Oded Farago: Past Research
- Computational modeling of bilayer membranes
One of the factors limiting the size of membranes in computer
simulations is the large number of solvent molecules which fill the
simulation cell. We have recently developed a novel computer model of
bilayer membranes in which the membranes are simulated without the
embedding solvent as if they were in vacuum. The lipids are modeled as
trimers with pair-interactions that implicitly account for the
hydrophobic effect. Using this new model we have been able to
investigate the behavior of large membranes containing 1000
lipids. Despite its conceptual simplicity, the model reproduces many
common features of bilayer membranes, such as a solid-fluid phase
transition, pore formation, and trans-bilayer diffusion
(flip-flop). Its unusual efficiency makes simulations of membranes
consisting of thousands of molecules feasible - much above the
capability of atomistic and other coarse-grained models where solvent
is modeled explicitly. This makes the model an excellent tool for
testing concepts and theories on the mesoscopic scale.
Figure: Equilibrium configuration of a fluid membrane consisting of 1000
molecules (500 molecules in each monolayer).
- Statistical-mechanics of fluctuating surfaces
Many monolayer and bilayer systems are frequently assumed to be
saturated, i.e., having a nearly-vanishing surface tension. The reason
for this assumption is the fact that the energy required to change the
area density of the constituent amphiphilic molecules is much larger
than the thermal and curvature energies. Consequently, the effect of
area elasticity (also known as Schulman elasticity) on the stretching
behavior of fluctuating bilayers has been very little investigated. We
have studied this issue using a statistical-mechanical model including
both the Schulman and curvature (Helfrich) energies. Our model
clarifies that elasticity of surfaces is determined by an interplay
between the Schulman elastic energy, curvature elasticity, and
entropy. Our theoretical results agree with micropipet aspiration
measurements of giant unilamellar vesicles.
In another study we used a statistical mechanical analysis to derive
virial expressions for the elastic coefficients of fluctuating
surfaces (surface tension, bending and Gaussian-curvature moduli),
relating them to the microscopic potentials and the distribution
functions of the molecules. We used these expressions to compute the
elastic coefficients of our computer-model membrane. The numerical
values of the elastic coefficients which we obtain from these
expressions are in agreement with the values extracted from a spectral
analysis of the thermal fluctuations.
Figure: The inverse of the spectral intensity for undulatory modes
as a function of the square wave number.
- Pulling knotted polymers
The static and dynamic behavior of single polymer chains (e.g., DNA)
and multichain systems (e.g., gels and rubber) is strongly influenced
by knots and permanent entanglements. In this work we used Monte Carlo
simulations to compare the force-extension relations of knotted and
unknotted self-avoiding chains of several sizes. The results of the
simulations of unknotted chains could be easily explained using simple
scaling arguments. By contrast, knotted polymers exhibit strong finite
size effects which can be interpreted in terms of a new length scale
related to the size of the knot. Based on this interpretation, we have
extracted the scaling dependence of the mean knot size on the length
of the polymer.
Figure: Two configurations of a knotted chain of 335 bonds. The (grey)
knotted regions consist of 112 (top) and 32 (bottom) bonds.
- Entropic elasticity of soft-matter systems
Systems of hard spheres tethered by inextensible bonds can be used to
model real soft matter systems whose thermodynamic properties are
determined by entropy rather than energy, like colloids and polymeric
gels. We have developed a method well suited for numerical calculation
of the elastic constants of such model systems, and demonstrated its
efficiency and accuracy on several systems. One of the interesting
problems which we addressed is related to the elastic behavior of
percolation networks near the sol-gel transition. We found (both in
two- and three-dimensions) that the shear modulus of such networks has
a power-law dependence on the distance from the percolation threshold,
with a characteristic exponent that is similar to the conductivity
exponent of random resistor networks. This result thus "closes a circle"
which began more than twenty years ago, when it became clear that the
analogy between the (entropic) gel elasticity and conductivity
proposed by de Gennes, is far from being obvious.
Figure: Equilibrium configuration of 2D percolation system
consisting of hard spheres and inextensible tethers.