Louis Reese 11.12.2006

TVI « Theoretical Biological Physics »

(Prof. Erwin Frey)

Betreuung durch Claus Heußinger

Fluctuation-Driven Transmembrane Transport

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Outline

1. The Cell Membrane• Protein activity in the Plasma Membrane• Transport Through Membranes

2. Transport due to Fluctuations• Modelling a Channel Protein • Developing a Theoretical Model• Solutions of the Fokker-Planck Equation

3. Outlook

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

The Cell Membrane

Lipid bilayer

hydrophilic

hydrophobic

Membrane maintains concentrations of solutes

Storage of Potential Energy

Hydrophobic Molecules(O2, CO2)

Small molecules, polar, uncharged (H2O, glycerol)

Large molecules, polar,uncharged (glucose)

Ions(H+, Na+, K+, …)

Motivation Hydrophobic barrier

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

The Plasma Membrane

Plasma Membrane

Ion gradients provide energy for

• ATP Synthese

• Transport mechanisms

• Electrical signals

Cell Boundary

Cytosol

Membraneous Cell Compartments

We need machines toperform these tasks:

Membrane Proteins

Ingest nutrients

Excrete metabolic waste

Motivation Membrane Activity

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Membrane Proteins

• ~30% of Genes (animals) encode Membrane Proteins• Membrane Proteins ~50% of the membrane mass

Membrane associated Reactions

Connection to Cytoskeleton

Transporter

Sensors/Receptors (external Signals)

Motivation Protein Functions

Nonequilibrium Fluctuations

Are supposed to be responsible for

A. E. Pelling, et al. (2004)

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

• Functional Proteins asure selectivity

Transport Through the Membrane

Motivation Transmembrane Transport

Active

Pumping « Uphill »Coupled to catalysing energy-source (Light, ATP, coupled-Carriers)

We’ll see soon that there are posibillities to make

these Channels « WORK »

Passive

Facilitated Diffusion « Downhill » the Concentration gradient

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Transport due to Fluctuations

• The Glycerol uptake Facilitator (GlpF)

Theoretical Model Molecular Restraints

Na+ SugarMolecule

X-Ray Structure shows Selectivity

AsymmetricPotential of Mean

Force (PMF)

Finally a realistic Potential!

Molecular Dynamics:

M. Ø. Jensen, et al. (2002)

Pulling

Needed, but poisons the cell at high concentrations.

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Modelling Transport

• Brownian Motion: The Langevin Equation

Theoretical Model Equation of Motion

VirtualFriction

Virtual Realistic

Potential ofMean Force

Langevin-

Force:White Noise

MembraneFluctuation-

Force

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Modelling the Transport Protein

Probability densities

Fokker-PlanckEquation

Theoretical Model Transport FPE

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Details of Molecular Flux

Theoretical Model Transport Flux

• Composition of Flux through Channel

Diffusion Acting ForcesAsymmetric Protein Potential

+ Membrane Fluctuation

We know already:Zero-Force & Constant-Force

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Transport enhenced by external Force

Results Outward Flux Periodic Force

• Periodic Force

Despite Force: High Barrier

out

in

in

out

Asymmetric Potential

Outward Transport

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Transport driven by Random-Telegraph-Force

• Fluctuating Force

Results Outward Flux Random Force

Poisson Mean Switching Time

We still expect outward fluxbeing better than inward flux.

But 2 more Questions arise:

1. How do switching times influence transport?

2. Which role plays the concentration gradient?

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Switching Times tune Transport

• Switching very fast ~10-9s does not influence flux.• Switching slowly ~10-2s, the time-dependence vanishes

Results Switching TimeTunes Transport

?

In between, at equal concentrations:

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Concentration Gradient Regulates outward Transport

• Current reversal depends on concentration gradient.

Results Concentration Gradient Regulates outward Transport

The passive Protein finally « WORKS » !

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Outlook

• Biological:Membrane Fluctuations could play a role in Cellular Transport Mechanisms– Protection against poisoning– Enhence nutrient uptake

• Theoretical Physics:Insight into processes spanning a timescale– From bottom-up simulations (~10-9s) to– Fluctuations (µs) to– Genetic mechanisms (~minutes)

Outlook BiologyPhysics

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Take-Home Message

• Membranes– Make the difference between

Life and Environment.

• Proteins– Are active or passive transporters

– Molecular structure/symmetries are crucial!

• Membrane Fluctuations – Influence protein-transport properties!

– Could be a hidden energy source

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Thank you for your attention!

Protein Fluorescence

Louis ReeseFluctuation-Driven Transmembrane Transport

Bibliography

Results:

I.Kosztin, K. Schulten, PRL 93, 238102, 2004

Additional Material:

B. Alberts et al., Molecular Biology of the Cell, (2002) 4th ed.

M. Ø. Jensen, et al., PNAS 99, 6731 (2002)

Homepage of Klaus Schulten.

Previous Seminar Talks:

„Forced thermal Ratchets“

„Fluctuation Driven Ratchets: Molecular Motors“

Appendix