IonChannelsFinal

# Overall state of the dna is described by the vector

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Overall state of the DNA is described by the vector where i refers to the state of hybridization of the i th base pair

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Ion channels Aim: compute the probability of finding the channel open, p open Boltzmann distr.: the probability of finding a state with energy E is If there is no external driving force, the energy as a function of σ is where ε open ( closed ) is the energy of the open (closed) state E = E( ) =?
Ion channels under applied tension For concreteness, we begin by considering the case of mechanosensitive channels. Driving force: the tension in the membrane Mechanosensitive channels have been hypothesized to serve as safety valves to protect cells against membrane rupture due to osmotic imbalance.

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Energy of Ion channel under applied tension => energy as a function of the applied tension τ where Δ A is the area change upon gating. In open state, the energy of the loading device is reduced favors the open state
Energy landscape for an ion channel The entire energy landscape for a channel as a function of the radius for different choices of external gating parameter (membrane tension, ligand concentration, or applied voltage): Presence of the driving force shifts the balance between the energies of the closed and open states.

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Open probability of the ion channel Compute the open probability of the channel. The energy is The partition function: => the open probability: Parameters: Δε = –5 k B T, Δ A =10 nm 2 To understand how a channel will behave under a driving force we need to know 2 things: (1) The intrinsic preference for each of its 2 states (2) how the external driving force alters the relative energies of these 2 states => stat. mech. allows us to compute the behavior of the channel under a range of driving forces
ion channel gating: experimental data Current trace 2-state idealization of the current trace A single channel incorporated into a pure lipid bilayer is subjected to different voltages. The resulting current is measured. Tuning the driving force for gating only changes the relative dwell time and not the existence of the states themselves. Keller et al., J.Gen.Physiol. 1986

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Ion gated channels: Acetylcholine
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Overall state of the DNA is described by the vector where i...

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