1. Adsorption and Desorption Profiles of MIT on POPA and POPC Membranes
Reporter: Guanglin Kuang

2. MIT domain
Microtubule Interacting and Trafficking domain of the chitin synthase of Saprolegnia monoica.

3. Interaction with membranes
POPA
POPC

4. Umbrella Sampling
Umbrella sampling is a technique used to improve the sampling of a system where ergodicity is hindered by the form of the system's energy landscape.
Main idea:
Divide the reaction coordinate ξ into different windows.
Apply a biasing window potential wi(ξ) in each window to enhance the sampling in the neighborhood of a chosen value 𝜉 𝑖 𝑐
Perform biased simulation in each window. Independently.
Combine the results in each window to get unbiased global free energy profile.
𝒘 𝒊 𝝃 = 𝑲 𝟐 (𝝃− 𝝃 𝒊 𝒄 )

5. Umbrella Sampling-Theory
Biased potential energy in window i:
𝑉 𝑏 𝒓 𝑵 =𝑉 𝒓 𝑵 + 𝑤 𝑖 (𝜉)
(1)
Biasing window potential in window i:
(2)
𝑤 𝑖 𝜉 = 𝐾 2 (𝜉− 𝜉 𝑖 𝑐 )
K is the force constant and 𝝃 𝒊 𝒄 is the center reaction coordinate in window i.
The unbiased distribution function in window i:
𝑃 𝑖 𝑢 𝜉 = exp −𝛽𝑉 𝒓 𝑵 𝛿[𝜉(𝑟)−𝜉]𝑑 𝒓 𝑵 exp −𝛽𝑉 𝒓 𝑵 𝑑 𝒓 𝑵
(3)
The biased distribution function in window i:
𝑃 𝑖 𝑏 𝜉 = exp {−𝛽 𝑉 𝒓 𝑵 + 𝒘 𝒊 𝝃 } 𝛿[𝜉(𝑟)−𝜉]𝑑 𝒓 𝑵 exp {−𝛽 𝑉 𝒓 𝑵 + 𝒘 𝒊 𝝃 } 𝑑 𝒓 𝑵
(4)

6. Umbrella Sampling-Theory
From (3) and (4):
Probability
𝑃 𝑖 𝑢 𝜉 = 𝑃 𝑖 𝑏 𝜉 ∙ exp 𝛽 𝑤 𝑖 𝜉 ∙ exp −𝛽 𝑤 𝑖 𝜉 exp −𝛽𝑉 𝒓 𝑵 𝑑 𝒓 𝑵 exp −𝛽𝑉 𝒓 𝑵 𝑑 𝒓 𝑵
= 𝑃 𝑖 𝑏 𝜉 ∙ exp 𝛽 𝑤 𝑖 𝜉 ∙<exp⁡[−𝛽 𝑤 𝑖 𝜉 ]>
(5)
The potential of mean force (PMF) at 𝜉 in window i is:
𝐴 𝑖 𝜉 =− 1 𝛽 𝑙𝑛 𝑃 𝑖 𝑢 𝜉 =− 1 𝛽 𝑙𝑛 𝑃 𝑖 𝑏 𝜉 − 𝑤 𝑖 𝜉 + 𝐹 𝑖
(6)
𝐹 𝑖 =− 1 𝛽 𝑙𝑛<exp⁡[−𝛽 𝑤 𝑖 𝜉 ]>
(7)

7. Weighted Histogram Analysis Method (WHAM)
The global distribution function is:
𝑃 𝑢 𝜉 = 𝑖 𝑁 𝑤 𝑐 𝑖 (𝜉)𝑃 𝑖 𝑢 𝜉
(8)
𝑐 𝑖 (𝜉) are weights chosen to minimize the statistical error:
𝜕 𝜎 2 [ 𝑃 𝑢 𝜉 ] 𝜕 𝑐 𝑖 (𝜉) =0
(9)
𝑖 𝑐 𝑖 (𝜉)=1
(10)
From (8), (9) and (10):
𝑃 𝑢 𝜉 = 𝑖 𝑁 𝑤 𝑔 𝑖 −1 𝑁 𝑖 𝑃 𝑖 𝑏 𝜉 𝑗 𝑁 𝑤 𝑔 𝑗 −1 𝑁 𝑖 exp⁡{−𝛽 [𝑤 𝑖 𝜉 − 𝐹 𝑖 ]}
(11)
𝑔 𝑖 =1+2 𝜏 𝑖
exp −𝛽 𝐹 𝑖 =< exp −𝛽 𝑤 𝑖 𝜉 >= exp −𝛽 𝑤 𝑖 𝜉 𝑃 𝑢 𝜉 𝑑𝜉 = exp {−𝛽 [𝐴 𝜉 +𝑤 𝑖 𝜉 ]} 𝑑𝜉
J Comput Phys. 1977, 23:
J Comput Chem. 1992, 13(8):
Comput Phys Commun. 1995, 91:
J. Chem. Theory Comput. 2010, 6: 3713–3720
Wires Comput Mol Sci. 2011, 1:
(12)

8. Gromacs 4.6.1, CHARMM27 for protein and lipid
Work Flow:
Gromacs 4.6.1, CHARMM27 for protein and lipid
Adsorption: 100 ns; COM Pull: 20 ns; Umbrella Sampling : 40x10 ns=400 ns

9. Different Adsorption Modes of MIT on the POPA Bilayer

10. Different Adsorption Modes of MIT on the POPC Bilayer

11. Adsorption and Desorption Profiles of MIT on POPA and POPC Bilayers

12. Binding Modes of MIT with POPA and POPC
Any way to quantify this residue-lipid interaction???
POPC
POPC

13. Conclusions Thank you for you attention!
The adsorption and desorption profiles of MIT on POPA and POPC are significantly different.
Salt-bridges between the arginine residues of MIT and POPA are the reason for the high affinity over POPC.
The initial configuration also influences the binding affinity, especially for POPA, where the configuration with the most arginine-phosphate interactions has the highest binding affinity.
Other factors, like hydrophobic interaction, electrostatic interaction and steric effect, also influence the binding affinity.
…..
Thank you for you attention!