Download Cell Biology Core

Cell Biology Core
•Cell Optimization and Robustness:
•Countless cycles of replication and death have occurred
and the criterion for survival is the passage of DNA despite
the challenges:
•1. number of proteins per cell
• 2. salinity and pH
• 3. Temperature
• 4. nutrient level
• 5. environmental factors
Cell Biology Core
•Cell Functions: Systems Bioengineering
•Cells optimize functions for efficiency and robustness, similar
to optimization of industrial production
•Functions can be dissected into steps performed by modules
•Modules contain many proteins and communicate with other
modules
•Quantitative measures of function are important: death vs. life
is far from full story
•Control theory approaches are useful
•Compartmentalization and term limits correlate robustness
Cell Biology Core
Neurofacin
Fz
GPCR(ai)
AC5,6
CRAC
(Ca++)
GPCR(aq)
IR
Wnt
AA
CK2
bg
DSH
aq
ai/o
PLC
DAG
cSrc
Grb2
1,4,5PIP3
Ca++ Ch
PDK
Ank-4
CITRON
Rap-GAP EPAC
GAP
cdc42
Rap1
IP3R
PDE
Ca++
BAD
Jak
JIP
STAT3
IQGAP
LIMK
PAK
a-catenin
PKA
MEK5
MEK6
MEK4
I1
PP1
PP2A
JNK/SAPK p38
HOMER
NO
BMK
NFAT
aq
Cofilin
Ras-GAP
a-actinin
Can
YOTIAO
MP1
profilin
MAPK1,2
Axin
MKP
GSK-3
Ran
cPLA2
Ran-GEF
S6K
MTOR
RSK
MNK
GRIP
Ran-GAP
L1
ankyrin
IF's
AMPAR
Plectin
SHP
2
60S
80S1
48S
E1
43S
S6
eEF2K
E2
GPCR(aq)
mGLU-R
cGMP
MAPKAP
Microtubule
NMDAR
glutamate
MEK1,2
PIP2
N cadherin
CaMKK
MLK3
RhoK
myosin
cSrc
CaMK2
PKB/AKT
MEKK
Raf-1
WAVE
Actin
Gelsolin
Ca++
PSD95
Ca++
cAMP
B-Raf
MARCK
Myosin
PPase
SMC
Vinculin
Na+Ch
as
AKAP-79
FYM
b-catenin
H202
bg
PKC
CAT
Cool/PIX
TAL PAX
ILK
AC1/8
CaM
a-actinin
Talin
IRS-1
Rac
IP3
CRK
integrin
PI3K
AC2
SoS
FAK
CAS
SHP2
SoS
SHC Grb2
Ras
Rho
Abl
GPCR(as)
RTK
80S2
60S S6
40s
Ca++
E
NSK
MUNC18
syntaxin
SNAP25
PHAS
Synaptophysin
Synaptobrevin
Ca++
Synaptotagmin
mRNA
CBP
cd2
FOS
LamininA,B
STAT3
Tcf/Lef
b-catenin
SIRP
2B
CoRest
NRSF
mSin3
Elk
AP1
jun
CREB
MEF2
CREM
SRE
NFAT
ATF2
CAMK4
ZIF268
Rabphilin
Rab3
RM
Cell Biology Core
•Cell Size and Number of Molecules
•Volume of a 3T3 cell of 15 mm in diameter (4/3pr3 = 2000 mm3
or 2 x 10-9 cm3) vs. bacterium two microns in length and 0.8
micron in diameter (volume lpr2 = 1 mm3 or 1x10-12 cm3)
•Protein Concentration in Cytoplasm ~180 mg/ml (average
protein is 50 kDa, the 3.2 mM protein or 2 x1018 molecules per
ml)
•No. Proteins/Cell is 4 x 109 molecules per eukaryotic cell or 2 x
106 molecules per prokaryotic cell (if 10,000 different proteins
for the eukaryotic and 2,000 for the prokaryotic, then about 105
molecules of a protein per cell)
Cell Biology Core
Cell Biology Core
Life at Low Reynolds Number
(diffusion and transport)
•Reynold’s number
R = vLr/h
•Example: fish vs. bacterium
Cell Biology Core
•Reynold’s number
R = vLr/h
•fish of density approximately that of water (r = 1 gm/cc),
length of 10 cm (L), moving at a velocity of 100 cm/sec (v) in
water (h = 0.01 g/cm sec),
we calculate R to be about 105.
•bacterium of the same density, length of 1 micron (L = 10-4
cm), moving at a velocity of 10-3 cm/sec through water,
we calculate R to be 10-5.
Cell Biology Core
Viscous Drag on Particles
•Einstein-Smoluchowski relation
•
vd fd = Fx
•The drift velocity of the particle (vd) is related to the external
force (Fx) by a constant called the frictional drag coefficient (fd)
Cell Biology Core
•Because the drag is the same for diffusion as for externally
applied forces, the diffusion coefficient can be derived
D = kT/ fd
•
•For the special case of a spherical particle, Stokes’
law gives the relationship between force and velocity.
•
f = 6phr v
Cell Biology Core
•For a sphere we know from Stokes’ law that fd = 6phr,
which enables us now to calculate D directly
•
Dsphere = kT/6phr
•For a one micron sphere in water fd = 9.5 x 10-6 g/sec
and Dsphere = 4.4 x 10-9 cm2/sec
Cell Biology Core
One-dimensional Diffusion
Assumptions:
1. Steps of r length occur at regular intervals (t)
2. The direction of each step is equally likely to be + or –
independent of previous steps.
3. Each object moves independent of other particles.
Cell Biology Core
Root-mean-square displacement
•Single particle tracking of gold particles or single
fluorescent molecules enables diffusion measurements at
the single molecule level.
•
2D1t = < DX2>
Cell Biology Core
Gaussian Distribution of Diffusing Particles
•If all of the particles are at the origin originally, the
distribution after many elemental steps follows a Gaussian
•
P(x)dx = (1/(4pDt)1/2) e-x2/4Dt dx
•For a normal curve the fraction of the area within one standard
deviation (s = (2Dt) 1/2) is approximately 68% of the total area
Cell Biology Core
•Practical Implications of the Diffusion
Equation
•For a cell (v = 3000 mm3 or a cylinder 2 mm high and 44
mm in diameter), diffusion of typical proteins would take
~40 sec to travel about 20 microns (D = 10-7 cm2/sec)
•For an axon one meter in length, typical proteins would
require 1011 seconds or about 3,000 years
Cell Biology Core
•Non-ideal Diffusive Processes
•Recent analyses of single particle tracking of
diffusing proteins, vesicles, etc in cytoplasm have
found many MSD versus time plots are non-linear
•Two different types of non-linearity are observed often in
cells; confined diffusion and flow plus diffusion
Cell Biology Core
•Confined Diffusion
•Many objects in cells have limited access to different
regions of cytoplasm.
•Endoplasm, MT
•Ectoplasm, cortex
Cell Biology Core
•Diffusion in a Flowing Medium
•If a particle is diffusing within a medium that is
moving or if the particle has a drift generated by a
constant force (e.g. magnetic), then MSD versus time
will show a positive deviation (quadratic).
•
< DX2> = 2D1t + (vt)2
Cell Biology Core
•Diffusive Transport
•We will consider a simple case of synthesis and
assembly in cytoplasm. Site A is where a protein
is being translated and folded properly. Site B is
where the protein is assembled into a working
complex. Proteins need to get from A to B for
assembly. How can we describe the process?
Cell Biology Core
•One-dimensional Diffusive Transport
•One way to understand diffusive transport is to go
back to the diffusing drunks and to talk about 2
bars at closing. Assume that the bars are one step
from each other and that 200 are in one vs. 100 in
the other bar. At early times will there be a net
transport?
Cell Biology Core
Fick’s Law.
Jx = -D dC/dx
where Jx is the flux in the x direction,
D is the diffusion coefficient, dC/dx is
the concentration gradient in the x
direction.
Cell Biology Core
Substrate Rigidity Can Direct Movement
•Lo et al., 2000. Biophys. J. 79:144-152
Cell Biology Core
Cell Biology Core
Cell Biology Core