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This thesis presents a statistical mechanical analysis of different formulations of quasispecies theory of molecular evolution. These theories, characterized by two different families of models, the Crow-Kimura and the Eigen model, constitute a microscopie description of evolution. These models are most often used for RNA viruses, where a phase transition is predicted, in agreement with experiments, between an organized or quasispecies phase, and a disordered non-selective phase when the mutation rate exceeds a critical value. The methods of statistical mechanics, in particular field-theoretic methods, are employed to obtain analytic solutions to four problems relevant to biological interest. The first chapter presents the study of evolution under a multiple-peak fitness landscape, with biological applications in the study of the proliferation of viruses or cancer under the control of drugs or the immune system. The second chapter studies the effect of incorporating different forms of horizontal gene transfer and two-parent recombination to the classical formulation of quasispecies models. As an example, we study the effect of the sign of epistasis of the fitness landscape on the advantage or disadvantage of recombination for the mean fitness. The third chapter considers the relaxation of the purine/pyrimidine assumption in the classical formulation of the models, by formulating and solving the parallel and Eigen models in the context of a four-letter alphabet. The fourth and final chapter studies finite population effects, both in the presence and in the absence of horizontal gene transfer.

Collagen, a fibrous protein, is an essential structural component of all connective tissues, including cartilage, skin, tendon, ligaments and bone. Type I collagen is an AAB heterotrimer assembled from two identical alpha1 and one alpha2 chain. Missense mutations in either the alpha1 or alpha2 chains of type I collagen, which lead to the substitution of Gly in the ubiquitous X-Y-Gly repeat by bulky amino acids lead to Osteogenesis imperfecta (OI) of varying severity. However, the majority of studies on the effects of amino acid substitutions on triple helix stability have been performed on collagen-like peptides homotrimers. We report the design, synthesis, self-assembly and characterization of a series of peptides that self-assemble to form collagen-like heterotrimers directed through electrostatic interactions. First, we utilize a series of peptides with net charge ranging from -10 to +10 to show the assembly of various AAB and ABC heterotrimers. We then analyze the ability of various charge pairs based upon naturally occurring amino acids, for instance E--R, E--K, D--R and D--K charge pairs, to stabilize a collagen triple helix. We report the synthesis of a surprisingly stable ABC heterotrimer, composed of (DOG)10, (PKG)10 and (POG) 10 chains (O = hydroxyproline), with a stability comparable to (POG) 10 homotrimer. This high stability heterotrimer is then used to develop a peptide model for OI, a hereditary disorder observed in type I collagen. We report the design of a novel peptide model that can mimic glycine mutations in either of the alpha1 or alpha2 chains of type I collagen. This design utilizes an electrostatic recognition motif in three chains that can force the interaction of any three peptides, including AAA (all same) homotrimers, AAB (two same, one different) heterotrimers and ABC (all different) heterotrimers. The component peptides can be designed in such a way that the mutations are present in none, one, two or all three chains. We successfully report collagen mutants, for the first time, with the structure relevant to the native forms of OI. Furthermore, we are able to differentiate between four triple helices that differ from each other in the frequency of glycine mutations at a particular position. Thus, the ease of preparation of heterotrimers, coupled with our ability to separate single mutations, provides us with a tool to understand mutations in natural collagens that lead to various connective tissue disorders in general and OI in particular. We also introduce another peptide model based upon the ABC heterotrimer to understand the effect of proline hydroxylation and fluorination to the stability of a collagen triple helix, in a chain dependent manner.

The electrostatic properties of lipid bilayer membranes play a significant role in many biological processes. Atomic force microscopy (AFM) is highly sensitive to membrane surface potential in electrolyte solutions. With fully characterized probe tips, AFM can perform quantitative electrostatic analysis of lipid membranes. Electrostatic interactions between Silicon nitride probes and supported zwitterionic dioleoylphosphatidylcholine (DOPC) bilayer with a variable fraction of anionic dioleoylphosphatidylserine (DOPS) were measured by AFM. Classical Gouy-Chapman theory was used to model the membrane electrostatics. The nonlinear Poisson-Boltzmann equation was numerically solved with finite element method to provide the potential distribution around the AFM tips. Theoretical tip-sample electrostatic interactions were calculated with the surface integral of both Maxwell and osmotic stress tensors on tip surface. The measured forces were interpreted with theoretical forces and the resulting surface charge densities of the membrane surfaces were in quantitative agreement with the Gouy-Chapman-Stern model of membrane charge regulation. It was demonstrated that the AFM can quantitatively detect membrane surface potential at a separation of several screening lengths, and that the AFM probe only perturbs the membrane surface potential by <2%. One important application of this technique is to estimate the dipole density of lipid membrane. Electrostatic analysis of DOPC lipid bilayers with the AFM reveals a repulsive force between the negatively charged probe tips and the zwitterionic lipid bilayers. This unexpected interaction has been analyzed quantitatively to reveal that the repulsion is due to a weak external field created by the internai membrane dipole moment. The analysis yields a dipole moment of 1.5 Debye per lipid with a dipole potential of +275 mV for supported DOPC membranes. This new ability to quantitatively measure the membrane dipole density in a noninvasive manner will be useful in identifying the biological effects of the dipole potential. Finally, heterogeneous model membranes were studied with fluid electric force microscopy (FEFM). Electrostatic mapping was demonstrated with 50 nm resolution. The capabilities of quantitative electrostatic measurement and lateral charge density mapping make AFM a unique and powerful probe of membrane electrostatics.

The lactose repressor protein (LacI), a prototypic negative transcriptional regulator in E. coli, relies on an allosteric conformational change for its function. Targeted molecular dynamics (TMD) simulation of this LacI transition predicts that residues located in/near the inducer binding pocket, especially D149 and S193, play a critical role in the early stage of this allosteric process. Single mutants at D149 and S193, characterized by a series of biochemical and biophysical experiments, present limited information about LacI allostery. In contrast, double mutants are much more informative: D149A/S193A exhibits wild-type properties, which exclude the requirement for inter-residue hydrogen bond formation in the allosteric response. However, D149C/S193C purified from cell extracts shows decreased sensitivity to inducer binding, while retaining wild-type binding affinities for both operator and inducer. By manipulating cysteine oxidation, the more reduced state of D149C/S193C responds to inducer more similarly to wild-type protein, whereas the more oxidized state displays diminished inducer sensitivity. D149C/S193C exhibits near wild-type binding parameters for operator DNA and inducer, with comparable rate constants for binding to IPTG and dissociation from operator DNA. These features of D149C/S193C indicate that the novel disulfide bond formed in this mutant impedes the allosteric transition, consistent with the role of this region predicted by TMD simulation. V150C/V192C displays wild-type binding properties, presumably due to its reduced state. Interestingly, S151C/V192C in a partially oxidized state displays wild-type DNA and IPTG binding affinities, and retains normal response to IPTG binding. These data suggest that mobility of the entire flexible loop (residues 149-156) may not be the crucial element for Lad allosteric regulation. Further, a molecular dynamics simulation method was used to probe the motions that are necessary for the conformational change in LacI. The results of this simulation indicate that the backbone of residue 149 is the feature that may play a critical role in LacI allosteric regulation. In summary, biochemical characterization and computational simulation of multiple LacI mutants provide evidence for the functional roles of specific residues (and their interaction) and shed light on LacI allostery.

Rational design of kinase inhibitors remains a challenge partly because there is no clear delineation of the molecular features that direct the pharmacological impact towards clinically relevant targets. In this thesis, we focus on a structural marker and construct a kinase classifier that enables the accurate prediction of pharmacological differences. Our indicator is a microenvironmental descriptor that quantifies the propensity for water exclusion around preformed polar pairs. The results suggest that targeting polar dehydration patterns heralds a new generation of drugs that enable a tighter control of specificity than designs aimed at promoting ligand-kinase pairwise interactions. As an application of the structural marker, we introduce a computational screening approach which provides a tool for extensive screening that uses experimentally obtained small-scale profiles as input data and makes predictions for a larger kinase set. These predictions result from a propagation of the reduced profile, exploiting a structural comparison of kinases based on a feature-similarity matrix. The comparison focuses on a molecular marker for specificity and promiscuity of kinase inhibitors. Our approach enables the computational high-throughput screening of entire libraries of compounds to search for suitable leads, mapping their inhibitory impact on a sizable sample of the human kinome. Yet another application of the structural marker is advocated by illustrating its cleaning efficacy. In this regard, we reassess the possibility to turn multi-target drugs into real clinical opportunities through judicious redesign. A general cleaning strategy, which adopts the structural marker as redesigning instruction, is proposed and exemplified by a workable approach.

Intracellular transport is a crucial process that requires the work of motor proteins to distribute necessary cargos. Many times the motors must move over long distances and against high opposing forces than those generated by single motors. To accomplish this task motors appear to act in teams, as suggested by experiments that show enhanced force production and extended travel lengths. Many motors have been characterized individually, but experiments to study their collective mechanics rely on non-specific groupings where the copy number and geometric arrangement are not explicitly known. In order to resolve the true extent to which each motor contributes enhanced transport properties, a system must be developed that precisely controls the number of motors that are studied. Within this work, a convergent self-assembly approach is presented that allows structurally-defined complexes of kinesin-1 to be created. This approach also provides synthetic control over intermotor spacing and the elasticity of the mechanical motor linkages to rigorously characterize the effects of system structure on the interactions of exactly two motors. This synthetic coupled motor system was then used to examine the extent to which motor grouping enhances the transport properties of cargos. It was determined that the average velocity of coupled kinesin proteins was statistically indistinguishable from that of the single motor, while the average run lengths of the two-motor system were slightly longer (≈ 2X), but less than estimated for a system of non-interacting motors (≈ 4X). This study concludes that, under low loads, intermotor strain in coupled kinesin proteins increases the rate of motor detachment from the microtubule and decreases the rate at which additional motors rebind. The presence of negative interference in these complexes implies that groupings of kinesins preferentially travel in a single motor-attachment state, and that only a subset of cargo-bound motors are used during transport.

To minimize copper (Cu) toxicity, organisms have evolved Cu transport pathways involving soluble metallochaperones that bind, transport, and deliver Cu+ to specific partner proteins, such as Cu-ATPases. The human Cu chaperone, Atox1, delivers Cu to the metal-binding domains of Menkes (MNK) and Wilson (WND) disease proteins that are Cu-ATPases in the Golgi network that transfer Cu to cuproenzymes (e.g., ceruloplasmin) that traverse the Golgi lumen. The metal binding motif, MetX1CysXXCys, and the ferredoxin-like fold appear conserved in both cytoplasmic Cu chaperones and the cytoplasmic metal-binding domains of the target Cu-ATPases from different organisms. The work reported here provides a basic understanding of in vitro holo- and apo-protein stability, Cu-dissociation mechanisms, and donor-acceptor interactions of key copper transport chaperones. Studies were conducted on purified protein variants using circular dichroism, fluorescence, and absorbance methods in equilibrium and time-resolved modes. We developed a kinetic assay to determine the Cu-dissociation mechanism of these proteins and a near-UV CD method for monitoring interactions between Atox1 and WND domains to complement NMR measurements and computer simulations. Despite the conservation of the overall structural fold, the chaperones Atox1 and its bacterial homolog, CopZ, and the metal-binding domains of WND, W2 and W4, have variable chemical and thermal stability in vitro. The role of residues proximal to the metal-binding site was determined using Atox1 as a prototypical Cu chaperone. Met10 is essential for structural stability of Atox1. Thr11 (position X1) seems to be conserved, not for integrity of protein structure, but for facilitating metal exchange between Atox1 and a receptor domain. The structural proximity of the charged side-chain of Lys60 neutralizes the Cu-thiolate center in Atox1. Replacement of Lys60 with an Ala or Tyr results in a higher rate and extent of loss of the metal to small molecule chelator, BCA, than those for wtAtox1. Lys60 also provides electrostatic interactions crucial for Atox1 interaction with W4. Thus, each proximal residue contributes to fine-tuning copper binding and its release mechanism to both the non-physiological Cu chelator, BCA, and the physiological acceptor of the WND protein, W4. Our new kinetic and spectral assays provide a comprehensive in vitro experimental platform for more advanced future mechanistic and kinetic studies.