Macromolecular Crowding

Macromolecular CrowdingKeng-Hwee ChiamMathematical and Theoretical Biology GroupGoodsell (1994)Macromolecular Crowding, Oct. 15, 2003 – p.1/33

OutlineWhat: introduction, definitionWhy: implications on cellular properties and processesHow: quantitative modelsMacromolecular Crowding, Oct. 15, 2003 – p.2/33

MotivationBiological media, e.g. cytoplasm:crowded with large moleculesbiophysical, biochemical, physiological propertiesaffectedin vitro assays:neglect non-ideal crowding by, e.g., using dilute solutionsresults cannot be extrapolated to in vivo situationMacromolecular Crowding, Oct. 15, 2003 – p.3/33

IntroductionCytoplasm packed with RNA, cytoskeletal elements, andother proteins that occupy 5%–40% of volumeD. discoideum, Medalia et al., Science (2002), E. coli, Goodsell (1999)Macromolecular Crowding, Oct. 15, 2003 – p.4/33

IntroductionRed blood cells packed with hemoglobin, blood serumpacked with antibodies, albumin proteins, etc.Goodsell (1999-2000)Macromolecular Crowding, Oct. 15, 2003 – p.5/33

DefinitionSum of all macromolecule-macromolecule andmacromolecule-solvent interactionsSteric: repulsion due to excluded volumeHydrodynamic: viscous drag owing to motionChemical: hydrophilic and hydrophobic effectsvan der WaalsElectrostaticNonequilibrium: energy and number fluxes throughmembranesMesoscopic: finite-size effectA messy situation!Macromolecular Crowding, Oct. 15, 2003 – p.6/33

Steric repulsionPresence of large molecules makes volume less accessible toother large moleculesEllis (2001)Energetically costly to add a large molecule to an alreadycrowded volumeMacromolecular Crowding, Oct. 15, 2003 – p.7/33

Steric repulsionNeglect Coulombic interactions for nowIdeal fluid of point particles: P V = NkTFluid of hard spheres: P (V − b) = NkTExcluded volume b is four times volume of spheresMacromolecular Crowding, Oct. 15, 2003 – p.8/33

Steric repulsionPresence of n hard spheres leaves (V − nv 0 ) available for(n + 1)-th sphereNumber 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:PT = ∂S∂V =NkV − Nv 0 /2 ,v 0 = 4 3 π(2a)3Macromolecular Crowding, Oct. 15, 2003 – p.9/33

ImplicationsTransport in the cytoplasmKinetics of metabolic channelingEfficiency of protein foldingCellular volume regulationAmyloid fibril formationMacromolecular Crowding, Oct. 15, 2003 – p.10/33

TransportMechanisms for transport of viruses, gene carriers, etc. in thecytoplasm?Diffusive or ballistic? Passive or active?Important to:Rational design of gene deliveryBioengineering of biocompatible materialsInsights into intracellular reaction-diffusion-typemodelingMacromolecular Crowding, Oct. 15, 2003 – p.11/33

TransportRate of self-diffusion of proteins lowered as crowdingincreases (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

TransportHow to obtain efficient transport in lieu of inefficientdiffusion?Active propagation along cytoskeletal elements?Crossover to active propagation as crowding increases2Transport exponent γ = d log 〈r 2 (t)〉 / d log t10 1Volume fraction φReplace ⃗ ∇ · [D(c) ⃗ ∇c] with ⃗ U(⃗x, c) · ⃗∇c + ⃗ ∇ · [D(c) ⃗ ∇c]Macromolecular Crowding, Oct. 15, 2003 – p.13/33

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

TransportInject tracers (e.g., fluorescent µspheres) into cytoplasmBrownian motion with dissipation depending on earliervelocities:m ˙v(t) = −∫ t0ζ(t − τ)v(τ)dτ + f R (t)where ζ(t) is memory functionIn thermal equilibrium, noise correlation:〈f R (0)f R (t)〉 = k B T ζ(t)Obtain velocity correlation in terms of measurable meansquare displacement 〈∆r 2 (t)〉Macromolecular Crowding, Oct. 15, 2003 – p.15/33

TransportSusceptibility:G(s) =k B Tπas〈∆r 2 (s)〉Real part G ′ (ω) is storage modulus, imaginary part G ′′ (ω) isloss modulusIn a fluid, 〈∆r 2 (t)〉 = 6Dt with D = k B T/6πηa:G ′ (ω) = 0,G ′′ (ω) = ηωIn a solid, 〈∆r 2 (t)〉 independent of t:G ′ (ω) = const., G ′′ (ω) = 0Macromolecular Crowding, Oct. 15, 2003 – p.16/33

TransportCytoplasm has non-zero G ′ (ω) and non-zero G ′′ (ω)Stiff Hookean solid at high deformation ratesSoft viscous liquid at low deformation ratesViscoelasticity arises from elastic macromolecules in viscousliquidReplace diffusion in reaction-diffusion models with ???Macromolecular Crowding, Oct. 15, 2003 – p.17/33

Metabolic channelingHow does crowding affect fluxes through signal transductionpathways?Posphoenolpyruvate:carbohydrate phosphotransferase system(PTS):Uptake and phosphorylation of carbohydratesPhosphoryl group transferred sequentially along a seriesof proteins to carbohydrate moleculeMacromolecular Crowding, Oct. 15, 2003 – p.18/33

Metabolic channelingRohwer, Westerhoff et al. (P. Natl. Acad. Sci. USA 95, 10547 (1998))measured steady-state flux through PTS in vitroFlux ∝ concentration 2 :low concentrationperfect channel, “hit and run”Flux ∝ concentration:high concentration and/or with crowdingenzymes exist as complexesMacromolecular Crowding, Oct. 15, 2003 – p.19/33

Metabolic channelingTotal flux and flux-response coefficient vs. total enzymeconcentration:Macromolecular Crowding, Oct. 15, 2003 – p.20/33

Metabolic channelingTwo-enzyme group-transfer model:Crowding added in as changes to association/disassociationratesMacromolecular Crowding, Oct. 15, 2003 – p.21/33

Efficiency of protein foldingProteins fold in central cage of GroEL/GroES chaperoninMartin and Hartl (P. Natl. Acad. Sci. USA 94, 1107 (1997)) showed:crowding helps retain nonnative polypeptideMacromolecular Crowding, Oct. 15, 2003 – p.22/33

Cellular volume regulationHow do cells detect changes in their volume?Minton et al. (P. Natl. Acad. Sci. USA 89, 10504 (1992)) proposed thatduring swelling:cellular interior less crowdedinhibits kinase relative to phosphatase activityincreases concentration of transporterMacromolecular Crowding, Oct. 15, 2003 – p.23/33

Amyloid fibril formationNeurodegenerative diseases, e.g., Parkinson’s disease,characterized by amyloid fibril formationShtilerman et al. (Biochemistry 41, 3855 (2002)) showed that crowdingreduced lag time for protofibril formation and conversion ofprotofibril to fibrilMacromolecular Crowding, Oct. 15, 2003 – p.24/33

Quantitative modelsHard spheres fluid, amenable to theoryAtomic-level models using molecular dynamicsContinuum modelsMacromolecular Crowding, Oct. 15, 2003 – p.25/33

Hard spheres fluidToy model: Spheres with hard core potential{∞ r < au(r) =0 r ≥ ain vacuumTwo parameters: radius of spheres a, and volume fraction φCalculate thermodynamic and kinetic properties in (a, φ)phase space using:tabulated virial coefficients (Hall and Minton, Biochim. Biophys. Acta1649, 127 (2003))Monte Carlo simulationsMacromolecular Crowding, Oct. 15, 2003 – p.26/33

Hard spheres fluidConsider effects on equilibrium of dimerizationA + A ⇌ A 2Calculate 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

Hard spheres fluidIn addition to hard spheres, to study transport:Mimic actin elements by stationary rodsModel binding and transport on these rodsMacromolecular Crowding, Oct. 15, 2003 – p.28/33

Atomic-level modelsElcock (P. Natl. Acad. Sci. USA 100, 2340 (2003)) modeled escape ofrhodanese from cavity of GroEL into crowded solventMacromolecular Crowding, Oct. 15, 2003 – p.29/33

Atomic-level modelsUses known GroEL conformationOmits GroESModels crowding agent as spheresIncorporates repulsive r −12 interaction between spheres andrhodaneseUses Brownian motion for crowder spheresAssumes periodic boundariesContains 64000 atomsMacromolecular Crowding, Oct. 15, 2003 – p.30/33

Atomic-level modelsCrowding enhances efficiency of chaperonins GroEL andGroES:Enhances association of GroEL and GroES, preventingescapeMacromolecular Crowding, Oct. 15, 2003 – p.31/33

Atomic-level modelsFriedel et al. (J. Chem. Phys. 118, 8106 (2003)) simulated a version ofthe 46 residue off-lattice minimalist model using moleculardynamicsRestricts protein to sphere with soft well repulsive potentialCrowding decreases folding timeMacromolecular Crowding, Oct. 15, 2003 – p.32/33

ConclusionsMacromolecular crowding has important biophysical,biochemical, and physiological implications on intracellularprocessesInteresting problems:Spatial dependence of transport in cytoplasm fromincreasing accurate modelingUnderstanding role of crowding in kinetics of metabolicchannelingMacromolecular Crowding, Oct. 15, 2003 – p.33/33