen never stopped moving (and were not possible to be killed, even by boiling. Then he found that all other material of this size (which we call colloidal particles) performs this
motion.
• Spontaneous spreading of matter due to thermal motion
• One type of transport phenomenon
2
3kT mu

2
2
• E.g. typical molecule of air (N2) with m=4.7x10-26kg at room temperature
(290K):
3
kT
2

1
→ Effective transport systems using this speed?
u


508
ms
m
• NO: Each molecule moves fast, but cannot move very far in a straight line
without colliding with another particle
→ Random motion
Diffusion – Brownian motion
• For a particle with step size ±, equal
probability in both directions and one step
every t seconds, one yields for the mean
square distance (one dimension):
2

x2
t  t

Distance from origin
Diffusion coefficient
steps
2
D
2
and gets
2
2




x
t

2
Dt

x

x
t

2
Dt
rms
• This kind of diffusion is called „normal diffusion“
(linear t dependence of MSD)
D: diffusion coefficient
Diffusion – Brownian motion

jdiffDn
ick‘s first equation of diffusion
With the conservation of mass
This gives the diffusion equation
(or Fick‘s second equation):
Fick‘s first diffusion law


jdiff0
tn
 t n = D n
2
The step size distribution is a solution to the diffusion equation,
with the initial condition n(r,0)=d(r), here in two dimensions
  r2 
1

P(r, t ) 
exp 
4Dt
 4 Dt 
MSD  r
 4 Dt
2
Conveniently, the mean square
displacement (MSD) characterizes
diffusion.
  r2 
1
  2dr
  r P(r, t )dr   r
exp 
4Dt
 4 Dt 
2
2
Diffusion – Brownian motion
Diffusion speed depends on friction z (Einstein relation)
D
k BT
z
In three dimensions, the friction coefficient z depnds on a, the radius of a
diffusing sphere, with the viscosity h: z6ha (Stokes relation).
In 2D, z is not well defined. If one considers, however, a 2D membrane with
viscosity h within a 3D liquid, the diffusion cooefficient of a cylinderical
protein with height h and radius a is given by the following expression:
D
k B T  hh 
ln  ' 
4hh  h a 
With h‘, the viscosity of the aqueous phase (h>>h‘). Note that D depends
logarithmically on a within this approximation.
P.G. Safman & M. Delbrück, PNAS 72 (1975), 3111
The compartments have membranes
- Three main domains of life
• A membrane-packed cell
Bacteria, archaea, eucaryota
- Empire of Procaryotes:
Archaea and Bacteria
have no nucleus!
- Eucaryota: have nucleus
Multicellular organisms:
plants, animals, fungi
- diversified, cells perform specific
functions in organs as nerves, leaves,
liver, roots, etc.
Picture from Lodish et al.
How the cell surface looks like – the plasma membrane
Membrane = Lipids + Proteins!
After Singer & Nicholson 1972, the proteins swin freely within a liquid ocean of lipids
(in a liquid-crystalline phase called La).
History of membrane models
Synopsis from: O.G. Mouritsen,
Life – as a Matter of Fat
Increasing complexity!!
How the bilayers were found with monolayers
•
Monolayer at the air/water interface – a simple
experimental model membrane
•
Gorter & Grendel proposed the dauble layer
model based on monolayer results 80 yrs ago
•
Further historic contributions by
•
•
Ben Franklin (~1770) Oil calms water
Agnes Pockels (~1895) developed first troughs,
measured first pressure-area isoterms in her
kitchen!!!
Rayleigh (~1890) Reported Relations between
surface tension monomelcular layers
Irving Langmuir (~1920) laid scientific
foundation of monomolecular films
Katherine Blodgett (~1920) works on transfer of
monolayers from water to solid support
•
•
•
Surface pressure 
   * 
*=surface tension of pure water
Langmuir`s film balance
Transport through membranes
• Transport through diffusion does not require
additional energy and is therefore called
„passive transport“
• H2O can pass a semipermeable lipid double
layer without proteins (osmosis)
→ Free diffusion
• Diffusion of different substances do not
interfere with each other (no competition)
• Substances can cross membranes by diffusion
if they can dissolve in the oily interior of the
membrane (hydrophobic)
→ Ions (like Na+, K+, and Cl-) can’t (almost)
Transport through membranes (by proteins)
Facilitated diffusion of ions
• Proteins act as carriers or pores
• Permit flux of substances that cannot diffuse
directly through the membrane
• Movement is still passive, from high
concentration to low
• Saturates when substance reaches high
concentrations due to lack of available protein
• Transport proteins resemble enzymes:
just as enzymes are substrate specific and only
catalyse certain substrates, transport proteins
are solute specific and only transport certain
solutes
• Related substances can compete for the same
carrier or pore
The non-protein part of the membrane:
Lipids
Rough composition of a membrane:
Self-assembled amphiphiles.
A phospholipid (phosphatidylcholine)
Why proteins in the membrane?
Amphiphilicity has challenging chemical/biochemical implications!!!!
Reduction of dimensionality (3->2) enhances bimolecular enzymatic reactions (Adam
& Delbrück 1968)
M. Eigen, 1974: „Nature‘s trick with membranes“
Lateral diffusion: Signalling
An example
Plasma
membrane
Signal
(primary
messenger
molecule)
attaches here
Phosphatidylinositol-4,5-bisphosphat [PI(4,5)P2] is a
key signalling molecule
E.g. the differentiation of a b-cell into an antibodyproducing plasma cell is triggered when an activated
b-cell receptor recruits PI3 kinase which binds to a
phosphatidylserin on the receptor complex
Lateral diffusion: Signalling
PIP3 kinase phophorylates PIP2 in the plasma membrane to form PIP3
which acts here as “second messenger”
Lateral diffusion: Signalling
Intracellular signal proteins then bind to PIP3:
In activated b-cells PIP3 recruits both the cytoplasmatic tyrosine kinase BTK and
phospholipase C (PLC) to the plasma membrane
→ Brings this two components into close proximity
→ BTK can activate PLC by phophorylation
Lateral diffusion: Signalling
Activated phospholipase C then splits additional PIP2 molecules into two fragments:
Soluble IP3 and diacylglycerol. Both of the fragments relay the signal onwards into
the interior of the cytoplasm.
Second messengers: extremely important for cell – cell communication.
Significant for: cell growth, division, and apoptosis (induced cell death)
Anomalous diffusion
Anomalous diffusion is a diffusion-like process characterised by a non-linear
dependence of the mean squared deviation (MSD) of a particle on time
x2 
Example:
thermal motion of colloidal tracer particles in entangled actin filament (Factin)
• Particle radius is comparable to the mesh size of the F-actin network

• In this regime, the ensemble-averaged MSD of the particles is proportional to
where 0    1 and 0
.1 100
sand depends only on the ratio of the probe
radius to mesh size
• By directly imaging hundreds of particles over 20 min it‘s found that this anomalous
subdiffusion is due to the dynamics of infrequent and large jumps particles make between
distinct pores in the network


Anomalous diffusion
Thermal motion of colloidal tracer particles in entangled F-actin
MSD of 0.25 μm spheres in F-actin with ξ = 0.75
μm (open triangles), 0.55 μm (solid circles), 0.30
μm (solid squares), 0.25 μm (solid triangles), and
0.17 μm (open squares), solid line: linear fit
The scaling of the diffusive exponent, γ, as a
function of a/ξ for several particle radii, a: 0.25
μm (open squares), 0.32 μm (diamonds), and 0.5
μm (triangles). Error bars indicate measured
sample-to-sample variation.
.
•Steep decrease of γ in this range
→ small variations in a or in ξcan have large effects on the bead mobility in a network
Results:
• Actin network is inhomogeneous
• Subdiffusive motion is traplike
Y. Wong et al., Anomalous Diffusion Probes Microstructure Dynamics of Entangled F-Actin Networks,
PhysRevLett.92.178101 (2004)
FRAP – Flourescence Recovery After
Photobleaching
• Membrane protein (fluorescently labelled) that lies in the membrane network of the
endoplasmatic reticulum
• Distinct part of the cell surface bleached by an intense lase beam
•Quick recovery → protein is very mobile in the plane of the membrane
Graphical presentation of data collected during a FRAP experiment
D = w2/4t1/2
With w, the spot width and
t1/2, time required to
recover half of its original
intensity
(Y/ X) x 100 = % recovery (almost never reaches 100% in practice)
X: Percentage of fluorescence lost due to photobleaching
Y: Amount of fluorescence that returned to the bleached area
lateral mobility is determined by the slope of the curve
FCS, fluorescence correlation spectroscopy
• A laser beam is first expanded by a telescope (L1 and L2)
• Then focused on a fluorescent sample (S) by a high-NA
objective lens (OBJ)
• The epi-fluorescence is collected by the same objective
and reflected by a dichroic mirror (DM), focused by a tube
lens (TL), filtered (F), and passed through a confocal
aperture (P) onto the detector (DET)
• Magnified focal volume (green) within which
the sample particles (black circles) are
illuminated.
• Focal volume: the distribution of laser
illumination at the focus of the objective
• Observation volume: region in space where
fluorescent molecules are both excited and
detected; contained within the focal volume
FCS
A nice application, in principle…
kT
D
6h
R
Changes in the hydrodynamic radius R
can cause changes in the diffusion
coefficient
→ Changes in R directly affect the
mobility of the molecule
• Examples for changes in diffusion
coefficients following protein
denaturation
• Albumin in the denaturated state
exhibits longer diffusion times τd, while
denaturated Calmodul diffuses faster
with shorter τd
E.g. the 3D structure and thus, the shape,
of a protein influences its mobility
→ It is in principle possible to monitor
protein folding or unfolding transitions
• Unfortunately, differences in the
diffusion coefficients between two
folding states are generally quite small
SPT – Single Particle Tracking
• The MSD can be calculated from the
evaluation of recorded tracer trajectories
 
N

n

2
1







x

t

r
j
t

n
t

r
j
t
N

n
j

1
2

r t 
t
position of particle at time t
time step between two successive pictures of
the labeled molecule
nt  t
n
# of steps such that
N
total # of steps in a track
Qian et al., Biophysical Journal 1994
SPT on
membranes
•
movements of membrane proteins at the level of individual molecules.
•
small colloidal gold particles to our target membrane proteins by way of ligands or antibodies against the
membrane protein.
•
The size of the gold particles: 40 nm in diameter, but 10 and 20 nm particles have also been used!
•
Visualized by contrast-enhanced optical microscopy.
•
Monitoring the movements of individual or small groups of membrane protein molecules on the surface of
single living cells in culture.
Rafting?
Biochemical evidence
Detergent resistent domains:
Liquid-ordered (Lo) phase
Physical observations
Confinements found for:
-lipids: 250-750 nm size
less than a second 2
-proteins: 100 nm to 1 µm size
from 3 – 35 s 3
1) Picture, right: K. Simons and G. Ikonen, Nature, 1997, 387, 569
2) G. J. Schütz et al. EMBO J., 2000, 19, 892; T. Fujiwara et al. J. Cell Biol., 2002, 157, 1071
3) E. D. Sheets et al. Biochemistry, 1997, 36, 12449; A. Kusumi et al., Biophys. J., 1993, 65, 2021;
C. Dietrich et al. Biophys. J., 2002, 82, 274
Results from the Kusumi lab
•
movements of transferrin receptor on the surface of NRK cells in culture.
•
Transferrin receptors are necessary for cells to internalize ferric ions.
Model on how the “membrane skeleton” can interact with protein motion
(A. Kusumi, cf. Web site)
A) membrane proteins bound to the cytoskeleton
B) Free motion, confined within a mesh from the cytosekeleton
C) partitioning into raft-like regions
Homework
SPT measurements of a colloidal model protein within a membrane with domains (rafts),
Trajectories of the protein are depicted in red.
Black area: raft-like ordered lipid phase, white area: liquid-like lipid phase.
Bright spot: fluorescent model protein.
Consider the differences measured for D and a in these observations: Can you
explain them? Draw conclusions about a possible biological significance.