Dynamics of an Intrinsically Disordered Protein Reveal Metastable Conformations That Potentially Seed Aggregation

This is a paper by Qiao, Qin, Gregory R. Bowman, and Xuhui Huang, appeared in Journal of the American Chemical Society 135.43 (2013): 16092-16101. Presented this paper as a part of a course (Simulation Techniques in Biology) which I audited.

Transcript

1. Qiao, Qin, Gregory R. Bowman, and Xuhui Huang Journal of the American Chemical Society 135.43 (2013): 16092-16101 Dynamics of an Intrinsically Disordered Protein Reveal Metastable Conformations That Potentially Seed Aggregation November 01, 2018
2. hIAPP (Human islet amyloid polypeptide or Human amylin) — 37-residue hormone; unstructured in soluble form (IDP) — secreted in pancreas by beta-cells; Insulin : Amylin — 100 :1 — Functions: Regulation of gastric emptying and insulin secretion Fibril formation is responsible for type II diabetes — 95% type II diabetes patients: Amyloid fibril deposits — induce apoptotic cell-death in beta-cells Image: MacDonald, P. E., & Rorsman, P. (2006). Oscillations, intercellular coupling, and insulin secretion in pancreatic β cells. PLoS biology, 4(2), Introduction
3. Image: Westermark, Per, Arne Andersson, and Gunilla T. Westermark. "Islet amyloid polypeptide, islet amyloid, and diabetes mellitus." Physiological reviews 91.3 (2011): 795-826. Mature amyloid fibers are stable Intermediate structures of amyloid formation are toxic states — Oligomers lead to disruption of cell membrane Fibril formation is nucleation dependent — A heterogeneity of pathways forming different oligomers Various mechanisms proposed to understand fibril formation — Understanding monomer structure is important — Time scales for monomers to transit between different metastable states; difficult to predict timescales in IDPs Experiments and simulations: Alpha helix near N-terminal and some beta hairpin structures
4. Goal: Investigate the dynamics of the hIAPP monomer Replica exchange molecular dynamics (REMD) — Capture conformations from a number of metastable states Markov state models (MSMs) — Predict long time scale dynamics from many short MD simulations
5. Protein folding: Difficult to obtain accurate canonical distributions at low temperatures; tend to get trapped in one of the local energy minima REMD Generalized ensemble method Multicanonical ensemble 1d random walk in energy space Simulated tempering 1d random walk in temperature space Probability weight factors not known a priori Short trail simulations are done to determine; non-trivial and tedious Replica exchange method Replica MC Multiple Markov chain method Parallel tempering REMD MC used: q and E(q) MD used: q, E(q) and p
6. REMD REMD: Enhanced sampling algorithm Sampling over a range of temperatures: To escape kinetic traps Start with n non-interacting copies (replicas) of the original system in the canonical ensemble at n different temperatures
7. A set of n independent configurations q0 = {q1,0, q2,0, …, qn,0} at corresponding temperatures {T1, T2, …, Tn} at time 0 After some time, a new set of configurations: q1 = {q1,1, q2,1, …, qn,1} An exchange of configurations qi,1 and qj,1 is tried with metropolis criterion 1, for 0 exp(- ), for > 0 w(qi,1|qj,1) = {  <latexit sha1_base64="XgqiacJN6LrQRRY6vHV079iylMM=">AAAB9HicdVDLSgNBEJyNrxhfUY9eBhPBU9hdA1lvQT14jGAekCxhdtKbDJmd3czMBkLId3jxoIhXP8abf+PkIahoQUNR1U13V5BwprRtf1iZtfWNza3sdm5nd2//IH941FBxKinUacxj2QqIAs4E1DXTHFqJBBIFHJrB8HruN8cgFYvFvZ4k4EekL1jIKNFG8oudG+Ca4A6HUbGbL9glp3zhlSvYLrmVssGcXHqu52GnZC9QQCvUuvn3Ti+maQRCU06Uajt2ov0pkZpRDrNcJ1WQEDokfWgbKkgEyp8ujp7hM6P0cBhLU0Ljhfp9YkoipSZRYDojogfqtzcX//LaqQ49f8pEkmoQdLkoTDnWMZ4ngHtMAtV8YgihkplbMR0QSag2OeVMCF+f4v9Jwy05ht+5herVKo4sOkGn6Bw5qIKq6BbVUB1RNEIP6Ak9W2Pr0XqxXpetGWs1c4x+wHr7BAg4kZ8=</latexit> <latexit 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8. Markov State Model Basis for MSM: Random walk of a dynamical system through a set of states — States are chosen sensibly and the dynamics is sufficiently complex — System will not remember how it go to its current state MSM represents a master equation framework Entire configuration space is divided into n states Writing states at time points separated by lag time (should be Markovian) Transition probability matrix: An n x n square matrix is constructed — Elements represent the probability of transitioning from one state to another state; diagonal entry - probability of staying in same state — Yield kinetic information and enumerations of possible pathways between any pair of states Eigendecomposition of transition probability matrix: — n element eigenvector corresponding to each eigenvalue: Magnitude and sign of each element explain the state contribution — Positive eigenvalues can be converted to physically meaningful timescales using the lag time ⌧ <latexit sha1_base64="Xume1MX9x8VFw+m8G8fpWNIvLIM=">AAAB7XicdVBNS8NAEJ3Ur1q/qh69LLaCp5DUQuOt6MVjBfsBbSib7aZd3WzC7kYoof/BiwdFvPp/vPlv3LQVVPTBwOO9GWbmBQlnSjvOh1VYWV1b3yhulra2d3b3yvsHHRWnktA2iXksewFWlDNB25ppTnuJpDgKOO0Gd5e5372nUrFY3OhpQv0IjwULGcHaSJ3qQOO0OixXHNutn3n1BnLsWqNukJNzr+Z5yLWdOSqwRGtYfh+MYpJGVGjCsVJ910m0n2GpGeF0VhqkiiaY3OEx7RsqcESVn82vnaETo4xQGEtTQqO5+n0iw5FS0ygwnRHWE/Xby8W/vH6qQ8/PmEhSTQVZLApTjnSM8tfRiElKNJ8agolk5lZEJlhiok1AJRPC16fof9Kp2a7h17VK82IZRxGO4BhOwYUGNOEKWtAGArfwAE/wbMXWo/VivS5aC9Zy5hB+wHr7BFpGjvs=</latexit> <latexit sha1_base64="Xume1MX9x8VFw+m8G8fpWNIvLIM=">AAAB7XicdVBNS8NAEJ3Ur1q/qh69LLaCp5DUQuOt6MVjBfsBbSib7aZd3WzC7kYoof/BiwdFvPp/vPlv3LQVVPTBwOO9GWbmBQlnSjvOh1VYWV1b3yhulra2d3b3yvsHHRWnktA2iXksewFWlDNB25ppTnuJpDgKOO0Gd5e5372nUrFY3OhpQv0IjwULGcHaSJ3qQOO0OixXHNutn3n1BnLsWqNukJNzr+Z5yLWdOSqwRGtYfh+MYpJGVGjCsVJ910m0n2GpGeF0VhqkiiaY3OEx7RsqcESVn82vnaETo4xQGEtTQqO5+n0iw5FS0ygwnRHWE/Xby8W/vH6qQ8/PmEhSTQVZLApTjnSM8tfRiElKNJ8agolk5lZEJlhiok1AJRPC16fof9Kp2a7h17VK82IZRxGO4BhOwYUGNOEKWtAGArfwAE/wbMXWo/VivS5aC9Zy5hB+wHr7BFpGjvs=</latexit> <latexit sha1_base64="Xume1MX9x8VFw+m8G8fpWNIvLIM=">AAAB7XicdVBNS8NAEJ3Ur1q/qh69LLaCp5DUQuOt6MVjBfsBbSib7aZd3WzC7kYoof/BiwdFvPp/vPlv3LQVVPTBwOO9GWbmBQlnSjvOh1VYWV1b3yhulra2d3b3yvsHHRWnktA2iXksewFWlDNB25ppTnuJpDgKOO0Gd5e5372nUrFY3OhpQv0IjwULGcHaSJ3qQOO0OixXHNutn3n1BnLsWqNukJNzr+Z5yLWdOSqwRGtYfh+MYpJGVGjCsVJ910m0n2GpGeF0VhqkiiaY3OEx7RsqcESVn82vnaETo4xQGEtTQqO5+n0iw5FS0ygwnRHWE/Xby8W/vH6qQ8/PmEhSTQVZLApTjnSM8tfRiElKNJ8agolk5lZEJlhiok1AJRPC16fof9Kp2a7h17VK82IZRxGO4BhOwYUGNOEKWtAGArfwAE/wbMXWo/VivS5aC9Zy5hB+wHr7BFpGjvs=</latexit> <latexit sha1_base64="Xume1MX9x8VFw+m8G8fpWNIvLIM=">AAAB7XicdVBNS8NAEJ3Ur1q/qh69LLaCp5DUQuOt6MVjBfsBbSib7aZd3WzC7kYoof/BiwdFvPp/vPlv3LQVVPTBwOO9GWbmBQlnSjvOh1VYWV1b3yhulra2d3b3yvsHHRWnktA2iXksewFWlDNB25ppTnuJpDgKOO0Gd5e5372nUrFY3OhpQv0IjwULGcHaSJ3qQOO0OixXHNutn3n1BnLsWqNukJNzr+Z5yLWdOSqwRGtYfh+MYpJGVGjCsVJ910m0n2GpGeF0VhqkiiaY3OEx7RsqcESVn82vnaETo4xQGEtTQqO5+n0iw5FS0ygwnRHWE/Xby8W/vH6qQ8/PmEhSTQVZLApTjnSM8tfRiElKNJ8agolk5lZEJlhiok1AJRPC16fof9Kp2a7h17VK82IZRxGO4BhOwYUGNOEKWtAGArfwAE/wbMXWo/VivS5aC9Zy5hB+wHr7BFpGjvs=</latexit>
9. Markov State Model p(n⌧) = Tn(⌧)p(0) <latexit sha1_base64="IIW85VOU6BzeMyO9L+gyivkaq80=">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</latexit> <latexit sha1_base64="IIW85VOU6BzeMyO9L+gyivkaq80=">AAACE3icdVDLSgMxFM34rPVVdekm2AqtizJTCx0XQtGNywp9QWcsmTTThmYyQ5IRytB/cOOvuHGhiFs37vwbM20FFT1w4eSce8m9x4sYlco0P4yl5ZXVtfXMRnZza3tnN7e335ZhLDBp4ZCFoushSRjlpKWoYqQbCYICj5GON75M/c4tEZKGvKkmEXEDNOTUpxgpLfVzJwXH85NoWuSOQnEJnsP03Zze8OJcWNhmqdDP5c2yVT21qzVoliu1qkZKzuyKbUOrbM6QBws0+rl3ZxDiOCBcYYak7FlmpNwECUUxI9OsE0sSITxGQ9LTlKOASDeZ3TSFx1oZQD8UuriCM/X7RIICKSeBpzsDpEbyt5eKf3m9WPm2m1AexYpwPP/IjxlUIUwDggMqCFZsognCgupdIR4hgbDSMWZ1CF+Xwv9Ju1K2NL+u5OsXizgy4BAcgSKwQA3UwRVogBbA4A48gCfwbNwbj8aL8TpvXTIWMwfgB4y3T59+nLw=</latexit> <latexit sha1_base64="IIW85VOU6BzeMyO9L+gyivkaq80=">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</latexit> <latexit sha1_base64="IIW85VOU6BzeMyO9L+gyivkaq80=">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</latexit> First order master equation
10. Simulation Details: REMD Two independent REMD simulations for initial sampling — Simulations starting from totally different conformations Energy minimization (steepest descent) 200 ps position restraint in NVT 2 ns NPT 200 ns REMD production run in NVT ensemble; exchange interval 2 ps amber99sb force field; tip3p water model 11020 water molecules; two Cl- Electrostatic interactions: Reaction field method, cutoff at 12 A Dielectric constant of solvent: 78.5 Cutoff for vdW: 11 A; potential goes to zero smoothly from 10 to 11 A LINCS algorithm for bond constraining Nose-Hoover thermostat with coupling frequency 0.4 ps-1
11. Convergence of REMD Simulation Helical structure (PDB ID: 2KB8) and coil structure Compare projections of free energy landscape onto Rg Compare number of H-bonds Weighted histogram analysis method (WHAM): To obtain thermodynamic property at each temperature Structure is more expanded and flexible at higher temperature
12. Simulation Details: Seeding MD Simulations All REMD conformations divided into 1200 clusters using k-centers clustering algorithm Two conformations randomly chosen from each cluster Run MD at 351K with velocity rescaling 1400 simulations collected; each with 20 ns long at least (total 70 x10-6 sec) Distributed computing: folding@home Folding@home is a project focused on disease research. The problems we’re solving require so many computer calculations – and we need your help to find the cures! The Folding@home software allows you to share your unused computer power with us – so that we can research even more potential cures https://foldingathome.org
13. Simulation Details: MSM Construction k-centers clustering algo: MD conformations divided into 10000 microstates Transition probability matrix constructed with some lag time Symmetrized and then normalized the transition count by column MSM construction performed using MSMBuilder software 10000 microstate model: Qualitative properties 200 microstate model: Folding mechanism — Microstates that interconvert quickly into the same metastable macrostate (Perron cluster cluster algorithm or PCCA) Population of each metastable macrostate is the sum of the equilibrium populations of the microstates it contains
14. Validation of MSM Implied timescales reach plateau around 5 ns (chosen as lag time) Residence probability test: Comparison of the probability for the system to remain in a certain state predicted by MSM with those directly obtained from MD simulations Implied timescales ⌧k = ⌧ ln k <latexit sha1_base64="omm2vyfNZ16Kxbrtik8p0QYwu3M=">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</latexit> <latexit sha1_base64="omm2vyfNZ16Kxbrtik8p0QYwu3M=">AAACEHicdVDLSsNAFJ3UV62vqEs3g63oxpLUQuNCKLpxWcHWQhPCZDpph04mYWYilNBPcOOvuHGhiFuX7vwbJ20FFT1w4XDOvTP3niBhVCrL+jAKC4tLyyvF1dLa+sbmlrm905FxKjBp45jFohsgSRjlpK2oYqSbCIKigJGbYHSR+ze3REga82s1TogXoQGnIcVIack3DyuuQqk/gmfwGLqhQDjLhUnmMg5dph/qI380qfhm2ara9ROn3oBWtdaoa+Tk1Kk5DrSr1hRlMEfLN9/dfozTiHCFGZKyZ1uJ8jIkFMWMTEpuKkmC8AgNSE9TjiIivWx60AQeaKUPw1jo4gpO1e8TGYqkHEeB7oyQGsrfXi7+5fVSFTpeRnmSKsLx7KMwZVDFME8H9qkgWLGxJggLqneFeIh0KkpnWNIhfF0K/yedWtXW/KpWbp7P4yiCPbAPjoANGqAJLkELtAEGd+ABPIFn4954NF6M11lrwZjP7IIfMN4+AcSNnHU=</latexit> <latexit sha1_base64="omm2vyfNZ16Kxbrtik8p0QYwu3M=">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</latexit> <latexit sha1_base64="omm2vyfNZ16Kxbrtik8p0QYwu3M=">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</latexit> 200 state MSM is also tested against residence probability test; microstates with population < 0.01% as independent states
15. Results A number of kinetically metastable states identified, no dominating state Intrinsically disordered nature is confirmed The Free Energy Landscape is Rugged: Many Local Metastable States without a Global Minimum
16. Results The Majority of Conformations are Random Coil Majority of residues (16 out of 37) are in random coil conformation Some bends and turns (~ 8) N-terminal residues 4-7 display a notable alpha-helical propensity Experimental comparisons on cross-section of hIAPP peptide and residue-based chemical shift values
17. Results Secondary structure preference for six most-populated metastable states Most residues have a high probability of being random coil, except residues 4-6, which are mostly in turn and alpha-helical structures due to the disulphide bond between Cys2 and Cys7 Compact structure: Rg is less than one-tenth of the length of extended PP The Majority of Conformations are Random Coil
18. Results Transitions between Different Metastable States are Slow Mean first passage times (MFPTs) between 50 most populated states Different metastable free energy minima are well separated kinetically — Time scales are comparable or even slower than the folding time scales — Involve breaking existing contacts, reorganising the conformation and forming new contacts Most populated states do not appear to act as kinetic hubs — Well-folded proteins: High kinetic accessibility of the native states; transitions from less well-populated state to more highly populated sites is faster than reverse transitions
19. Results Extended hydrophobic surface can induce collapse Hydrophobic interactions may bring individual hIAPP peptides together; flat geometry facilitates further growth of aggregates Other conformational states constitute less favorable path for aggregation Probable Aggregation Prone States: Flat Beta-Sheet Geometry with Extended Hydrophobic Surfaces Few metastable states (~ 1%) contain a significant amount of beta-sheet — Beta hairpin segments with around 10 residues or longer Connected hydrophobic residues near the turn and exposed to the solvent Beta hairpins and extended solvent-accessible hydrophobic surface areas: — Aggregation prone — Preserved under different force fields and ionic strengths
20. Results On collision, aggregation prone states are selectively stabilised via conformation selection mechanism MSM: Rate of collision is similar to the time scales for reaching the aggregation prone state Probable Aggregation Prone States: Flat Beta-Sheet Geometry with Extended Hydrophobic Surfaces
21. Thank You Conclusions Constructed MSMs from extensive MD simulations Free energy landscape contains many local minima; no dominant local minima Transitions time scales between different local minima: Microsec. to millisec.; comparable to or even slower than the folding time scale Monomer is generally random coiled, occasionally alpha-helix or beta-sheet Aggregation prone states: Beta-hairpins and extended hydrophobic surface; induce hydrophobic collapse, flat geometry provides a template for growth of aggregation via conformation selection