Postdoctoral fellow - **UPDATE**: Moved to U Chicago Physics (May 2015), Faculty webpage
Michael Brenner's group, SEAS, Harvard
Current research interests
Problems at the interface between materials science and biology. Current research includes design of responsive nano-scale materials, membranes with associative memory, specificity in binding interactions, non-equilibrium error correction and active self-assembly. I use the methods of statistical mechanics, soft matter and computer science. Interests in high-energy physics include gauge-gravity duality and entanglement entropy.
Research experience & education CV
Member Institute for Advanced Study, Princeton, NJ Aug 09 – Aug 12
Visiting Researcher Rockefeller University, New York City, NY Aug 09 – Aug 12
PhD (Physics) Princeton University, Princeton, NJ Sep 04 – Jul 09
B.S. (Mathematics) California Institute of Technology, Pasadena, CA Sep 00 – Jun 04
Multifarious Assembly Mixtures: Systems Allowing Retrieval of Diverse Stored Structures, in collaboration with: Z. Zeravcic, S. Leibler and M. Brenner
Undesired usage and the robust self-assembly of heterogeneous structures, in collaboration with: J. Zou, and M. Brenner
Nature Communications 6, 6203 (Jan 2015) Nat Comm.
Biological implications of dynamical phases in non-equilibrium reaction networks, in collaboration with: S. Vaikuntanathan
invited contribution to the Journal of Statistical Physics (special issue), to appear
Discriminatory proofreading regimes in non-equilibrium systems, in collaboration with: D.A. Huse, and S. Leibler
Physical Review X 4 (2), 021016 PRX
Speed, dissipation, and error in kinetic proofreading, in collaboration with: D.A. Huse, and S. Leibler
AdS4/CFT3 - squashed, stretched and warped, in collaboration with: I.R.Klebanov and T.Klose
Journal of High Energy Physics 0903 140 (2009) arxiv:0809.3773 [hep-th] PDF
Goldstone Bosons and Global Strings in a Warped Resolved Conifold, in collaboration with: I. R. Klebanov, D. Rodriguez-Gomez and J. Ward
Journal of High Energy Physics 0805, 090 (2008), arXiv:0712.2224 [hep-th] PDF
Entanglement as a Probe of Confinement, in collaboration with: I. R. Klebanov and D. Kutasov
Nuclear Physics B 796, 274 (2008), arXiv:0709.2140 [hep-th] PDF
Gauge/Gravity Duality and Warped Resolved Conifold, in collaboration with: I. R. Klebanov
Journal of High Energy Physics 0703, 042 (2007), arXiv:hep-th/0701064 PDF
On D3-brane potentials in compactifications with fluxes and wrapped D-branes
in collaboration with: D. Baumann, A. Dymarsky, I. R. Klebanov, J. M. Maldacena and L. P. McAllister
Journal of High Energy Physics 0611, 031 (2006), arXiv:hep-th/0607050 PDF
Fatgraph expansion for noncritical superstrings, in collaboration with: A. Kapustin
arXiv:hep-th/0404238 (2004) PDF
Associative memory and multi-stability in materials
Biological materials are often adaptable - the same building blocks can show different collective behaviors in response to external signals. However, traditional synthetic bottom-up methods, such as self-assembly, DNA origami and shaping of membranes, have focused on programming a single target structure into the local interactions of a material. Can a set of particles (proteins, DNA tiles) can have interactions that simultaneously stabilize different arrangements of those particles into macromolecular complexes? Can one controllably program multiple folding or buckling behaviors in mechanical systems, generalizing single behavior mechanisms like the Hoberman sphere or Mirua Ori?
Programmable multi-stability and its limits have been extensively studied in the theory of Associative Memory in neural networks and in spin glass physics. In perfect analogy to ideas in neural networks, we are finding that disordered materials allow storage and retrieval of different behaviors through association. For example, in self-assembling systems, a specific stored arrangement of particles be induced using a seed that only need resemble the desired structure (by ``association’’). Similarly, disordered membranes can show the ability to ``learn’’ different crumpled configurations and recall such configurations by ``association’’ - a physical impulse or initial condition that resembles one stored configuration more than others induces that configuration.
Associative memory in these diverse material systems (self-assembly, DNA origami and disordered membranes) relies on a balance of promiscuity and frustration — we expand allowed local transformations for single building blocks (`promiscuity') by programming multiple behaviors but the material as a whole produces a coherent behavior due to cross-checks between degrees of freedom on a global scale (`frustration’).
Multifarious Assembly Mixtures: Systems Allowing Retrieval of Diverse Stored Structures, with Zorana Zeravcic, Stanislas Leibler and Michael Brenner (accepted at PNAS, arXiv version).
Dynamic associative memory in interacting particles (in preparation)
Undesired usage and robust self-assembly
Self-assembly is a bottom-up method of assembling structures from interacting particles. Local control parameters — like binding energies between different species of particles and their concentrations — are chosen to pick out a spontaneous assembly of a desired structure. However, in real systems, many undesired structures are also produced. We show that self-assembly is enhanced by choosing control parameters that are 'off-target' ; for example, the optimal supply of components to produce a structure A-B-A might be supplying A and B in a ratio of 100 to 1 (instead of 2 to 1), depending on the physics of assembly and the undesirablity of various competing structures formed. Such 'off-target' rules strike a balance between enhancing the desired stricture and suppressing undesired ones.
In general, the control parameters cannot be chosen based on the desired structure alone and need to reflect a balance between desired and undesired structures.
Undesired usage and the robust self-assembly of heterogeneous structures, (accepted at Nature Communications) with James Zou and Michael Brenner.
Towards an information theory of 'shape': specificity in natural and synthetic systems
A wide range of natural and synthetic systems rely on the existence of specific interactions between several species of particles (or binding sites). The physics and chemistry of interaction between particles limit the number of unique 'lock and key’ pairs that a system can support without significant `cross-talk’ (i.e., undesired interactions) across pairs. Such a limit is at the heart of many phenomena, from functioning of the immune system, signaling pathways, artificial molecular sensors ('artificial noses') and synthetic self-assembly. Inspired by on Shanon's theory of coding, we develop a framework on coding specific interactions using shape and surface chemistry. Our framework reveals how different aspects of physical interactions affect the amount of information that can be encoded in particle interactions.
An information theory of 'shape', (in preparation) with Miriam Huntley and Michael Brenner.
Non-equilibrium error correction
It is widely appreciated that energy is required to carry out mechanical work. At the molecular scale in biology, energy is used to maintain order and correct 'errors' in various biochemical processes. For example, the error rate in DNA replication and protein synthesis is much lower than expectations from equilibrium thermodynamics. The low error rate in such enzymatic reactions has been explained using the non-equilibrium mechanism of `Kinetic Proofreading' by John Hopfield and Jacques Ninio. What are the general principles behind this mechanism? How would you program a general non-equilibrium system with such 'error correcting' ability? Can you incorporate these ideas into materials synthesis methods, using energy to fix errors in synthesis?
We show that the central principle behind kinetic proofreading is ``dynamic instability'' along the reaction coordinate. That is, a reaction, while proceeding from start to finish, must be repeatedly reset to earlier stages using energy from an external source. This coarse-grained view of kinetic proofreading connects the original enzymatic mechanism to diverse phenomena, such as microtubule growth and foraging and search strategies. Our view also reveals fundamental trade-offs between speed, energy and accuracy, including a regime with a large gain in speed at a small cost in accuracy. We are working to implement these principles in synthetic systems (for e.g, hybridization of DNA strands), using DNA strand displacement as an energy source.
Discriminatory proofreading regimes in non-equilibrium systems, with: D.A. Huse, and S. Leibler Phys. Rev. X 4, 021016 (2014)
Quantum entanglement has been a fruitful idea in many areas of physics but until recently, it had not found much use in particle physics. We proposed entanglement between quarks as a subtle test of whether quarks are inseparably bound (``confined'') in any given theory of quarks and gluons. Our proposal was validated by lattice simulations by groups at Argonne National Labs/U Chicago and ITEP (Moscow). Entanglement entropy has since found many other applications in particle physics and string theory and has become a popular area of research in recent years.
Entanglement as a probe of Confinement, with David Kutasov and Igor Klebanov, Nuclear Physics B (796), 274 (2008)
Geometric interpretations of problems in inflationary cosmology and renormalization group theory
The AdS/CFT correspondence shows how problems in particle physics can be mathematically translated to geometric problems in Einstein’s theory of gravity in higher dimensional spacetimes. We used this correspondence to show how difficult calculations in models of inflationary cosmology could be solved easily using the geometric interpretation. For example, it is difficult to derive predictions from some models of inflationary cosmology due to strongly interacting quantum fields present in such models. We showed that this problem was equivalent to a simpler system of gravitational interactions a particle and a membrane in curved spacetimes.
I also studied other strongly interacting behavior in quantum field theories (renormalization group flows, conformal field theory) using geometric problems in gravity through the AdS/CFT correspondence.
On D3-brane potentials in compactifications with fluxes and wrapped D-branes, with: D. Baumann, A. Dymarsky, I. R. Klebanov, J. M. Maldacena and L. P. McAllister PDF
Gauge/Gravity Duality and Warped Resolved Conifold, with: I. R. Klebanov PDF
AdS4/CFT3 - squashed, stretched and warped, with: I.R.Klebanov and T.Klose PDF
Goldstone Bosons and Global Strings in a Warped Resolved Conifold, with: I. R. Klebanov, D. Rodriguez-Gomez and J. Ward PDF
Fatgraph expansion for noncritical superstrings, with: A. Kapustin PDF