BIOPHYSICS – The importance of common length scales
• level of understandingModern Physics: bottom up approach Chemistry
particles – atoms – complex molecules Physical Chem.Biology: Top down approach
organisms – cells – proteins, nucleic acids Organic Chem.
• technological developmentsSolid state – miniaturizationChemistry – increasing complexity
(synthesis and modeling)
nm -- µm
H. Rohrer, IBM Zürich
BIOTECHNOLOGIES – learn from nature
CELLULAR FUNCTIONS and INFORMATION STORAGEcarried out by SINGLE MOLECULES!!!
DNA: highly condensed genetic information
Motor Proteins: actuators, mechanical contraction,cell motility
Ion Channels: electrical signalingNano-scale biological conductors - coupled transport
R. MacKinnon. Nature. 2001.
from: Lambert (13):7248-7253 (2000)et. al. Proc. Natl. Acad. Sci. 97DNA Capsids
Questions:- How is a stiff, highly charged molecule like DNA compacted into such a tight condensate?- What could be the mechanism of spontaneous DNA-toroid formation?
- DNA is condensed and encapsulated into 50 nm radius capsids (hexagonal),- then released and delivered to a target cell or liposome - DNA toroids are spontaneously formed in liposomes containing spermine (polyamine)
Implications: information storage, gene therapy, self-assembly
Myosin
- a motor protein
- responsible for muscle contraction (pulls actin filaments)
Energy source:- ATP hydrolysis
Physical Measurements of Biological Systems
AtomicForce
Microscope
imaging tool
pN force sensor
molecular tweezer
specialized chemical sensor
AFM Imaging ModesTapping Mode:• cantilever oscillated near its resonance frequency• amplitude feedback (repulsive or attractive interactions)
Contact Mode:• deflection feedback• constant applied force (repulsive)
Advantages:-reduces shear & adhesive forces- phase imaging for material contrastDisadvantages:- low Q-factor in liquids (poor interaction sensitivity)- increased normal forces- phase contrast difficult to interpret
Force Volume Imaging:Measures an interaction vs. height profile at each point in an image (an array of f(z) curves).
Force-Distance Curves
HardSurface
Non contact
Van der Waalsattraction
surface adhesion
Pauli repulsion
ApproachRetract
Electrostaticrepulsion
Deflection
Verticalposition
Polymer structural transitions
Ruptureforce
MolecularPullingEvent
Viscoelastic Responsecontactpoint
(electrostatics supressed)
23213
4 δυ−
=ERFHertz indentation model:
Conditions for High-Resolution Imaging(in liquids)
• sharp tip – good machining techniques• flat surface - to avoid tip convolution• small applied loads to the sample
- for delicate membranes & molecules- tapping mode (intermittent contact)
• small tip-sample separations- steep part of the force curve for greatest sensitivity
{electrostatics – controlled with pH & salt concentration
tip
samplez
ztip
samplez
tip
sample
+
- - -
-- - --- -
- -++
+++ +
+ ++
++ +
tip
sample- - -
-- - --- -
- -
++
+ + +
longscreening
shortscreening
+ 1 ions+
+ 2 ions+
High Resolution Imaging - Pore Complexes
Müller et. al. Biophys. J. 76:1101-1111 (1999)Oesterhelt et. al. Science, 288, 7 April 2000, 143-146.
Bacteriorhodopsinsin purple membrane
Porin OmpF from E. coliin purple membrane
Vary electrolyte concentration to reduce, but not eliminate, theelectrostatic tip-sample forces.
Visualizing DNA Anselmetti et.al. Single Mol. 1(1):53-58(2000)
linear λ-DNA circular DNA plasmids circular supercoiled DNA
DNA – enzyme interactions
Hae IIIrestriction
endonuclease- causes a 90deg bend when bound
to DNA
AFM as a molecular scalpel
The Cytoskeleton & Mechanical Structure of CellsActin Filaments:• cellular integrity• shape• part of the contractile apparatus (actomyosin)• dynamic remodelingWhole Cells:• underlying cytoskeletal structure visable• restructuring in response to stimulation• mechanical properties measurable
Microtubules:• organelle allignment• cell division• intracellular trafficing
Intermediate Filaments:• linkers• mechanical rigidityeg: Neuro-filaments- side chains, un-structured entropic springs- maintain interfilament spacing- neuronal polarity and permeability Kumar and Hoh. Traffic (2001) 2:746-756.
Force-Volume Imaging - Elasticity Mapping
From: Rotsch :520-535 (2000).et.al. Biophys. J. 78
Height Images True Topograpy
Fluorescence images Elasticity map
Alcaraz et. al. Biophys. J. 2003. 84(3):2071-2079.
Viscoelasticity Measurements Mahaffy et. al. PRL 2000. 85(4):880-883.
zd
δ
Lock-in Amplifier
A φ
−= )0(
41
1
1
0
biFR
ωδδ
23213
4 δυ−
=ERFHertz model (standard):
+
−= 1
*10
23002 2
3)1(3
4 δδδυ
EERFHertz model (extended):
)1(2"'
**
υ+=+=
EiGGGComplex Modulus:
-600 -400 -200 0 200 400 600 800 10000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
5-HTloss modulus
storage modulusG
"/k
G'/k
time (s)
Viscoelastic Response to 10 µM 5-HT
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Structural Damping Model:
ibfffiGG ++= αη ))(1( 00* )2/tan(παη =
Affinity Imaging / Receptor Mapping• mixed group A and O red blood cells
• ligands tethered to the AFM tip with long-chain polymers, so that specific rupture forces can be clearly distinguished.• contrast based only on the measured strength of adhesion to receptor glycolipids, present in group A RBCs only.
Grandbois et. al. J. Histochem. & Cytochem. 48(5):719-724 (2000).
Molecular Forces & Stretching Molecules4 levels of forces1. smallest – Langevin Forces – thermal agitations.
Brownian fluctuations give a lower limit to force measurements. For a small 2µm cell or bead: FL~ 10 (fN/Hz1/2)Compare to the weight of a cell: ~10 fN“Every second, a cell experiences a thermal knock equal to its weight.”
2/1)12( dTkF BL ηπ=η=viscosity of fluidd=size of the species
2. Entropic Forces – reduction of the # of possible configurations of the molecular system. eg: force needed to elongate a molecule, reducing its degrees of rotational freedom.Stretching models: Freely-jointed chain, Worm-like chain
!measurable4pN~
)(nmlTkF B
E ≈typical for molecularmotors
Kuhn lengthPersistence length: the length for which the chain persists in one direction before turning on itself. For charged polymers, the degree of screening by counter-ions becomes very important.
3. Non-Covalent Forcesinter-molecular - ligand-receptor bonds,
- breaking or rearangement of manyVdW, hydrogen, or ionic bonds
intra-molecular - structural phase transition,- stretching covalent bonds,- protein folding
pNnmeVFnc
160~11~
4. Covalent bondsImportant upper limit for fixing the ends of a molecule to a tip.See: Grandbois et.al. “How strong is a covalent bond”.Science 283:1727-1730 (1999).
nNeVF oc 6.1~1
1~Α
Pulling Molecules:examples
DNAStructural transition are induced. Transition forces depend on bond type.
Titin - immunoglobularmuscle protein
Protein Folding- Energy landscapes have traditionally beeninvestigated by thermal denaturation
- Some bio-molecules are designed to withstand external loads (eg. muscle proteins)
- Mechanical properties are essential to their function
- AFM force spectroscopy used to characterize the mechanics of unfolding secondary and tertiary protein structures
Rief :109-1112 (1997)et.al. Science 276
1
Loading Rate Dependent Force MeasurementsEquilibrium Reaction:• Reversible – no hysteresis• all configuration states are accessible• obtain: FREE ENTHALPY (area under the force curve)
Non-Equilibrium Reaction:• Irreversible – probabilistic event, ∆G ~ kBT• un-binding force depends on the loading rate• obtain: DISSOCIATION RATE(S) (off-rates)
11*1 −−− −∆=∆ FxGG
Free Energy reduction under force:
TkFx BekFk 1)0()( 11−
−− =
Dissociation Rate, force dependence:
=
−−
−
11
1 )0(ln
xTkk
rx
TkFB
B
Most probable unbinding force,dependent on loading rate:
Energy Landscape
Evans et.al. Biophys. J. ’95, ’97, ’99.Nature. ’99.
Guthold et.al. Biomed. Microdevices. 2001.