RESEARCH 

Please check the publications section to read about
my contributions in the following areas. 

Protein
SelfAssociation and Aggregation in Biopharmaceutics (in
collaboration with Genentech Inc.) 

Motivation 
1. Therapeutic
protein antibody solutions become highly viscous at high
concentrations 
2. Reversible
selfassociation of these proteins is the likely cause
for high viscosities 
3. These antibody molecules are very large biomolecules
(~20,000 atoms). Hence it is not practical to study say
1000 of these 
using Molecular
Dynamics (MD) (~ 20 million atoms). 
4.
Selfassociation occurs at long time scales, which also
makes MD unfeasible. 
5. Need
coarsegrained (CG) models to study the above systems 


For this study, Coarsegrained computational models of
two therapeutic monoclonal antibodies are constructed to
understand the 
effect of domainlevel chargecharge electrostatics on
the selfassociation phenomena at high protein
concentrations. Two different 
models are constructed for each antibody for a compact
Yshaped and an extended Yshaped configuration. The
resulting simulations of 
these coarsegrained antibodies that interact through
screened electrostatics are done at six different
concentrations.It is observed 
that a particular monoclonal antibody (hereafter
referred to as MAb1) forms three dimensional
heterogeneous mesophase structures with 
dense regions compared to a different monoclonal
antibody (hereafter referred to as MAb2) that forms more
homogeneous structures. 
These structures, together with the potential mean force
(PMF) and radial distribution functions (RDF) between
pairs of coarsegrained 
regions on the MAbs, are qualitatively consistent with
the experimental observation that MAb1 has a
significantly higher viscosity 
compared to MAb2, especially at concentrations > 50
mg/ml. It is also observed that the structures in MAb1
are formed due to stronger 
FabFab interactions in corroboration with experimental
observations. In contrast, the structures in MAb2 appear
to be formed via Fab 
Fc interactions. The coarsegrained representations are
effective in picking up differences based on local
charge distributions of domains 
and make predictions on the selfassociation
characteristics of these protein solutions. This is the
first computational study of its kind to 
show that there are differences in structures formed by
two different monoclonal antibodies at high
concentrations. (in review) 


Multiscale Methods for Complex Fluids and Phase Change
Processes 

Motivation 
1. Multiphase
and multicomponent systems have varying length and time
scales. 
2. The
biggest challenge is to model these systems with all the
complexity built in. 
3. Continuum approaches have been successfully applied
to systems at macroscopic scales. Similarly atomistic
methods are 
good for systems at
nanoscale. But most of the systems and processes in
nature fall in between these two scales. 


Multiscale modeling can be done in primarily two ways:
sequential or hierarchical
modeling in which finer scale models are
coarsegrained 
to larger scale models to transfer information between
scales, and concurrent modeling
in which simultaneous coupled calculations are 
done in different regions with different resolutions.
Sequential modeling includes popular methods such as
Molecular Dynamics (MD), 
Monte Carlo, CoarseGrained MD, mesoscopic methods such
as Brownian Dynamics, Stokesian Dynamics, Lattice
Boltzmann, Lattice Gas, 
Dissipative Particle Dynamics and electronic structure
methods such as Density Functional Theory, Tight Binding
etc. Concurrent model 
ing on the other hand includes methods such as Quantum
Mechanics/Molecular Mechanics (QMMM), hybrid MD/FEM
coupled models, 
Quasicontinuum methods and other kinds of hybrid
methods. 

My research interests focus on the sequential
methodology,
which is at the heart of statistical mechanics. One
major assumption that 
goes into these models is that the physics is clearly
separated between the finer and coarser levels so that
information can be 
easily transmitted between models at different scales
(i.e. sequentially). This methodology leads to the
problem being mapped to 
a Stochastic Differential Equation from an Atomistic
Hamiltonian (formally using Projection Operators). The
assumption behind this process 
is that the fast degrees of freedom are averaged and
equations of motion are written for the slower degrees
of freedom. The effect of the 
faster degrees of freedom show up as dissipation and
random fluctuations. Often the Markovian assumption is
used to reduce the problem 
to a simpler level by choosing Gaussian (white or
colored) noise for the random fluctuations. There is a
whole new field dedicated to this 
area of research called as Stochastic Processes. 

Some Examples where Multiscale
Models are necessary: 


Blood
Morphology
Blood RBC
size: µm
(Ref:
National Cancer Institute,
http://www.nctimes.com/articles/2007/06/12/health/17_40_576_7_07.txt) 
Phase
Change Thermal Management
Bubble
Departure Rate: µsms, Bubble Size: nmmm
(Ref: You
Research Group, Univ. of Texas Arlington,
http://wwwheat.uta.edu/coating/coating.html) 


Dissipative Particle
Dynamics: Constant Temperature 
Dissipative particle dynamics (DPD) is a discrete
particle based mesoscale method that conserves linear
momentum locally and includes 
hydrodynamics by modeling the solvent medium explicitly.
The DPD equations are stochastic differential equations
of the Langevin type. 
The DPD fluid particles are called as 'beads', which
refer to a collection of atoms, molecules or monomers.
The position and momenta of 
these beads is tracked in time using Newton's equations
of motion. The beads interact via a collection of
conservative, dissipative and 
random forces. The dissipative and random forces arise
due to the 'coarsegraining' from atomistic dynamics.
These additional forces 
that are absent in an atomistic setting can be viewed as
the 'thermostat' forces.
Intuitively these forces come from the variables that 
are 'irrelevant' in the
coarsegrained model but become a part of the 'bath' and
affect the 'relevant' system variables through
dissipation 
and fluctuations. In this
way the thermostatted modeling of atomistic dynamics is
similar in spirit to the
DPD modeling of systems. 

The DPD method was analyzed thoroughly and a consistent
nondimensionalization for multicomponent systems has
been proposed by us. 
Although a lot of work has been done in setting up the
theoretical foundations of DPD using statistical
mechanics, very little work has 
actually gone in establishing a clear link between the
atomistic regime and DPD. The DPD equations are based on
empirical parameters 
that match the physics qualitatively, but quantitative
estimates are hard to get. My major interest is in
linking the MD and DPD regimes 
using principles of coarsegraining to clearly obtain
the DPD parameters from fundamental atomistic physics,
which is something I intend 
to work on in the future. 

Some simple examples showing the
applicability of the DPD method that I have worked on
are: 
1. Binary fluid phase segregation
(Int. J. Num. Methods Fluids 2009) 
2.
Deformable particle suspensions in shear flows (APS
meeting 2007) 
3. Liddriven cavity flow 
4. Couette flow 

I have also done some work on integration algorithms for
the DPD stochastic differential equations (SDE) to
characterize dynamic 
property calculations (Phys. Rev. E 2010). 

Dissipative Particle
Dynamics: Energy Conserving 
The isothermal model of DPD described above is unable to
handle temperature gradients as the
FluctuationDissipation theorem that 
relates the dissipative and random forces maintains the
temperature and serves as a 'thermostat'. To model
temperature gradients i.e. 
heat transfer in systems, an additional internal
variable has to be introduced that keeps track of the
dissipated energy and distributes 
it evenly between the beads without losing it to the
environment. An internal energy evolution equation is
written and is coupled to the 
momentum equation through a viscous heating term. A heat
conduction term is also added to account for differences
in particle temper 
atures. A major assumption is that the internal state
of a bead is in thermodynamic equilibrium and hence
particle entropy and 
temperature variables can be introduced. 

I have used this energy conserving model to develop and
model problems in heat transfer: 
1. One dimensional transient and steadystate heat
conduction (J. Heat Transfer 2009) 
2. Two dimensional steadystate heat conduction (J. Heat Transfer 2009) 
3. RaleighBénard
convection cells (arXiv:1201.3641v1 [condmat.statmech]) 

Dissipative Particle
Dynamics: Phase Change 
The heat transfer and fluid flow processes associated
with liquidvapor phase change phenomena are among the
most complex transport 
conditions that are encountered in engineering
applications. The existing framework on dissipative
particle dynamics is not suited to 
handle liquidvapor interfaces. In order to model phase
change heat transfer using a mesoscopic framework, a new
potential function 
has to be defined that takes into account the
inhomogeneities that arise because of interfaces. I have
worked on incorporating 
liquidvapor phase change using ideas from density
functional theory of inhomogeneous fluids. Using density
functional theory, a free 
energy functional is written and expanded in terms
involving gradients of density. A standard equation of
state can be used to define 
the nonideal contribution to the free energy. The
second order terms in the free energy functional are
used to model the interfacial 
effects. The free energy can then be used to define a
potential function and a multibody force that is
nonlocal in character. I am using 
this framework to study the problem of homogeneous
bubble nucleation in single phase fluids. This study
will serve as a first step 
towards modeling highly complex phenomena such as
boiling using a particle based mesoscopic framework.
arXiv:1203.0069v1 [condmat.statmech] 

Atomistic Methods:
Molecular Dynamics 
Molecular dynamics is a classical method that uses
empirical or semiempirical force fields and Newton's
equations of motion to track 
the positions and momenta of a bunch of atoms or
molecules. The macroscopic or bulk properties of a
system are based on averages 
or correlations of these variables and are linked
rigorously through statistical mechanics. Molecular
dynamics was developed almost four 
decades ago and has reached a certain level of maturity
with respect to force fields, integration schemes,
property estimation etc. 

My initial work at Penn involved developing models
and codes for investigating flow of fluids at nanoscopic
scales mainly in confined 
spaces such as nanotubes. Carbon nanotubes were a
natural choice for their very crystalline structure,
high electronic and thermal con 
ductivity properties, which could be put in good use
for drug delivery systems, FET devices, labonachip
devices, wherever fluids 
need to be transferred in small amounts such as cells
etc. Very good mechanical properties have also found
good use in developing high 
resilience structures for aircraft wings, buildings etc. 



MD models for the following were developed during the
initial years of my PhD and are explained in the
following links: 
1.
Argon flow in carbon nanotubes (MD
Study of Argon Flow in CNT) 
2.
Bulk water simulations 
3.
Water flow in carbon nanotubes 
4.
Mechanical property estimation of carbon nanotubes 

Miscellaneous Projects/Interests 
Apart from the above I have also taken a number of very
interesting classes and worked on course projects that
are very different from 
the above, though having many commonalities in terms of
the physics and mathematics involved. 

1. Stars: Evolution, Stability and Statistical
Mechanics (inspired by the work by Prof. Subramanyan
Chandrasekhar) 
2. Nanobiology: Transport Phenomena in Ion
Channels (inspired by the work by Prof. Roderick
Mackinnon) 
3. Univariate and Multivariate FokkerPlanck
Equations (set of interesting papers by Daniel T. Gillespie) 
