TVI « Theoretical Biological Physics »
(Prof. Erwin Frey)
Fluctuation-Driven Transmembrane Transport
Louis Reese
11.12.2006
Betreuung durch Claus Heußinger
Protein Fluorescence
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
Fluctuation-Driven Transmembrane Transport
Louis Reese
Motivation
Hydrophobic barrier
Protein Fluorescence
The Cell Membrane
Lipid bilayer
Membrane maintains
concentrations of solutes
hydrophilic
Hydrophobic Molecules
(O2, CO2)
Small molecules, polar,
uncharged (H2O, glycerol)
hydrophobic
Large molecules, polar,
uncharged (glucose)
Ions
(H+, Na+, K+, …)
 Storage of Potential Energy
Fluctuation-Driven Transmembrane Transport
Louis Reese
Motivation
Membrane Activity
Protein Fluorescence
The Plasma Membrane
Plasma Membrane
Cytosol
Cell Boundary
Ingest nutrients
Excrete metabolic waste
Membraneous
Cell Compartments
Ion gradients provide energy for
• ATP Synthese
• Transport mechanisms
We need machines to
perform these tasks:
Membrane Proteins
• Electrical signals
Fluctuation-Driven Transmembrane Transport
Louis Reese
Motivation
Protein Functions
Protein Fluorescence
Membrane Proteins
• ~30% of Genes (animals) encode Membrane Proteins
• Membrane Proteins ~50% of the membrane mass
Transporter
Sensors/Receptors (external Signals)
Membrane associated Reactions
Connection to Cytoskeleton
Are supposed to be responsible for
Nonequilibrium
Fluctuations
A. E. Pelling, et al. (2004)
Fluctuation-Driven Transmembrane Transport
Louis Reese
Motivation
Transmembrane
Transport
Transport Through the Membrane
•
Functional Proteins asure selectivity
Active
Pumping « Uphill »
Coupled to catalysing
energy-source
(Light, ATP, coupled-Carriers)
Passive
Facilitated Diffusion « Downhill »
the Concentration gradient
We’ll see soon that
there are posibillities to make
these Channels « WORK »
Fluctuation-Driven Transmembrane Transport
Louis Reese
Protein Fluorescence
Theoretical Model
Molecular Restraints
Protein Fluorescence
Transport due to Fluctuations
• The Glycerol uptake Facilitator (GlpF)
Needed, but poisons the cell at high concentrations.

Na+

Sugar
Molecule
Pulling
X-Ray Structure
shows Selectivity
Molecular Dynamics:
Asymmetric
Potential of Mean
Force (PMF)
M. Ø. Jensen, et al. (2002)
Fluctuation-Driven Transmembrane Transport
Finally a realistic Potential!
Louis Reese
Theoretical Model
Equation of Motion
Protein Fluorescence
Modelling Transport
• Brownian Motion: The Langevin Equation



Virtual
Friction
Virtual Realistic
Potential of
Mean Force
LangevinForce:
White Noise
Fluctuation-Driven Transmembrane Transport
Louis Reese
Membrane
FluctuationForce
Theoretical Model
Transport FPE
Protein Fluorescence
Modelling the Transport Protein
Probability densities
Fokker-Planck
Equation
Fluctuation-Driven Transmembrane Transport
Louis Reese
Theoretical Model
Transport Flux
Protein Fluorescence
Details of Molecular Flux
• Composition of Flux through Channel
Diffusion
Acting Forces
Asymmetric Protein Potential
+ Membrane Fluctuation
We know already:
Zero-Force & Constant-Force
Fluctuation-Driven Transmembrane Transport
Louis Reese
Results
Outward Flux
Periodic Force
Protein Fluorescence
Transport enhenced by external Force
• Periodic Force

in
Despite Force: High Barrier

out

out

in
Fluctuation-Driven Transmembrane Transport
Asymmetric Potential

Outward Transport
Louis Reese
Results
Outward Flux
Random Force
Protein Fluorescence
Transport driven by Random-Telegraph-Force
• Fluctuating Force
Poisson Mean Switching Time
We still expect outward flux
being better than inward flux.
But 2 more Questions arise:
1. How do switching times influence transport?
2. Which role plays the concentration gradient?
Fluctuation-Driven Transmembrane Transport
Louis Reese
Results
Switching Time
Tunes Transport
Protein Fluorescence
Switching Times tune Transport
• Switching very fast ~10-9s does not influence flux.
• Switching slowly ~10-2s, the time-dependence vanishes
In between, at equal concentrations:
?
Fluctuation-Driven Transmembrane Transport
Louis Reese
Results
Concentration Gradient
Regulates outward Transport
Protein Fluorescence
Concentration Gradient Regulates outward Transport
• Current reversal depends on concentration gradient.
 The passive Protein finally « WORKS » !
Fluctuation-Driven Transmembrane Transport
Louis Reese
Outlook
Biology
Physics
Protein Fluorescence
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)
Fluctuation-Driven Transmembrane Transport
Louis Reese
Protein Fluorescence
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
Fluctuation-Driven Transmembrane Transport
Louis Reese
Protein Fluorescence
Thank you for your attention!
Fluctuation-Driven Transmembrane Transport
Louis Reese
Appendix
Protein Fluorescence
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“
Fluctuation-Driven Transmembrane Transport
Louis Reese