Integrated Calendar

Molecular recognition plays a central role in cellular behavior and immunological response in the human body, and is the basis for many bioanalytical techniques. Using atomic force microscopy, we have measured directly the molecular recognition forces between individual ligand-receptor, antibody-antigen, and DNA-DNA molecules with high force and displacement sensitivity. Now, can force also be used to develop novel biosensors with single molecule sensitivity? From this concept we have developed several unique biosensors that use DNA or antibody-based microarrays, magnetic microbeads, and sensors (optical, mechanical and magnetic field sensors) to detect and identify biological molecules. The magnetic microbeads, which provides the pulling force originally generated by the atomic force microscope, serve two additional purposes: (1) as a label to detect molecular recognition between molecules, and (2) as an actuator to utilize the range of bonding forces between molecules. The latter purpose permits one to discriminate between specifically (strongly) and non-specifically (weakly) bound species thereby improving assay selectivity (fewer false positives and negatives) and sensitivity (lower background). We have applied this technology to detect proteins, viruses and bacteria used as biological warfare agents.

Recent advances in technology have enabled studying the dynamics of single molecules. What new
insights can be revealed by these experiments which cannot be seen in bulk measurements? In this talk
I will focus on two examples where we showed that studying single molecules reveals new phenomena.
The first is the case of anomalous diffusion in an equilibrium environment. The continuous time
random walk with a power-law distribution of sojourn times is a common model to describe subdiffusion
processes. A particle which undergoes such a process will visit all sites of a finite system, yet
the process is non-ergodic. We clarify the concept of weak ergodicity breaking and calculate the
distribution of occupation times from which the time averages of physical observables can be derived.
Unlike in ergodic systems even at the infinite long time limit, the occupation times (and therefore the
physical observables) are random quantities. I will also discuss another model for anomalous diffusion
due to coupling between stochastic processes which can lead to ergodic or non-ergodic behavior for
different coupling functions. In both models the single molecule properties provide an insight into the
dynamical mechanism, which could not be obtained from ensemble measurements. The second
example I will discuss is a non-equilibrium system, a single molecule excited by a monochromatic laser
field. I will introduce an extension of the generating function technique for the calculation of photon
emission statistics for systems governed by multi-level quantum dynamics. This extension enables
studying the statistics of photons that are emitted from specific transitions and subject to quantum
coherence. Several model calculations illustrate the generality of the technique and highlight
quantitative and qualitative differences between quantum mechanical models and related stochastic
approximations. I will also introduce the moment-generating function for photon emissions in which
the frequencies of the fluoresced photons are explicitly considered. Calculations were performed for the
case of a two-level dye molecule, showing that measured photon statistics will display a strong and
nonintuitive dependence on detector bandwidth. It will also be demonstrated that the anti-bunching
phenomenon, associated with negative values of Mandel's Q parameter, results from correlations
between photons with well separated frequencies. These two examples show that single molecule
measurements can provide new information about the observed system both in equilibrium and non equilibrium
conditions. Moreover, new phenomena which are observed only at the single molecule
level can favor certain microscopic models over others.

Self-assembly is a process in which pre-existing components form an organized structure without an external guidance. This process occurs at different scales from atoms to organisms.
This presentation describes two self-assembled systems: one comprises of biomolecules (short peptides) and the other millimeter-sized objects (electrets). Both systems aim to understand concepts related to the folding of biopolymers. The first system is a new class of self-assembled peptides discovered during the study of the formation of amyloid fibrils– a misfolded state of protein which is the hallmark of several diseases such as Alzheimer’s disease, Type II diabetes and Prion diseases. This class of peptides comprises homo-aromatic dipeptides that self-assemble under mild conditions into highly ordered structures including spheres, tubes and plates. The nanometric structures are useful for various applications such as casting mold for metal wires, sensor fabrication and drug delivery.
The second system physically represents the simplest theoretical model for folding¬¬– the “beads-on-a-string” model. This system comprises millimeter ¬scale Teflon and Nylon-6,6 (spherical or cylindrical) beads (~ 6 mm in diameter) separated by smaller (~3 mm) PMMA spherical beads, on a flexible string. During agitation of the sequence of beads on a planar, horizontal surface, contact electrification caused the larger Nylon-6,6 and Teflon beads to charge oppositely, while the smaller beads did not charge significantly; the resulting electrostatic interactions caused the string to fold. The physical system offers a tool for polymer scientists to test theories related to folding and can inspire the construction of other self-assembled systems that model molecular processes.

The statistical properties of the largest eigenvalue of a
random matrix are of interest in diverse fields ranging from
disordered systems to statistical data analysis and even to string theory.
In this talk I'll discuss some recent developements on the theory of extremely
rare fluctuations of the largest eigenvalue and its various
applications.