Computationally Guided Monomerization of Red Fluorescent Proteins of the Class Anthozoa

Red fluorescent proteins (RFPs) have attracted significant engineering focus because of the promise of near infrared fluorescent proteins, whose light penetrates biological tissue, and which would allow imaging inside of vertebrate animals. The RFP landscape, which numbers ~200 members, is mostly populated by engineered variants of four native RFPs, leaving the vast majority of native RFP biodiversity untouched. This is largely due to the fact that native RFPs are obligate tetramers, limiting their usefulness as fusion proteins. Monomerization has imposed critical costs on these evolved tetramers, however, as it has invariably led to loss of brightness, and often to many other adverse effects on the fluorescent properties of the derived monomeric variants. Here we have attempted to understand why monomerization has taken such a large toll on Anthozoa class RFPs, and to outline a clear strategy for their monomerization. We begin with a structural study of the far-red fluorescence of AQ143, one of the furthest red emitting RFPs. We then try to separate the problem of stable and bright fluorescence from the design of a soluble monomeric β-barrel surface by engineering a hybrid protein (DsRmCh) with an oligomeric parent that had been previously monomerized, DsRed, and a pre-stabilized monomeric core from mCherry. This allows us to use computational design to successfully design a stable, soluble, fluorescent monomer. Next we took HcRed, which is a previously unmonomerized RFP that has far-red fluorescence (λemission = 633 nm) and attempted to monomerize it making use of lessons learned from DsRmCh. We engineered two monomeric proteins by pre-stabilizing HcRed’s core, then monomerizing in stages, making use of computational design and directed evolution techniques such as error-prone mutagenesis and DNA shuffling. We call these proteins mGinger0.1 (λem = 637 nm / Φ = 0.02) and mGinger0.2 (λem = 631 nm Φ = 0.04). They are the furthest red first generation monomeric RFPs ever developed, are significantly thermostabilized, and add diversity to a small field of far-red monomeric FPs. We anticipate that the techniques we describe will be facilitate future RFP monomerization, and that further core optimization of the mGingers may allow significant improvements in brightness.

A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method

The Maxwell integral equations of transfer are applied to a series of problems involving flows of arbitrary density gases about spheres. As suggested by Lees a two sided Maxwellian-like weighting function containing a number of free parameters is utilized and a sufficient number of partial differential moment equations is used to determine these parameters. Maxwell's inverse fifth-power force law is used to simplify the evaluation of the collision integrals appearing in the moment equations. All flow quantities are then determined by integration of the weighting function which results from the solution of the differential moment system. Three problems are treated: the heat-flux from a slightly heated sphere at rest in an infinite gas; the velocity field and drag of a slowly moving sphere in an unbounded space; the velocity field and drag torque on a slowly rotating sphere. Solutions to the third problem are found to both first and second-order in surface Mach number with the secondary centrifugal fan motion being of particular interest. Singular aspects of the moment method are encountered in the last two problems and an asymptotic study of these difficulties leads to a formal criterion for a "well posed" moment system. The previously unanswered question of just how many moments must be used in a specific problem is now clarified to a great extent.

A singularly perturbed linear two-point boundary-value problem

We consider the following singularly perturbed linear two-point boundary-value problem:

Ly(x) ≡ Ω(ε)D_xy(x) - A(x,ε)y(x) = f(x,ε) 0≤x≤1 (1a)

By ≡ L(ε)y(0) + R(ε)y(1) = g(ε) ε → 0^+ (1b)

Here Ω(ε) is a diagonal matrix whose first m diagonal elements are 1 and last m elements are ε. Aside from reasonable continuity conditions placed on A, L, R, f, g, we assume the lower right mxm principle submatrix of A has no eigenvalues whose real part is zero. Under these assumptions a constructive technique is used to derive sufficient conditions for the existence of a unique solution of (1). These sufficient conditions are used to define when (1) is a regular problem. It is then shown that as ε → 0^+ the solution of a regular problem exists and converges on every closed subinterval of (0,1) to a solution of the reduced problem. The reduced problem consists of the differential equation obtained by formally setting ε equal to zero in (1a) and initial conditions obtained from the boundary conditions (1b). Several examples of regular problems are also considered.

A similar technique is used to derive the properties of the solution of a particular difference scheme used to approximate (1). Under restrictions on the boundary conditions (1b) it is shown that for the stepsize much larger than ε the solution of the difference scheme, when applied to a regular problem, accurately represents the solution of the reduced problem.

Furthermore, the existence of a similarity transformation which block diagonalizes a matrix is presented as well as exponential bounds on certain fundamental solution matrices associated with the problem (1).

Edge function method applied to thin plates resting on Winkler foundation

The Edge Function method formerly developed by Quinlan⁽²⁵⁾ is applied to solve the problem of thin elastic plates resting on spring supported foundations subjected to lateral loads the method can be applied to plates of any convex polygonal shapes, however, since most plates are rectangular in shape, this specific class is investigated in this thesis. The method discussed can also be applied easily to other kinds of foundation models (e.g. springs connected to each other by a membrane) as long as the resulting differential equation is linear. In chapter VII, solution of a specific problem is compared with a known solution from literature. In chapter VIII, further comparisons are given. The problems of concentrated load on an edge and later on a corner of a plate as long as they are far away from other boundaries are also given in the chapter and generalized to other loading intensities and/or plates springs constants for Poisson's ratio equal to 0.2

Formal methods for control synthesis in partially observed environments : application to autonomous robotic manipulation

Modern robots are increasingly expected to function in uncertain and dynamically challenging environments, often in proximity with humans. In addition, wide scale adoption of robots requires on-the-fly adaptability of software for diverse application. These requirements strongly suggest the need to adopt formal representations of high level goals and safety specifications, especially as temporal logic formulas. This approach allows for the use of formal verification techniques for controller synthesis that can give guarantees for safety and performance. Robots operating in unstructured environments also face limited sensing capability. Correctly inferring a robot's progress toward high level goal can be challenging.

This thesis develops new algorithms for synthesizing discrete controllers in partially known environments under specifications represented as linear temporal logic (LTL) formulas. It is inspired by recent developments in finite abstraction techniques for hybrid systems and motion planning problems. The robot and its environment is assumed to have a finite abstraction as a Partially Observable Markov Decision Process (POMDP), which is a powerful model class capable of representing a wide variety of problems. However, synthesizing controllers that satisfy LTL goals over POMDPs is a challenging problem which has received only limited attention.

This thesis proposes tractable, approximate algorithms for the control synthesis problem using Finite State Controllers (FSCs). The use of FSCs to control finite POMDPs allows for the closed system to be analyzed as finite global Markov chain. The thesis explicitly shows how transient and steady state behavior of the global Markov chains can be related to two different criteria with respect to satisfaction of LTL formulas. First, the maximization of the probability of LTL satisfaction is related to an optimization problem over a parametrization of the FSC. Analytic computation of gradients are derived which allows the use of first order optimization techniques.

The second criterion encourages rapid and frequent visits to a restricted set of states over infinite executions. It is formulated as a constrained optimization problem with a discounted long term reward objective by the novel utilization of a fundamental equation for Markov chains - the Poisson equation. A new constrained policy iteration technique is proposed to solve the resulting dynamic program, which also provides a way to escape local maxima.

The algorithms proposed in the thesis are applied to the task planning and execution challenges faced during the DARPA Autonomous Robotic Manipulation - Software challenge.

Structure Prediction of G-Protein Coupled Receptors

G-protein coupled receptors (GPCRs) form a large family of proteins and are very important drug targets. They are membrane proteins, which makes computational prediction of their structure challenging. Homology modeling is further complicated by low sequence similarly of the GPCR superfamily.

In this dissertation, we analyze the conserved inter-helical contacts of recently solved crystal structures, and we develop a unified sequence-structural alignment of the GPCR superfamily. We use this method to align 817 human GPCRs, 399 of which are nonolfactory. This alignment can be used to generate high quality homology models for the 817 GPCRs.

To refine the provided GPCR homology models we developed the Trihelix sampling method. We use a multi-scale approach to simplify the problem by treating the transmembrane helices as rigid bodies. In contrast to Monte Carlo structure prediction methods, the Trihelix method does a complete local sampling using discretized coordinates for the transmembrane helices. We validate the method on existing structures and apply it to predict the structure of the lactate receptor, HCAR1. For this receptor, we also build extracellular loops by taking into account constraints from three disulfide bonds. Docking of lactate and 3,5-dihydroxybenzoic acid shows likely involvement of three Arg residues on different transmembrane helices in binding a single ligand molecule.

Protein structure prediction relies on accurate force fields. We next present an effort to improve the quality of charge assignment for large atomic models. In particular, we introduce the formalism of the polarizable charge equilibration scheme (PQEQ) and we describe its implementation in the molecular simulation package Lammps. PQEQ allows fast on the fly charge assignment even for reactive force fields.