Sam Norris' 2015 REU presentation

1. Using a Lattice
Model to Study the
Nuclear Pore
Complex
Samantha Norris
Mentors: Meredith Betterton, Loren Hough, Mike Stefferson
August 6, 2015

2. What is the Nuclear Pore Complex (NPC)?
"NuclearPore crop" by The original uploader was R. S. Shaw at English Wikipedia - Transferred from en.wikipediato Commons.. Licensed under CC BY-SA 2.5 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:NuclearPore_crop.png#/media/File:NuclearPore_crop.png
protein
Transport
factor
Strands of
nucleoporins
with FG
sequence
repeats
(FG nups)
Nucleus
Cytoplasm

3. What I Did
• To better understand the diffusion of
proteins through the NPC
• To find the parameters which most
significantly affect diffusion
Purpose
• Built Monte-Carlo lattice model from scratch
• Included particle and polymer lattice moves
• Tested various sets of parameters

4. Experimental Progress
• Modelling the NPC with a hydrogel mimic
• Hydrogel consists of FG-nups in strands
Figure: Loren Hough

5. A Lattice Model
• Monte Carlo method – each particle (whether TF
or FG) takes random walk around the grid
• When a TF and FG collide, probability 𝑘 𝑜𝑛 of
binding
• When separating, probability 𝑘 𝑜𝑓𝑓 of unbinding

6. A Lattice Model
Probability:
𝑘 𝑜𝑛
Probability:
𝑘 𝑜𝑓𝑓

7. A Lattice Model
inlet outlet

8. Strand Statistics
• Movement rules adapted from Haire et. al.
• Anchored at one point
• If movement breaks strand in 1 place, rest of strand compensates
• If movement breaks strand in 2 places, move rejected

9. Strand Statistics
Deviation from center
#
1 strand, length 200, T = 100,000

10. Strand Statistics
Leftmost figure reprinted from "A Monte Carlo Lattice model for Chain Diffusion
in Dense Polymer Systems and its Interlocking with Molecular Dynamics
Simulation," by K.R. Haire et. al., 2001, Computational and Theoretical Polymer
Science

11. Calculating Diffusion Coefficients
bindable particles
unbindable particles
Slope ∝ diffusion coefficient

12. Calculating Mean Square Displacement
• Old Method: Find distance from starting position
for each particle at each time steps, average over
particles
• New Method: Same as above, but average over
different “time origins”, doesn’t choose starting
position preferentially

13. Parameters
• kon, koff (binding and unbinding probability)
• Concentration of FG-nups and TFs
• Gel width
• TF size

14. 𝑪𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝑭𝑮𝒔
𝑘 𝑜𝑛 = .5
𝑘 𝑜𝑓𝑓 = 𝑘 𝑜𝑛/10
TF # = 1
Length = 100
Gel width = 50
Conclusion: Lower concentration = Higher diffusion
FG %

15. 𝒌 𝒐𝒏
FG conc. = 10%
𝑘 𝑜𝑓𝑓 = 𝑘 𝑜𝑛/10
TF # = 1
Length = 100
Gel width = 100
Conclusion: higher 𝑘 𝑜𝑛 = Higher diffusion

16. 𝒌 𝒐𝒇𝒇
FG conc. =10%
𝑘 𝑜𝑛 = 0.5
TF # = 1
Length = 100
Gel width = 100
Conclusion: Significant only when 𝒌 𝒐𝒇𝒇 ≈ 𝟎

17. FG radius
Conclusion: No effect, requires more study
FG conc. = 5% of gel
𝑘 𝑜𝑛=0.5
𝑘 𝑜𝑓𝑓 = 𝑘 𝑜𝑛/10
TF # = 1
Length = 100

18. Future Plans
• Reproduce figures from other papers on diffusion on lattice grid
• Study the long-time behavior of diffusion
• Possibly add more complex situations (TFs moving and pushing FGs,
etc.)

19. Thank you!
• REU organizers
• Meredith Betterton, Loren Hough (mentors)
• Mike Stefferson (graduate student)
• Jeff Moore, Adam Lamson, Andrea Egan