Computational research making use of molecular dynamics (MD) simulations has begun to expand the paradigm of structural biology to include dynamics as the mediator between structure and function. This work aims to expand the utility of MD simulations by developing Principal Component Analysis (PCA) techniques to extract the biologically relevant information in these increasingly complex data sets. Gramicidin is a simple protein with a very clear functional role and a long history of experimental, theoretical and computational study, making it an ideal candidate for detailed quantitative study and the development of new analysis techniques. First we quantify the convergence of our PCA results to underwrite the scope and validity of three 64 ns simulations of gA and two covalently linked analogs (SS and RR) solvated in a glycerol mono-oleate (GMO) membrane. Next we introduce a number of statistical measures for identifying regions of anharmonicity on the free energy landscape and highlight the utility of PCA in identifying functional modes of motion at both long and short wavelengths. We then introduce a simple ansatz for extracting physically meaningful modes of collective dynamics from the results of PCA, through a weighted superposition of eigenvectors. Applied to the gA, SS and RR backbone, this analysis results in a small number of collective modes which relate structural differences among the three analogs to dynamic properties with functional interpretations. Finally, we apply elements of our analysis to the GMO membrane, yielding two simple modes of motion from a large number of noisy and complex eigenvectors. Our results demonstrate that PCA can be used to isolate covariant motions on a number of different length and time scales, and highlight the need for an adequate structural and dynamical account of many more PCs than have been conventionally examined in the analysis of protein motion.

Forkhead box Class O (FOXO), one subfamily of the Forkhead box (Fox) family, which is featured by the Forkhead (FH) DNA-binding domain, includes four human transcription factors: FOXO1, FOXO3a, FOXO4, and FOXO6. The tumor suppressor FOXO3a is involved in multiple physiological and pathological processes, such as breast cancer and acute myeloid leukemia, and is related to human longevity. It plays essential role in metabolism, cell cycle arrest, DNA repair, and apoptosis. Besides the FH domain, FOXO3a contains three other regions (CR1-3), conserved within FOXO subfamily. It specifically binds a consensus Forkhead response element (FRE) DNA sequence through the FH domain, and recruits transcriptional coactivator CBP/p300 to activate gene transcription. FOXO3a functions through interacting with other proteins as well. FOXO3a binds p53 through the FH domain and the CR3 region, which are also engaged in an intramolecular interaction, and the solution structure of the former one was determined. This intramolecular interaction regulates coactivator recruitment and is disrupted by FRE DNA. A novel transactivation domain (TAD) CR2C was identified in addition to the known TAD CR3, both of which promiscuously associate with the KIX domain of CBP/p300 in equilibrium between two conformational states, the structures of which were determined by NMR spectroscopy. These two TADs of FOXO3a form additional multivalent binding to the TAZ1 and TAZ2 domains of CBP/p300, further increasing the promiscuity and complexity of the interaction. The coactivator recruitment is modulated by AMPK phosphorylation, which enhances the multivalent interaction between FOXO3a and CBP/p300, and thus the transactivation. These results indicate the significance of intrinsically disordered regions (IDRs) of FOXO3a in transcriptional activation and protein interaction, provide insight of the role of FOXO3a in gene transcription and apoptosis under various conditions, and potentially contribute to the cancer therapy.

Cytochrome c oxidase couples the reduction of dioxygen to proton pumping against an electrochemical gradient. The D-channel provides the principal uptake pathway for protons. A water chain is thought to mediate the relay of protons through the D-channel, but it is interrupted at N139 in all crystallographic structures. Here, free energy simulations are used to examine the proton uptake pathway in the wild type and in single-point mutants N139V and N139A, where reduction and pumping is compromised. A general approach for the calculation of water occupancy in protein cavities is presented and demonstrates that combining efficient sampling algorithms with long simulation times is required to achieve statistical convergence of equilibrium properties in the protein interior. The relative population of conformational and hydration states of the D-channel is characterized. Results shed light onto the role of N139 in the mechanism of proton uptake and clarify the physical basis for inactive phenotypes.

Single particle electron cryomicroscopy (cryo-EM) is a rapidly developing structural biology technique for the study of macromolecular protein complexes. Presently, cryo-EM fills an important niche by facilitating acquisition of 3-D structures of protein complexes not amenable to structure determination by other techniques. Expansion of cryo-EM beyond this niche requires continued improvement in the types of specimens that can be studied as well as the final resolutions achieved. Two studies were undertaken to address these issues. The first examined resolution limitations by quantifying the effect of beam-induced motion in images of beam-sensitive paraffin crystals. The second explored the possibility of using cryo-EM to study the interaction of small effector proteins with a large multi-protein complex, V-ATPase. The results of these studies exposed the fact that fundamental aspects of the imaging and specimen preparation processes remain poorly understood and must be addressed to facilitate future improvements in cryo-EM structure determination.

Forkhead box Class O (FOXO), one subfamily of the Forkhead box (Fox) family, which is featured by the Forkhead (FH) DNA-binding domain, includes four human transcription factors: FOXO1, FOXO3a, FOXO4, and FOXO6. The tumor suppressor FOXO3a is involved in multiple physiological and pathological processes, such as breast cancer and acute myeloid leukemia, and is related to human longevity. It plays essential role in metabolism, cell cycle arrest, DNA repair, and apoptosis. Besides the FH domain, FOXO3a contains three other regions (CR1-3), conserved within FOXO subfamily. It specifically binds a consensus Forkhead response element (FRE) DNA sequence through the FH domain, and recruits transcriptional coactivator CBP/p300 to activate gene transcription. FOXO3a functions through interacting with other proteins as well. FOXO3a binds p53 through the FH domain and the CR3 region, which are also engaged in an intramolecular interaction, and the solution structure of the former one was determined. This intramolecular interaction regulates coactivator recruitment and is disrupted by FRE DNA. A novel transactivation domain (TAD) CR2C was identified in addition to the known TAD CR3, both of which promiscuously associate with the KIX domain of CBP/p300 in equilibrium between two conformational states, the structures of which were determined by NMR spectroscopy. These two TADs of FOXO3a form additional multivalent binding to the TAZ1 and TAZ2 domains of CBP/p300, further increasing the promiscuity and complexity of the interaction. The coactivator recruitment is modulated by AMPK phosphorylation, which enhances the multivalent interaction between FOXO3a and CBP/p300, and thus the transactivation. These results indicate the significance of intrinsically disordered regions (IDRs) of FOXO3a in transcriptional activation and protein interaction, provide insight of the role of FOXO3a in gene transcription and apoptosis under various conditions, and potentially contribute to the cancer therapy.

Cytochrome c oxidase couples the reduction of dioxygen to proton pumping against an electrochemical gradient. The D-channel provides the principal uptake pathway for protons. A water chain is thought to mediate the relay of protons through the D-channel, but it is interrupted at N139 in all crystallographic structures. Here, free energy simulations are used to examine the proton uptake pathway in the wild type and in single-point mutants N139V and N139A, where reduction and pumping is compromised. A general approach for the calculation of water occupancy in protein cavities is presented and demonstrates that combining efficient sampling algorithms with long simulation times is required to achieve statistical convergence of equilibrium properties in the protein interior. The relative population of conformational and hydration states of the D-channel is characterized. Results shed light onto the role of N139 in the mechanism of proton uptake and clarify the physical basis for inactive phenotypes.

Abstract: Nonlinear multicontrast microscopy is established in this study as an important tool for understanding biological structure and function of muscle cells. Second harmonic generation, third harmonic generation and multi-photon excitation fluorescence are acquired simultaneously in order to establish the origin of nonlinear signal generation in myocytes, and investigate myocyte structure and functionality during muscle contraction. Using structural cross-correlation image analysis, an algorithm developed specifically for this research, for the first time, third harmonic generation is shown to originate from the mitochondria in myocytes. The second harmonic, which is generated from the anisotropic bands of the sarcomeres, is further shown to be dependent on the crystalline order of the sarcomeres, thereby providing a potential diagnostic tool to evaluate disorder in muscle cells. The combination of the second and third harmonic provides complementary information that can be used to further elucidate the basic principles of muscle contraction. Time-lapse nonlinear microscopic imaging showed structural and functional dynamics in the myocytes. The second harmonic contrast revealed nonsynchronized nanocontractions of sarcomeres in relaxed, non-contracting, cardiomyocytes and Drosophila muscle samples, providing insight into the asynchronous behaviour of individual sarcomeres. Furthermore, macrocontracting samples were found to exhibit a synchronization of nanocontractions, providing new evidence for how muscles contract. Dynamic image correlation analysis, another algorithm developed specifically for this investigation, is used to reveal networks of mitochondria, which show fluctuations of multi-photon excitation fluorescence and third harmonic generation signals. The intensity fluctuations in the networks reveal both slow and fast dynamics; phase shifts of the slow dynamics between different networks are observed. Fast dynamics appear only in the inner networks, suggesting functional difference between interfibrillar and subsarcolemma mitochondria. The groundwork for studying bioenergetics of mitochondria in cardiomyocytes with nonlinear multimodal microscopy is fully developed in this work. The origin of the nonlinear signals and the development of the image analysis techniques provide a solid foundation to further study of muscle contractility and bioenergetics.

Computational research making use of molecular dynamics (MD) simulations has begun to expand the paradigm of structural biology to include dynamics as the mediator between structure and function. This work aims to expand the utility of MD simulations by developing Principal Component Analysis (PCA) techniques to extract the biologically relevant information in these increasingly complex data sets. Gramicidin is a simple protein with a very clear functional role and a long history of experimental, theoretical and computational study, making it an ideal candidate for detailed quantitative study and the development of new analysis techniques. First we quantify the convergence of our PCA results to underwrite the scope and validity of three 64 ns simulations of gA and two covalently linked analogs (SS and RR) solvated in a glycerol mono-oleate (GMO) membrane. Next we introduce a number of statistical measures for identifying regions of anharmonicity on the free energy landscape and highlight the utility of PCA in identifying functional modes of motion at both long and short wavelengths. We then introduce a simple ansatz for extracting physically meaningful modes of collective dynamics from the results of PCA, through a weighted superposition of eigenvectors. Applied to the gA, SS and RR backbone, this analysis results in a small number of collective modes which relate structural differences among the three analogs to dynamic properties with functional interpretations. Finally, we apply elements of our analysis to the GMO membrane, yielding two simple modes of motion from a large number of noisy and complex eigenvectors. Our results demonstrate that PCA can be used to isolate covariant motions on a number of different length and time scales, and highlight the need for an adequate structural and dynamical account of many more PCs than have been conventionally examined in the analysis of protein motion.

Nonlinear microscopy has become an indispensable tool in the study of biological systems. It includes many nonlinear contrast mechanisms, each sensitive to different biological structures. However, interpretation of the images generated in nonlinear microscopy is a complex matter due to factors such as the structural complexity of the sample, phase relationships between the excitation beam and the detected signal and the nonlinear interactions in the focal volume of the microscope. This thesis contains a new theoretical and numerical framework that describes the focusing of an excitation beam in a nonlinear microscope, the nonlinear optical interactions with the material in the focal volume, and the resulting nonlinear optical signal in the far field. The framework is the first to include reflection and refraction of the excitation beam and nonlinear signals by an arbitrary number of interfaces in the focal volume, which is especially significant for the interpretation of third harmonic generation (THG). It also uses the chirp-z transform to speed up calculations by orders of magnitude compared to numerical integration techniques. The framework is used to investigate second harmonic generation (SHG) by collagen. Focusing effects alter polarization-dependent SHG measurements of collagen properties compared to the plane wave approximation, and this is verified experimentally. Furthermore, a technique of imaging the far field SHG radiation from collagen fibres is proposed, which can be used to extract the orientation of collagen fibres unambiguously. The framework is then applied to analyze the influence of interfaces on THG. Reflection effects at interfaces significantly affect THG, which leads to the development of a new super-resolution THG imaging technique based on backward-propagating THG. This super-resolution technique is experimentally demonstrated by imaging surface profiles with tens of nanometers resolution, which is the first time that such resolution is obtained in coherent nonlinear microscopy. Therefore, this imaging technique shows promise to become an important tool in high-resolution imaging of (biological) samples. The theoretical and numerical framework provides a foundation for future research on the origin of nonlinear microscopy signals. The new imaging techniques based on this framework have great potential in quantifying fibrillar structures and interfaces in biological samples.

Nonlinear microscopy has become an indispensable tool in the study of biological systems. It includes many nonlinear contrast mechanisms, each sensitive to different biological structures. However, interpretation of the images generated in nonlinear microscopy is a complex matter due to factors such as the structural complexity of the sample, phase relationships between the excitation beam and the detected signal and the nonlinear interactions in the focal volume of the microscope. This thesis contains a new theoretical and numerical framework that describes the focusing of an excitation beam in a nonlinear microscope, the nonlinear optical interactions with the material in the focal volume, and the resulting nonlinear optical signal in the far field. The framework is the first to include reflection and refraction of the excitation beam and nonlinear signals by an arbitrary number of interfaces in the focal volume, which is especially significant for the interpretation of third harmonic generation (THG). It also uses the chirp-z transform to speed up calculations by orders of magnitude compared to numerical integration techniques. The framework is used to investigate second harmonic generation (SHG) by collagen. Focusing effects alter polarization-dependent SHG measurements of collagen properties compared to the plane wave approximation, and this is verified experimentally. Furthermore, a technique of imaging the far field SHG radiation from collagen fibres is proposed, which can be used to extract the orientation of collagen fibres unambiguously. The framework is then applied to analyze the influence of interfaces on THG. Reflection effects at interfaces significantly affect THG, which leads to the development of a new super-resolution THG imaging technique based on backward-propagating THG. This super-resolution technique is experimentally demonstrated by imaging surface profiles with tens of nanometers resolution, which is the first time that such resolution is obtained in coherent nonlinear microscopy. Therefore, this imaging technique shows promise to become an important tool in high-resolution imaging of (biological) samples. The theoretical and numerical framework provides a foundation for future research on the origin of nonlinear microscopy signals. The new imaging techniques based on this framework have great potential in quantifying fibrillar structures and interfaces in biological samples.