Macromolecular Crowding

Transcription

1 Macromolecular Crowding Keng-Hwee Chiam Mathematical and Theoretical Biology Group Goodsell (1994) Macromolecular Crowding, Oct. 15, 2003 p.1/33

2 Outline What: introduction, definition Why: implications on cellular properties and processes How: quantitative models Macromolecular Crowding, Oct. 15, 2003 p.2/33

3 Motivation Biological media, e.g. cytoplasm: crowded with large molecules biophysical, biochemical, physiological properties affected in vitro assays: neglect non-ideal crowding by, e.g., using dilute solutions results cannot be extrapolated to in vivo situation Macromolecular Crowding, Oct. 15, 2003 p.3/33

4 Introduction Cytoplasm packed with RNA, cytoskeletal elements, and other proteins that occupy 5% 40% of volume D. discoideum, Medalia et al., Science (2002), E. coli, Goodsell (1999) Macromolecular Crowding, Oct. 15, 2003 p.4/33

5 Introduction Red blood cells packed with hemoglobin, blood serum packed with antibodies, albumin proteins, etc. Goodsell ( ) Macromolecular Crowding, Oct. 15, 2003 p.5/33

6 Definition Sum of all macromolecule-macromolecule and macromolecule-solvent interactions Steric: repulsion due to excluded volume Hydrodynamic: viscous drag owing to motion Chemical: hydrophilic and hydrophobic effects van der Waals Electrostatic Nonequilibrium: energy and number fluxes through membranes Mesoscopic: finite-size effect A messy situation! Macromolecular Crowding, Oct. 15, 2003 p.6/33

7 Steric repulsion Presence of large molecules makes volume less accessible to other large molecules Ellis (2001) Energetically costly to add a large molecule to an already crowded volume Macromolecular Crowding, Oct. 15, 2003 p.7/33

8 Steric repulsion Neglect Coulombic interactions for now Ideal fluid of point particles: P V = N kt Fluid of hard spheres: P (V b) = NkT Excluded volume b is four times volume of spheres Macromolecular Crowding, Oct. 15, 2003 p.8/33

9 Steric repulsion Presence of n hard spheres leaves (V nv 0 ) available for (n + 1)-th sphere Number of microstates and entropy: Ω V (V v 0 ) [V (N 1)v 0 ] S = k log V + k log(v v 0 ) + + k log[v (N 1)v 0 ] Equation of state: P T = S V = Nk V Nv 0 /2, v 0 = 4 3 π(2a)3 Macromolecular Crowding, Oct. 15, 2003 p.9/33

10 Implications Transport in the cytoplasm Kinetics of metabolic channeling Efficiency of protein folding Cellular volume regulation Amyloid fibril formation Macromolecular Crowding, Oct. 15, 2003 p.10/33

11 Transport Mechanisms for transport of viruses, gene carriers, etc. in the cytoplasm? Diffusive or ballistic? Passive or active? Important to: Rational design of gene delivery Bioengineering of biocompatible materials Insights into intracellular reaction-diffusion-type modeling Macromolecular Crowding, Oct. 15, 2003 p.11/33

12 Transport Rate of self-diffusion of proteins lowered as crowding increases (Zimmerman and Minton, Annu. Rev. Biophys. Biomol. Struct. 22, 27 (1993)): Replace D 2 c with [D(c) c] Macromolecular Crowding, Oct. 15, 2003 p.12/33

13 Transport How to obtain efficient transport in lieu of inefficient diffusion? Active propagation along cytoskeletal elements? Crossover to active propagation as crowding increases 2 Transport exponent γ = d log r 2 (t) / d log t Volume fraction φ Replace [D(c) c] with U( x, c) c + [D(c) c] Macromolecular Crowding, Oct. 15, 2003 p.13/33

14 Transport Measure local transport properties of cytoplasm, e.g. Wirtz et al. (Biophys. J. 83, 3162 (2002), Biophys. J. 78, 1736 (2000)) and Sackmann et al. (Biophys. J. 76, 573 (1999), Biophys. J. 75, 2038 (1998)) Macromolecular Crowding, Oct. 15, 2003 p.14/33

15 Transport Inject tracers (e.g., fluorescent µspheres) into cytoplasm Brownian motion with dissipation depending on earlier velocities: m v(t) = t 0 ζ(t τ)v(τ)dτ + f R (t) where ζ(t) is memory function In thermal equilibrium, noise correlation: f R (0)f R (t) = k B T ζ(t) Obtain velocity correlation in terms of measurable mean square displacement r 2 (t) Macromolecular Crowding, Oct. 15, 2003 p.15/33

16 Transport Susceptibility: G(s) = k B T πas r 2 (s) Real part G (ω) is storage modulus, imaginary part G (ω) is loss modulus In a fluid, r 2 (t) = 6Dt with D = k B T/6πηa: G (ω) = 0, G (ω) = ηω In a solid, r 2 (t) independent of t: G (ω) = const., G (ω) = 0 Macromolecular Crowding, Oct. 15, 2003 p.16/33

17 Transport Cytoplasm has non-zero G (ω) and non-zero G (ω) Stiff Hookean solid at high deformation rates Soft viscous liquid at low deformation rates Viscoelasticity arises from elastic macromolecules in viscous liquid Replace diffusion in reaction-diffusion models with??? Macromolecular Crowding, Oct. 15, 2003 p.17/33

18 Metabolic channeling How does crowding affect fluxes through signal transduction pathways? Posphoenolpyruvate:carbohydrate phosphotransferase system (PTS): Uptake and phosphorylation of carbohydrates Phosphoryl group transferred sequentially along a series of proteins to carbohydrate molecule Macromolecular Crowding, Oct. 15, 2003 p.18/33

19 Metabolic channeling Rohwer, Westerhoff et al. (P. Natl. Acad. Sci. USA 95, (1998)) measured steady-state flux through PTS in vitro Flux concentration 2 : low concentration perfect channel, hit and run Flux concentration: high concentration and/or with crowding enzymes exist as complexes Macromolecular Crowding, Oct. 15, 2003 p.19/33

20 Metabolic channeling Total flux and flux-response coefficient vs. total enzyme concentration: Macromolecular Crowding, Oct. 15, 2003 p.20/33

21 Metabolic channeling Two-enzyme group-transfer model: Crowding added in as changes to association/disassociation rates Macromolecular Crowding, Oct. 15, 2003 p.21/33

22 Efficiency of protein folding Proteins fold in central cage of GroEL/GroES chaperonin Martin and Hartl (P. Natl. Acad. Sci. USA 94, 1107 (1997)) showed: crowding helps retain nonnative polypeptide Macromolecular Crowding, Oct. 15, 2003 p.22/33

23 Cellular volume regulation How do cells detect changes in their volume? Minton et al. (P. Natl. Acad. Sci. USA 89, (1992)) proposed that during swelling: cellular interior less crowded inhibits kinase relative to phosphatase activity increases concentration of transporter Macromolecular Crowding, Oct. 15, 2003 p.23/33

24 Amyloid fibril formation Neurodegenerative diseases, e.g., Parkinson s disease, characterized by amyloid fibril formation Shtilerman et al. (Biochemistry 41, 3855 (2002)) showed that crowding reduced lag time for protofibril formation and conversion of protofibril to fibril Macromolecular Crowding, Oct. 15, 2003 p.24/33

25 Quantitative models Hard spheres fluid, amenable to theory Atomic-level models using molecular dynamics Continuum models Macromolecular Crowding, Oct. 15, 2003 p.25/33

26 Hard spheres fluid Toy model: Spheres with hard core potential { r < a u(r) = 0 r a in vacuum Two parameters: radius of spheres a, and volume fraction φ Calculate thermodynamic and kinetic properties in (a, φ) phase space using: tabulated virial coefficients (Hall and Minton, Biochim. Biophys. Acta 1649, 127 (2003)) Monte Carlo simulations Macromolecular Crowding, Oct. 15, 2003 p.26/33

27 Hard spheres fluid Consider effects on equilibrium of dimerization A + A A 2 Calculate non-ideal contribution to K vs. volume fraction φ (Hall and Minton, Biochim. Biophys. Acta 1649, 127 (2003)) Macromolecular Crowding, Oct. 15, 2003 p.27/33

28 Hard spheres fluid In addition to hard spheres, to study transport: Mimic actin elements by stationary rods Model binding and transport on these rods Macromolecular Crowding, Oct. 15, 2003 p.28/33

29 Atomic-level models Elcock (P. Natl. Acad. Sci. USA 100, 2340 (2003)) modeled escape of rhodanese from cavity of GroEL into crowded solvent Macromolecular Crowding, Oct. 15, 2003 p.29/33

30 Atomic-level models Uses known GroEL conformation Omits GroES Models crowding agent as spheres Incorporates repulsive r 12 interaction between spheres and rhodanese Uses Brownian motion for crowder spheres Assumes periodic boundaries Contains atoms Macromolecular Crowding, Oct. 15, 2003 p.30/33

31 Atomic-level models Crowding enhances efficiency of chaperonins GroEL and GroES: Enhances association of GroEL and GroES, preventing escape Macromolecular Crowding, Oct. 15, 2003 p.31/33

32 Atomic-level models Friedel et al. (J. Chem. Phys. 118, 8106 (2003)) simulated a version of the 46 residue off-lattice minimalist model using molecular dynamics Restricts protein to sphere with soft well repulsive potential Crowding decreases folding time Macromolecular Crowding, Oct. 15, 2003 p.32/33

33 Conclusions Macromolecular crowding has important biophysical, biochemical, and physiological implications on intracellular processes Interesting problems: Spatial dependence of transport in cytoplasm from increasing accurate modeling Understanding role of crowding in kinetics of metabolic channeling Macromolecular Crowding, Oct. 15, 2003 p.33/33