Large proteasome complexes in a bacterial cytoplasm can be modelled as rigid spheres…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch Free energy at work: states, weights and entropic forces

Problem

Large proteasome complexes in a bacterial cytoplasm can be modelled as rigid spheres of effective radius

R = 15\,\mathrm{nm}

, moving through a background of smaller cytoplasmic proteins that together occupy a volume fraction

\phi \approx 0.35

of the cytoplasm and have a typical radius

\delta = 3\,\mathrm{nm}

. ((a)) State the assumptions needed to treat the small proteins as an ideal, non-interacting crowder fluid for the purpose of the Asakura-Oosawa depletion result

F_{\rm dep}(d) = -\Pi V_{\rm ov}(d)

, and comment on how well the condition

R\gg\delta

used in that result is satisfied here. ((b)) Using

F_{\rm dep}\approx-\tfrac32\phi(R/\delta)k_BT

for the contact depletion free energy between two proteasomes, evaluate

F_{\rm dep}

in units of

k_BT

and in

\mathrm{kJ\,mol^{-1}}

at body temperature,

310\,\mathrm{K}

(use

1k_BT=2.58\,\mathrm{kJ\,mol^{-1}}

310\,\mathrm{K}

). ((c)) Use the zero-flux Boltzmann profile

e^{-F_{\rm dep}(d)/k_BT}

to estimate how many times more often a pair of proteasomes is found at contact than beyond the range of the attraction, and comment on whether this depletion attraction is likely to matter for the spatial organisation of such large complexes in the cytoplasm.

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