UNIVERSITA’ DELLA CALABRIA
Dipartimento di Ingegneria Chimica e dei Materiali
A Monte Carlo simulation of protein nucleation on porous membranes
Efrem Curcio1,2, Valerio Curcio3, Gianluca Di Profio2, Enrico Drioli1,2
1. Department of Chemical Engineering and Materials, University of Calabria - Via P. Bucci CUBO 44A, 87030 Rende (CS) Italy
2. Institute on Membrane Technology ITM-CNR, c/o University of Calabria - Via P. Bucci CUBO 17C, 87030 Rende (CS) Italy
3. I.S.A. "Michele Fanoli", Viale dello Sport 28, 35013 Cittadella (PD) Italy
Aim of the work
Two-dimensional Ising model has been used to study the heterogeneous nucleation of protein crystals on porous polymeric hydrophobic membranes. 2D Ising model has been successfully
applied to study heterogeneous nucleation on square lattice with nearest-neighbour interactions and free boundary conditions[1]. Sear (2006) used the same approach to determine the
heterogeneous nucleation rate on microscopic impurities, and it was found more than four orders of magnitude faster than homogeneous nucleation[2].
Energy function of the system for spin-spin and spin-field interactions:
A
B
C
D
E    J   i j  h  i  J s   i j
ij
i
ij
ij=1 is the state of spin, J is the coupling constant between free
neighbouring spins, h the external magnetic field, and Js is the strength of
the coupling between a free spin and a fixed spin of the wall. It is assumed
Js=0, that is the polymeric surface does not preferentially attract either
phase.
Interfacial tension  between the bulk spin-up and spin-down phases
in 2D Ising model:

J  

 1  exp   2   
kT

J

 


2
 ln

kT
kT
J  

 1  exp   2   
kT   


Simulation snapshots of the system 40x40 sites in size and J7kT = 0.8,
h/kT = 0.05. Fixed spins are in red, spin-up phase in blue.
Simulation results
INDUCTION
TIME
D
C
B
A
Number of spin-up sites, as a function of number of cycles in the 40x40 lattice.
HEW lysozyme crystal grown on a microporous polypropylene membrane
(pore size: 0.2 m)
 The
heterogeneous nucleation rate (related to the reciprocal of the induction time) is faster on porous membranes than on flat surfaces, in agreement with predictions of
Classical Nucleation Theory;
 the
 an
nucleation process proceeds via two steps: 1) nucleation into the pore; 2) nucleation out of the pore, both to be considered activated processes;
optimal pore size, corresponding to maximum of the nucleation rate function, exists (pore approximately of the same size of the critical nucleus).
Bibliography
[1] E.N.M. Cirillo, J.L. Lebowitz, “Metastability in the two-dimensional Ising model with free boundary conditions,” J. Stat. Phys. 90 (1998) 211–226
[2] R.P.Sear, Heterogeneous and Homogeneous Nucleation Compared: Rapid Nucleation on Microscopic Impurities, J. Phys. Chem. B 110 (2006) 4985-4989
“Gricu 2004” - Ischia (Napoli), Italia, 12-15 settembre 2004