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.