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Fluctuation-Driven Transmembrane Transport. Betreuung durch Claus Heußinger. The Cell Membrane Protein activity in the Plasma Membrane Transport Through Membranes Transport due to Fluctuations Modelling a Channel Protein Developing a Theoretical Model
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Fluctuation-Driven Transmembrane Transport Betreuung durch Claus Heußinger Louis Reese 11.12.2006
The Cell Membrane Protein activity in the Plasma Membrane Transport Through Membranes Transport due to Fluctuations Modelling a Channel Protein Developing a Theoretical Model Solutions of the Fokker-Planck Equation Outlook Outline
Lipid bilayer Membrane maintains concentrations of solutes Hydrophobic Molecules(O2, CO2) hydrophilic Small molecules, polar, uncharged (H2O, glycerol) hydrophobic Large molecules, polar,uncharged (glucose) Ions(H+, Na+, K+, …) Storage of Potential Energy The Cell Membrane
Cytosol Cell Boundary Ingest nutrients Excrete metabolic waste Membraneous Cell Compartments We need machines toperform these tasks: Membrane Proteins The Plasma Membrane Plasma Membrane • Ion gradients provide energy for • ATP Synthese • Transport mechanisms • Electrical signals
Are supposed to be responsible for Nonequilibrium Fluctuations A. E. Pelling, et al. (2004) 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
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 makethese Channels « WORK » Transport Through the Membrane • Functional Proteins asure selectivity
Pulling X-Ray Structure shows Selectivity Na+ SugarMolecule Molecular Dynamics: AsymmetricPotential of Mean Force (PMF) Finally a realistic Potential! M. Ø. Jensen, et al. (2002) Transport due to Fluctuations • The Glycerol uptake Facilitator (GlpF) Needed, but poisons the cell at high concentrations.
New MembraneFluctuation-Force Modelling Transport • Brownian Motion: The Langevin Equation VirtualFriction Virtual RealisticPotential ofMean Force Langevin-Force:White Noise
Modelling the Transport Protein Probability densities Fokker-PlanckEquation
Details of Molecular Flux • Composition of Flux through Channel Diffusion Acting Forces AsymmetricProtein Potential + Membrane Fluctuation We know already:Zero-Force & Constant-Force
in out Despite Force: High Barrier Asymmetric PotentialOutward Transport out in Transport enhenced by external Force • Periodic Force
Poisson Mean Switching Time We still expect outward fluxbeing better than inward flux.But 2 more Questions arise: Transport driven by Random-Telegraph-Force • Fluctuating Force • How do switching times influence transport? • Which role plays the concentration gradient?
In between, at equal concentrations: ? Switching Times tune Transport • Switching very fast ~10-9s does not influence flux. • Switching slowly ~10-2s, the time-dependence vanishes
Concentration Gradient Regulates outward Transport • Current reversal depends on concentration gradient. The passive Protein finally « WORKS »!
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)
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
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“