# Energy landscape in the two state model (Boltzmann distribution)

Homework Statement:
Draw an energy landscape such as shown in Figure 7.7 for
the voltage-gated sodium channel presented in Figure 7.2.
In particular, show how the landscape changes as a function
of the applied voltages shown in Figure 7.2(C).
Relevant Equations:
E(σ ) = σ εopen + (1 − σ )εclosed − στA

Gtension = − τΔs × (R /Rout)× ΔR × (2πRout/s)

Gtension = −τ2πRΔR

ΔΑ= 2πRΔR

Popen = e^−β(εopen−τΔA) /(e^−β(εopen−τΔA) + e^−βεclosed)

β=1/ ΚΤ
From an excel file I can get the probability of each energy state Εi and I saw at Wikipedia that the probability of each energy is proportional with

e^−Εi/KT, from this I find the energy of every micro state. Also from the formula
which I found on a paper I can get a curve like the curve shown in fig7.7 (almost) whith the probabilities I took.

My problem is that it must be an energy as a function of the Radius, so I must put in there somehow the R. I can take the formula with Popen and to put on the denominator all of the energies and on the numerator the energy of each microstate but then I don't have the R.
If i put the whole energies of each state I could put ΔΑ but i don't see how with that I could made curves like fig7.7 and also instead of τ I must put v (volts), the probabilities I took was from -105 mVolts, if I put that the result doesn't makes sense.

So I want the different probabilities to use the formula
but I can't find a way to put radius in. That's the way I am thinking it, I would appreciated if someone could tell me if I am in the right direction and maybe give a hint how to move forward or to give me a hint for another direction.
Also, fig 7.2 has the Δε which indicates the it may be useful for the drawing of the energy landscape but I can't figure out how.

Thanks

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