Geometry and Dynamics in Highly Bidisperse Systems

Transcript

1. Geometry and Dynamics in Highly Bidisperse Systems Wendell Smith1, Mark Shattuck2,3, Christine Jacobs-Wagner4, and Corey O’Hern3,1,5 1Department of Physics, Yale University, 2Benjamin Levich Institute and Physics Department, City College of New York, 3Department of Mechanical Engineering and Materials Science, Yale University, 4Department of Molecular, Cellular and Developmental Biology, Yale University, and 5Department of Applied Physics, Yale University
2. Introduction Geometry Dynamics Conclusions Motivation Cellular Cytoplasm highly polydisperse, very crowded volume fraction ~40–60% with glass-like properties1 Experimental Data 1Parry, B. R. et al. The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity. Cell 156, 183–194 (2014).
3. Introduction Geometry Dynamics Conclusions Motivation Cellular Cytoplasm highly polydisperse, very crowded volume fraction ~40–60% with glass-like properties1 Experimental Data 1Parry, B. R. et al. The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity. Cell 156, 183–194 (2014).
4. Introduction Geometry Dynamics Conclusions Motivation Cellular Cytoplasm highly polydisperse, very crowded volume fraction ~40–60% with glass-like properties1 Experimental Data Not slope 1! 1Parry, B. R. et al. The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity. Cell 156, 183–194 (2014).
5. Introduction Geometry Dynamics Conclusions Motivation Cellular Cytoplasm highly polydisperse, very crowded volume fraction ~40–60% with glass-like properties1 Experimental Data Not slope 1! Why is it glass-like? 1Parry, B. R. et al. The Bacterial Cytoplasm Has Glass-like Properties and Is Fluidized by Metabolic Activity. Cell 156, 183–194 (2014).
6. Introduction Geometry Dynamics Conclusions Jamming Bidisperse Spheres such as proteins and ribosomes Parameters N = 400 Size ratio, r = large radius small radius Relative volume fraction, m = nsVs nlVl Fast quenched r = 3.5, m = 0.22
7. Introduction Geometry Dynamics Conclusions How do they pack? 10-1 100 Relative volume fraction, m=ns Vs nl Vl 100 101 Size ratio, r=rl rs proteins & ribosomes Large particles 0 1 Fraction in the backbone
8. Introduction Geometry Dynamics Conclusions How do they pack? 10-1 100 Relative volume fraction, m=ns Vs nl Vl 100 101 Size ratio, r=rl rs proteins & ribosomes Small particles 0 1 Fraction in the backbone
9. Introduction Geometry Dynamics Conclusions How do they pack? 10-1 100 Relative volume fraction, m=ns Vs nl Vl 100 101 Size ratio, r=rl rs proteins & ribosomes Small particles 0 1 Fraction in the backbone For r 1, small particles jam when they take up more than 64% of the space “left-over” by large particles
10. Introduction Geometry Dynamics Conclusions Pore Networks Where can a small particle move? r=1.5, m=0.38 Line thicknesses not to scale with box Thicker lines are wider pores
11. Introduction Geometry Dynamics Conclusions Pore Networks Where can a small particle move? r=2.3, m=0.29 Line thicknesses not to scale with box Thicker lines are wider pores
12. Introduction Geometry Dynamics Conclusions Pore Networks Where can a small particle move? r=3.5, m=0.13 Line thicknesses not to scale with box Thicker lines are wider pores
13. Introduction Geometry Dynamics Conclusions Dynamics Collision-Driven with Brownian Dynamics r = 2.3, m = 0.29, ∆φ = φ − φJ = −0.1
14. Introduction Geometry Dynamics Conclusions Diffusion 10-1 100 101 102 103 104 105 Time 10-4 10-3 10-2 10-1 100 101 102 103 104 MSD r=1.5, m=0.1, ∆φ=−0.4 Individual particles Average Diffusion (slope 1)
15. Introduction Geometry Dynamics Conclusions Diffusion? 10-1 100 101 102 103 104 105 Time 10-5 10-4 10-3 10-2 10-1 100 101 102 103 MSD r=1.5, m=0.38, ∆φ=−0.02 Individual particles Average Diffusion (slope 1)
16. Introduction Geometry Dynamics Conclusions Diffusion? 10-1 100 101 102 103 104 105 Time 10-5 10-4 10-3 10-2 10-1 100 101 102 103 MSD r=2.3, m=0.29, ∆φ=−0.02 Individual particles Average Diffusion (slope 1)
17. Introduction Geometry Dynamics Conclusions Diffusion? 10-1 100 101 102 103 104 105 Time 10-5 10-4 10-3 10-2 10-1 100 101 102 103 MSD r=3.5, m=0.1, ∆φ=−0.02 Individual particles Average Diffusion (slope 1)
18. Introduction Geometry Dynamics Conclusions Summary r=1.5, m=0.38 ⇓ 10-1 100 101 102 103 104 105 Time 10-5 10-4 10-3 10-2 10-1 100 101 102 103 MSD r=2.3, m=0.29 ⇓ 10-1 100 101 102 103 104 105 Time 10-5 10-4 10-3 10-2 10-1 100 101 102 103 MSD r=3.5, m=0.13 ⇓ 10-1 100 101 102 103 104 105 Time 10-5 10-4 10-3 10-2 10-1 100 101 102 103 MSD
19. Introduction Geometry Dynamics Conclusions Can we explain the cytoplasm dynamics?
20. Introduction Geometry Dynamics Conclusions Acknowledgments The Raymond and Beverly Sackler Institute The Yale High Performance Computing Center The Shattuck and the O’Hern Groups Brad Parry and Ivan Surovtsev
21. Introduction Geometry Dynamics Conclusions Calculating Networks Packing Delaunay Triangulation Apollonius’ Problem =⇒ =⇒