Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.

Resonance Energy Transfer-Based Molecular Switch Designed Using a Systematic Design Process Based on Monte Carlo Methods and Markov Chains

A RET network consists of a network of photo-active molecules called chromophores that can participate in inter-molecular energy transfer called resonance energy transfer (RET). RET networks are used in a variety of applications including cryptographic devices, storage systems, light harvesting complexes, biological sensors, and molecular rulers. In this dissertation, we focus on creating a RET device called closed-diffusive exciton valve (C-DEV) in which the input to output transfer function is controlled by an external energy source, similar to a semiconductor transistor like the MOSFET. Due to their biocompatibility, molecular devices like the C-DEVs can be used to introduce computing power in biological, organic, and aqueous environments such as living cells. Furthermore, the underlying physics in RET devices are stochastic in nature, making them suitable for stochastic computing in which true random distribution generation is critical.

In order to determine a valid configuration of chromophores for the C-DEV, we developed a systematic process based on user-guided design space pruning techniques and built-in simulation tools. We show that our C-DEV is 15x better than C-DEVs designed using ad hoc methods that rely on limited data from prior experiments. We also show ways in which the C-DEV can be improved further and how different varieties of C-DEVs can be combined to form more complex logic circuits. Moreover, the systematic design process can be used to search for valid chromophore network configurations for a variety of RET applications.

We also describe a feasibility study for a technique used to control the orientation of chromophores attached to DNA. Being able to control the orientation can expand the design space for RET networks because it provides another parameter to tune their collective behavior. While results showed limited control over orientation, the analysis required the development of a mathematical model that can be used to determine the distribution of dipoles in a given sample of chromophore constructs. The model can be used to evaluate the feasibility of other potential orientation control techniques.

De novo design and molecular assembly of a transmembrane diporphyrin-binding protein complex.

The de novo design of membrane proteins remains difficult despite recent advances in understanding the factors that drive membrane protein folding and association. We have designed a membrane protein PRIME (PoRphyrins In MEmbrane) that positions two non-natural iron diphenylporphyrins (Fe(III)DPP's) sufficiently close to provide a multicentered pathway for transmembrane electron transfer. Computational methods previously used for the design of multiporphyrin water-soluble helical proteins were extended to this membrane target. Four helices were arranged in a D(2)-symmetrical bundle to bind two Fe(II/III) diphenylporphyrins in a bis-His geometry further stabilized by second-shell hydrogen bonds. UV-vis absorbance, CD spectroscopy, analytical ultracentrifugation, redox potentiometry, and EPR demonstrate that PRIME binds the cofactor with high affinity and specificity in the expected geometry.

Anti-AIDS agents 81. Design, synthesis, and structure-activity relationship study of betulinic acid and moronic acid derivatives as potent HIV maturation inhibitors.

In our continuing study of triterpene derivatives as potent anti-HIV agents, different C-3 conformationally restricted betulinic acid (BA, 1) derivatives were designed and synthesized in order to explore the conformational space of the C-3 pharmacophore. 3-O-Monomethylsuccinyl-betulinic acid (MSB) analogues were also designed to better understand the contribution of the C-3' dimethyl group of bevirimat (2), the first-in-class HIV maturation inhibitor, which is currently in phase IIb clinical trials. In addition, another triterpene skeleton, moronic acid (MA, 3), was also employed to study the influence of the backbone and the C-3 modification toward the anti-HIV activity of this compound class. This study enabled us to better understand the structure-activity relationships (SAR) of triterpene-derived anti-HIV agents and led to the design and synthesis of compound 12 (EC(50): 0.0006 microM), which displayed slightly better activity than 2 as a HIV-1 maturation inhibitor.

Purification, crystallization and preliminary X-ray diffraction studies of a complex between G protein-coupled receptor kinase 2 and Gbeta1gamma2.

G protein-coupled receptor kinase 2 (GRK2) phosphorylates activated G protein-coupled receptors (GPCRs), which ultimately leads to their desensitization and/or downregulation. The enzyme is recruited to the plasma membrane via the interaction of its carboxyl-terminal pleckstrin-homology (PH) domain with the beta and gamma subunits of heterotrimeric G proteins (Gbetagamma). An improved purification scheme for GRK2 has been developed, conditions under which GRK2 forms a complex with Gbeta(1)gamma(2) have been determined and the complex has been crystallized in CHAPS detergent micelles. Crystals of the GRK2-Gbetagamma complex belong to space group C2 and have unit-cell parameters a = 187.0, b = 72.1, c = 122.0 A, beta = 115.2 degrees. A complete data set has been collected to 3.2 A resolution with Cu Kalpha radiation.

Three-dimensional broadband omnidirectional acoustic ground cloak.

The control of sound propagation and reflection has always been the goal of engineers involved in the design of acoustic systems. A recent design approach based on coordinate transformations, which is applicable to many physical systems, together with the development of a new class of engineered materials called metamaterials, has opened the road to the unconstrained control of sound. However, the ideal material parameters prescribed by this methodology are complex and challenging to obtain experimentally, even using metamaterial design approaches. Not surprisingly, experimental demonstration of devices obtained using transformation acoustics is difficult, and has been implemented only in two-dimensional configurations. Here, we demonstrate the design and experimental characterization of an almost perfect three-dimensional, broadband, and, most importantly, omnidirectional acoustic device that renders a region of space three wavelengths in diameter invisible to sound.