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Macromolecular CrowdingKeng-Hwee Chiam
Mathematical and Theoretical Biology Group
Goodsell (1994)Macromolecular Crowding, Oct. 15, 2003 – p.1/33
Outline
What: introduction, definition
Why: implications on cellular properties and processes
How: quantitative models
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Motivation
Biological media, e.g. cytoplasm:crowded with large moleculesbiophysical, biochemical, physiological propertiesaffected
in vitro assays:neglect non-ideal crowding by, e.g., using dilute solutionsresults cannot be extrapolated to in vivo situation
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Introduction
Cytoplasm packed with RNA, cytoskeletal elements, andother proteins that occupy 5%–40% of volume
D. discoideum, Medalia et al., Science (2002), E. coli, Goodsell (1999)
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Introduction
Red blood cells packed with hemoglobin, blood serumpacked with antibodies, albumin proteins, etc.
Goodsell (1999-2000)
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Definition
Sum of all macromolecule-macromolecule andmacromolecule-solvent interactions
Steric: repulsion due to excluded volumeHydrodynamic: viscous drag owing to motionChemical: hydrophilic and hydrophobic effectsvan der WaalsElectrostatic
Nonequilibrium: energy and number fluxes throughmembranes
Mesoscopic: finite-size effect
A messy situation!
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Steric repulsion
Presence of large molecules makes volume less accessible toother large molecules
Ellis (2001)
Energetically costly to add a large molecule to an alreadycrowded volume
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Steric repulsion
Neglect Coulombic interactions for now
Ideal fluid of point particles: PV = NkT
Fluid of hard spheres: P (V − b) = NkT
Excluded volume b is four times volume of spheres
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Steric repulsion
Presence of n hard spheres leaves (V − nv0) available for(n + 1)-th sphere
Number of microstates and entropy:
Ω ∝ V (V − v0) · · · [V − (N − 1)v0]
S = k log V + k log(V − v0) + · · · + k log[V − (N − 1)v0]
Equation of state:
P
T=
∂S
∂V=
Nk
V − Nv0/2, v0 =
4
3π(2a)3
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Implications
Transport in the cytoplasm
Kinetics of metabolic channeling
Efficiency of protein folding
Cellular volume regulation
Amyloid fibril formation
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Transport
Mechanisms 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-typemodeling
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Transport
Rate of self-diffusion of proteins lowered as crowdingincreases (Zimmerman and Minton, Annu. Rev. Biophys. Biomol. Struct. 22, 27 (1993)):
Replace D∇2c with ~∇ · [D(c)~∇c]
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Transport
How to obtain efficient transport in lieu of inefficientdiffusion?
Active propagation along cytoskeletal elements?
Crossover to active propagation as crowding increases
0 1
1
2
Volume fraction φ
Tra
nspo
rt e
xpon
ent γ
= d
log
⟨r2 (t)⟩
/ d
log
t
Replace ~∇ · [D(c)~∇c] with ~U(~x, c) · ~∇c + ~∇ · [D(c)~∇c]Macromolecular Crowding, Oct. 15, 2003 – p.13/33
Transport
Measure 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))
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Transport
Inject tracers (e.g., fluorescent µspheres) into cytoplasm
Brownian motion with dissipation depending on earliervelocities:
mv(t) = −
∫
t
0
ζ(t − τ)v(τ)dτ + fR(t)
where ζ(t) is memory function
In thermal equilibrium, noise correlation:
〈fR(0)fR(t)〉 = kBTζ(t)
Obtain velocity correlation in terms of measurable meansquare displacement 〈∆r2(t)〉
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Transport
Susceptibility:
G(s) =kBT
πas〈∆r2(s)〉
Real part G′(ω) is storage modulus, imaginary part G′′(ω) isloss modulus
In a fluid, 〈∆r2(t)〉 = 6Dt with D = kBT/6πηa:
G′(ω) = 0, G′′(ω) = ηω
In a solid, 〈∆r2(t)〉 independent of t:
G′(ω) = const., G′′(ω) = 0
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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 viscousliquid
Replace diffusion in reaction-diffusion models with ???
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Metabolic channeling
How 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 molecule
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Metabolic channeling
Rohwer, Westerhoff et al. (P. Natl. Acad. Sci. USA 95, 10547 (1998))
measured steady-state flux through PTS in vitro
Flux ∝ concentration2:low concentrationperfect channel, “hit and run”
Flux ∝ concentration:high concentration and/or with crowdingenzymes exist as complexes
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Metabolic channeling
Total flux and flux-response coefficient vs. total enzymeconcentration:
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Metabolic channeling
Two-enzyme group-transfer model:
Crowding added in as changes to association/disassociationrates
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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
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Cellular volume regulation
How 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 transporter
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Amyloid fibril formation
Neurodegenerative diseases, e.g., Parkinson’s disease,characterized by amyloid fibril formation
Shtilerman et al. (Biochemistry 41, 3855 (2002)) showed that crowdingreduced lag time for protofibril formation and conversion ofprotofibril to fibril
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Quantitative models
Hard spheres fluid, amenable to theory
Atomic-level models using molecular dynamics
Continuum models
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Hard spheres fluid
Toy model: Spheres with hard core potential
u(r) =
∞ r < a
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
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Hard spheres fluid
Consider effects on equilibrium of dimerization
A + A A2
Calculate non-ideal contribution to K vs. volume fraction φ
(Hall and Minton, Biochim. Biophys. Acta 1649, 127 (2003))
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Hard spheres fluid
In addition to hard spheres, to study transport:
Mimic actin elements by stationary rods
Model binding and transport on these rods
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Atomic-level models
Elcock (P. Natl. Acad. Sci. USA 100, 2340 (2003)) modeled escape ofrhodanese from cavity of GroEL into crowded solvent
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Atomic-level models
Uses known GroEL conformation
Omits GroES
Models crowding agent as spheres
Incorporates repulsive r−12 interaction between spheres andrhodanese
Uses Brownian motion for crowder spheres
Assumes periodic boundaries
Contains 64000 atoms
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Atomic-level models
Crowding enhances efficiency of chaperonins GroEL andGroES:
Enhances association of GroEL and GroES, preventingescape
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Atomic-level models
Friedel et al. (J. Chem. Phys. 118, 8106 (2003)) simulated a version ofthe 46 residue off-lattice minimalist model using moleculardynamics
Restricts protein to sphere with soft well repulsive potential
Crowding decreases folding time
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Conclusions
Macromolecular crowding has important biophysical,biochemical, and physiological implications on intracellularprocesses
Interesting problems:Spatial dependence of transport in cytoplasm fromincreasing accurate modelingUnderstanding role of crowding in kinetics of metabolicchanneling
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