Anuj Chaudhri

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RESEARCH
Please check the publications section to read about my contributions in the following areas.
Protein Self-Association and Aggregation in Biopharmaceutics (in collaboration with Genentech Inc.)
 
Motivation
1. Therapeutic protein antibody solutions become highly viscous at high concentrations
2. Reversible self-association 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. Self-association occurs at long time scales, which also makes MD unfeasible.
5. Need coarse-grained (CG) models to study the above systems

 
For this study, Coarse-grained computational models of two therapeutic monoclonal antibodies are constructed to understand the
effect of domain-level charge-charge electrostatics on the self-association phenomena at high protein concentrations. Two different
models are constructed for each antibody for a compact Y-shaped and an extended Y-shaped configuration. The resulting simulations of
these coarse-grained 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 coarse-grained
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
Fab-Fab interactions in corroboration with experimental observations. In contrast, the structures in MAb2 appear to be formed via Fab-
Fc interactions. The coarse-grained representations are effective in picking up differences based on local charge distributions of domains
and make predictions on the self-association 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 coarse-grained
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, Coarse-Grained 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: m

(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: s-ms, Bubble Size: nm-mm

(Ref: You Research Group, Univ. of Texas Arlington, http://www-heat.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 'coarse-graining' 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 coarse-grained 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 coarse-graining 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.  Lid-driven 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 Fluctuation-Dissipation 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 steady-state heat conduction (J. Heat Transfer 2009)
2.  Two dimensional steady-state heat conduction (J. Heat Transfer 2009)
3.  Raleigh-Bnard convection cells (arXiv:1201.3641v1 [cond-mat.stat-mech])
 
Dissipative Particle Dynamics: Phase Change
The heat transfer and fluid flow processes associated with liquid-vapor 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 liquid-vapor 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
liquid-vapor 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 non-ideal 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 [cond-mat.stat-mech]
 
Atomistic Methods: Molecular Dynamics
Molecular dynamics is a classical method that uses empirical or semi-empirical 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, lab-on-a-chip 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 Fokker-Planck Equations (set of interesting papers by Daniel T. Gillespie)
 
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© Anuj Chaudhri (2009-12)