Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws.

Characterization of porous, dexamethasone-releasing polyurethane coatings for glucose sensors.

Commercially available implantable needle-type glucose sensors for diabetes management are robust analytically but can be unreliable clinically primarily due to tissue-sensor interactions. Here, we present the physical, drug release and bioactivity characterization of tubular, porous dexamethasone (Dex)-releasing polyurethane coatings designed to attenuate local inflammation at the tissue-sensor interface. Porous polyurethane coatings were produced by the salt-leaching/gas-foaming method. Scanning electron microscopy and micro-computed tomography (micro-CT) showed controlled porosity and coating thickness. In vitro drug release from coatings monitored over 2 weeks presented an initial fast release followed by a slower release. Total release from coatings was highly dependent on initial drug loading amount. Functional in vitro testing of glucose sensors deployed with porous coatings against glucose standards demonstrated that highly porous coatings minimally affected signal strength and response rate. Bioactivity of the released drug was determined by monitoring Dex-mediated, dose-dependent apoptosis of human peripheral blood derived monocytes in culture. Acute animal studies were used to determine the appropriate Dex payload for the implanted porous coatings. Pilot short-term animal studies showed that Dex released from porous coatings implanted in rat subcutis attenuated the initial inflammatory response to sensor implantation. These results suggest that deploying sensors with the porous, Dex-releasing coatings is a promising strategy to improve glucose sensor performance.

Characterization of porous, dexamethasone-releasing polyurethane coatings for glucose sensors

© 2014 Acta Materialia Inc.Commercially available implantable needle-type glucose sensors for diabetes management are robust analytically but can be unreliable clinically primarily due to tissue-sensor interactions. Here, we present the physical, drug release and bioactivity characterization of tubular, porous dexamethasone (Dex)-releasing polyurethane coatings designed to attenuate local inflammation at the tissue-sensor interface. Porous polyurethane coatings were produced by the salt-leaching/gas-foaming method. Scanning electron microscopy and micro-computed tomography (micro-CT) showed controlled porosity and coating thickness. In vitro drug release from coatings monitored over 2 weeks presented an initial fast release followed by a slower release. Total release from coatings was highly dependent on initial drug loading amount. Functional in vitro testing of glucose sensors deployed with porous coatings against glucose standards demonstrated that highly porous coatings minimally affected signal strength and response rate. Bioactivity of the released drug was determined by monitoring Dex-mediated, dose-dependent apoptosis of human peripheral blood derived monocytes in culture. Acute animal studies were used to determine the appropriate Dex payload for the implanted porous coatings. Pilot short-term animal studies showed that Dex released from porous coatings implanted in rat subcutis attenuated the initial inflammatory response to sensor implantation. These results suggest that deploying sensors with the porous, Dex-releasing coatings is a promising strategy to improve glucose sensor performance.

Sortase as a Tool in Biotechnology and Medicine

We have harnessed two reactions catalyzed by the enzyme sortase A and applied them to generate new methods for the purification and site-selective modification of recombinant protein therapeutics.

We utilized native peptide ligation —a well-known function of sortase A— to attach a small molecule drug specifically to the carboxy-terminus of a recombinant protein. By combining this reaction with the unique phase behavior of elastin-like polypeptides, we developed a protocol that produces homogenously-labeled protein-small molecule conjugates using only centrifugation. The same reaction can be used to produce unmodified therapeutic proteins simply by substituting a single reactant. The isolated proteins or protein-small molecule conjugates do not have any exogenous purification tags, eliminating the potential influence of these tags on bioactivity. Because both unmodified and modified proteins are produced by a general process that is the same for any protein of interest and does not require any chromatography, the time, effort, and cost associated with protein purification and modification is greatly reduced.

We also developed an innovative and unique method that attaches a tunable number of drug molecules to any recombinant protein of interest in a site-specific manner. Although the ability of sortase A to carry out native peptide ligation is widely used, we demonstrated that Sortase A is also capable of attaching small molecules to proteins through an isopeptide bond at lysine side chains within a unique amino acid sequence. This reaction —isopeptide ligation— is a new site-specific conjugation method that is orthogonal to all available protein-small conjugation technologies and is the first site-specific conjugation method that attaches the payload to lysine residues. We show that isopeptide ligation can be applied broadly to peptides, proteins, and antibodies using a variety of small molecule cargoes to efficiently generate stable conjugates. We thoroughly assessed the site-selectivity of this reaction using a variety of analytical methods and showed that in many cases the reaction is site-specific for lysines in flexible, disordered regions of the substrate proteins. Finally, we showed that isopeptide ligation can be used to create clinically-relevant antibody-drug conjugates that have potent cytotoxicity towards cancerous cells

On Provable Algorithms for Determination of Continuous Protein Interdomain Motions from Residual Dipolar Couplings

Dynamics of biomolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis and signaling. However, reconstruction of biomolecular dynamics from experimental observables requires the determination of a conformational probability distribution. Unfortunately, these distributions cannot be fully constrained by the limited information from experiments, making the problem an ill-posed one in the terminology of Hadamard. The ill-posed nature of the problem comes from the fact that it has no unique solution. Multiple or even an infinite number of solutions may exist. To avoid the ill-posed nature, the problem needs to be regularized by making assumptions, which inevitably introduce biases into the result.

Here, I present two continuous probability density function approaches to solve an important inverse problem called the RDC trigonometric moment problem. By focusing on interdomain orientations we reduced the problem to determination of a distribution on the 3D rotational space from residual dipolar couplings (RDCs). We derived an analytical equation that relates alignment tensors of adjacent domains, which serves as the foundation of the two methods. In the first approach, the ill-posed nature of the problem was avoided by introducing a continuous distribution model, which enjoys a smoothness assumption. To find the optimal solution for the distribution, we also designed an efficient branch-and-bound algorithm that exploits the mathematical structure of the analytical solutions. The algorithm is guaranteed to find the distribution that best satisfies the analytical relationship. We observed good performance of the method when tested under various levels of experimental noise and when applied to two protein systems. The second approach avoids the use of any model by employing maximum entropy principles. This 'model-free' approach delivers the least biased result which presents our state of knowledge. In this approach, the solution is an exponential function of Lagrange multipliers. To determine the multipliers, a convex objective function is constructed. Consequently, the maximum entropy solution can be found easily by gradient descent methods. Both algorithms can be applied to biomolecular RDC data in general, including data from RNA and DNA molecules.