Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Functional surface chemistry of carbon-based nanostructures

The recently discovered abilities to synthesize single-walled carbon nanotubes and prepare single layer graphene have spurred interest in these sp2-bonded carbon nanostructures. In particular, studies of their potential use in electronic devices are many as silicon integrated circuits are encountering processing limitations, quantum effects, and thermal management issues due to rapid device scaling. Nanotube and graphene implementation in devices does come with significant hurdles itself. Among these issues are the ability to dope these materials and understanding what influences defects have on expected properties. Because these nanostructures are entirely all-surface, with every atom exposed to ambient, introduction of defects and doping by chemical means is expected to be an effective route for addressing these issues. Raman spectroscopy has been a proven characterization method for understanding vibrational and even electronic structure of graphene, nanotubes, and graphite, especially when combined with electrical measurements, due to a wealth of information contained in each spectrum. In Chapter 1, a discussion of the electronic structure of graphene is presented. This outlines the foundation for all sp2-bonded carbon electronic properties and is easily extended to carbon nanotubes. Motivation for why these materials are of interest is readily gained. Chapter 2 presents various synthesis/preparation methods for both nanotubes and graphene, discusses fabrication techniques for making devices, and describes characterization methods such as electrical measurements as well as static and time-resolved Raman spectroscopy. Chapter 3 outlines changes in the Raman spectra of individual metallic single-walled carbon nantoubes (SWNTs) upon sidewall covalent bond formation. It is observed that the initial degree of disorder has a strong influence on covalent sidewall functionalization which has implications on developing electronically selective covalent chemistries and assessing their selectivity in separating metallic and semiconducting SWNTs. Chapter 4 describes how optical phonon population extinction lifetime is affected by covalent functionalization and doping and includes discussions on static Raman linewidths. Increasing defect concentration is shown to decrease G-band phonon population lifetime and increase G-band linewidth. Doping only increases G-band linewidth, leaving non-equilibrium population decay rate unaffected. Phonon mediated electron scattering is especially strong in nanotubes making optical phonon decay of interest for device applications. Optical phonon decay also has implications on device thermal management. Chapter 5 treats doping of graphene showing ambient air can lead to inadvertent Fermi level shifts which exemplifies the sensitivity that sp2-bonded carbon nanostructures have to chemical doping through sidewall adsorption. Removal of this doping allows for an investigation of electron-phonon coupling dependence on temperature, also of interest for devices operating above room temperature. Finally, in Chapter 6, utilizing the information obtained in previous chapters, single carbon nanotube diodes are fabricated and characterized. Electrical performance shows these diodes are nearly ideal and photovoltaic response yields 1.4 nA and 205 mV of short circuit current and open circuit voltage from a single nanotube device. A summary and discussion of future directions in Chapter 7 concludes my work.

Microfluidic platforms for the characterization of in meso membrane protein crystallization

Membrane proteins, which reside in the membranes of cells, play a critical role in many important biological processes including cellular signaling, immune response, and material and energy transduction. Because of their key role in maintaining the environment within cells and facilitating intercellular interactions, understanding the function of these proteins is of tremendous medical and biochemical significance. Indeed, the malfunction of membrane proteins has been linked to numerous diseases including diabetes, cirrhosis of the liver, cystic fibrosis, cancer, Alzheimer's disease, hypertension, epilepsy, cataracts, tubulopathy, leukodystrophy, Leigh syndrome, anemia, sensorineural deafness, and hypertrophic cardiomyopathy.1-3 However, the structure of many of these proteins and the changes in their structure that lead to disease-related malfunctions are not well understood. Additionally, at least 60% of the pharmaceuticals currently available are thought to target membrane proteins, despite the fact that their exact mode of operation is not known.4-6 Developing a detailed understanding of the function of a protein is achieved by coupling biochemical experiments with knowledge of the structure of the protein. Currently the most common method for obtaining three-dimensional structure information is X-ray crystallography. However, no a priori methods are currently available to predict crystallization conditions for a given protein.7-14 This limitation is currently overcome by screening a large number of possible combinations of precipitants, buffer, salt, and pH conditions to identify conditions that are conducive to crystal nucleation and growth.7,9,11,15-24 Unfortunately, these screening efforts are often limited by difficulties associated with quantity and purity of available protein samples. While the two most significant bottlenecks for protein structure determination in general are the (i) obtaining sufficient quantities of high quality protein samples and (ii) growing high quality protein crystals that are suitable for X-ray structure determination,7,20,21,23,25-47 membrane proteins present additional challenges. For crystallization it is necessary to extract the membrane proteins from the cellular membrane. However, this process often leads to denaturation. In fact, membrane proteins have proven to be so difficult to crystallize that of the more than 66,000 structures deposited in the Protein Data Bank,48 less than 1% are for membrane proteins, with even fewer present at high resolution (< 2Å)4,6,49 and only a handful are human membrane proteins.49 A variety of strategies including detergent solubilization50-53 and the use of artificial membrane-like environments have been developed to circumvent this challenge.43,53-55 In recent years, the use of a lipidic mesophase as a medium for crystallizing membrane proteins has been demonstrated to increase success for a wide range of membrane proteins, including human receptor proteins.54,56-62 This in meso method for membrane protein crystallization, however, is still by no means routine due to challenges related to sample preparation at sub-microliter volumes and to crystal harvesting and X-ray data collection. This dissertation presents various aspects of the development of a microfluidic platform to enable high throughput in meso membrane protein crystallization at a level beyond the capabilities of current technologies. Microfluidic platforms for protein crystallization and other lab-on-a-chip applications have been well demonstrated.9,63-66 These integrated chips provide fine control over transport phenomena and the ability to perform high throughput analyses via highly integrated fluid networks. However, the development of microfluidic platforms for in meso protein crystallization required the development of strategies to cope with extremely viscous and non-Newtonian fluids. A theoretical treatment of highly viscous fluids in microfluidic devices is presented in Chapter 3, followed by the application of these strategies for the development of a microfluidic mixer capable of preparing a mesophase sample for in meso crystallization at a scale of less than 20 nL in Chapter 4. This approach was validated with the successful on chip in meso crystallization of the membrane protein bacteriorhodopsin. In summary, this is the first report of a microfluidic platform capable of performing in meso crystallization on-chip, representing a 1000x reduction in the scale at which mesophase trials can be prepared. Once protein crystals have formed, they are typically harvested from the droplet they were grown in and mounted for crystallographic analysis. Despite the high throughput automation present in nearly all other aspects of protein structure determination, the harvesting and mounting of crystals is still largely a manual process. Furthermore, during mounting the fragile protein crystals can potentially be damaged, both from physical and environmental shock. To circumvent these challenges an X-ray transparent microfluidic device architecture was developed to couple the benefits of scale, integration, and precise fluid control with the ability to perform in situ X-ray analysis (Chapter 5). This approach was validated successfully by crystallization and subsequent on-chip analysis of the soluble proteins lysozyme, thaumatin, and ribonuclease A and will be extended to microfluidic platforms for in meso membrane protein crystallization. The ability to perform in situ X-ray analysis was shown to provide extremely high quality diffraction data, in part as a result of not being affected by damage due to physical handling of the crystals. As part of the work described in this thesis, a variety of data collection strategies for in situ data analysis were also tested, including merging of small slices of data from a large number of crystals grown on a single chip, to allow for diffraction analysis at biologically relevant temperatures. While such strategies have been applied previously,57,59,61,67 they are potentially challenging when applied via traditional methods due to the need to grow and then mount a large number of crystals with minimal crystal-to-crystal variability. The integrated nature of microfluidic platforms easily enables the generation of a large number of reproducible crystallization trials. This, coupled with in situ analysis capabilities has the potential of being able to acquire high resolution structural data of proteins at biologically relevant conditions for which only small crystals, or crystals which are adversely affected by standard cryocooling techniques, could be obtained (Chapters 5 and 6). While the main focus of protein crystallography is to obtain three-dimensional protein structures, the results of typical experiments provide only a static picture of the protein. The use of polychromatic or Laue X-ray diffraction methods enables the collection of time resolved structural information. These experiments are very sensitive to crystal quality, however, and often suffer from severe radiation damage due to the intense polychromatic X-ray beams. Here, as before, the ability to perform in situ X-ray analysis on many small protein crystals within a microfluidic crystallization platform has the potential to overcome these challenges. An automated method for collecting a "single-shot" of data from a large number of crystals was developed in collaboration with the BioCARS team at the Advanced Photon Source at Argonne National Laboratory (Chapter 6). The work described in this thesis shows that, even more so than for traditional structure determination efforts, the ability to grow and analyze a large number of high quality crystals is critical to enable time resolved structural studies of novel proteins. In addition to enabling X-ray crystallography experiments, the development of X-ray transparent microfluidic platforms also has tremendous potential to answer other scientific questions, such as unraveling the mechanism of in meso crystallization. For instance, the lipidic mesophases utilized during in meso membrane protein crystallization can be characterized by small angle X-ray diffraction analysis. Coupling in situ analysis with microfluidic platforms capable of preparing these difficult mesophase samples at very small volumes has tremendous potential to enable the high throughput analysis of these systems on a scale that is not reasonably achievable using conventional sample preparation strategies (Chapter 7). In collaboration with the LS-CAT team at the Advanced Photon Source, an experimental station for small angle X-ray analysis coupled with the high quality visualization capabilities needed to target specific microfluidic samples on a highly integrated chip is under development. Characterizing the phase behavior of these mesophase systems and the effects of various additives present in crystallization trials is key for developing an understanding of how in meso crystallization occurs. A long term goal of these studies is to enable the rational design of in meso crystallization experiments so as to avoid or limit the need for high throughput screening efforts. In summary, this thesis describes the development of microfluidic platforms for protein crystallization with in situ analysis capabilities. Coupling the ability to perform in situ analysis with the small scale, fine control, and the high throughput nature of microfluidic platforms has tremendous potential to enable a new generation of crystallographic studies and facilitate the structure determination of important biological targets. The development of platforms for in meso membrane protein crystallization is particularly significant because they enable the preparation of highly viscous mixtures at a previously unachievable scale. Work in these areas is ongoing and has tremendous potential to improve not only current the methods of protein crystallization and crystallography, but also to enhance our knowledge of the structure and function of proteins which could have a significant scientific and medical impact on society as a whole. The microfluidic technology described in this thesis has the potential to significantly advance our understanding of the structure and function of membrane proteins, thereby aiding the elucidation of human biology, the development of pharmaceuticals with fewer side effects for a wide range of diseases. References (1) Quick, M.; Javitch, J. A. P Natl Acad Sci USA 2007, 104, 3603. (2) Trubetskoy, V. S.; Burke, T. J. Am Lab 2005, 37, 19. (3) Pecina, P.; Houstkova, H.; Hansikova, H.; Zeman, J.; Houstek, J. Physiol Res 2004, 53, S213. (4) Arinaminpathy, Y.; Khurana, E.; Engelman, D. M.; Gerstein, M. B. Drug Discovery Today 2009, 14, 1130. (5) Overington, J. P.; Al-Lazikani, B.; Hopkins, A. L. Nat Rev Drug Discov 2006, 5, 993. (6) Dauter, Z.; Lamzin, V. S.; Wilson, K. S. Current Opinion in Structural Biology 1997, 7, 681. (7) Hansen, C.; Quake, S. R. Current Opinion in Structural Biology 2003, 13, 538. (8) Govada, L.; Carpenter, L.; da Fonseca, P. C. A.; Helliwell, J. R.; Rizkallah, P.; Flashman, E.; Chayen, N. E.; Redwood, C.; Squire, J. M. J Mol Biol 2008, 378, 387. (9) Hansen, C. L.; Skordalakes, E.; Berger, J. M.; Quake, S. R. P Natl Acad Sci USA 2002, 99, 16531. (10) Leng, J.; Salmon, J.-B. Lab Chip 2009, 9, 24. (11) Zheng, B.; Gerdts, C. J.; Ismagilov, R. F. Current Opinion in Structural Biology 2005, 15, 548. (12) Lorber, B.; Delucas, L. J.; Bishop, J. B. J Cryst Growth 1991, 110, 103. (13) Talreja, S.; Perry, S. L.; Guha, S.; Bhamidi, V.; Zukoski, C. F.; Kenis, P. J. A. The Journal of Physical Chemistry B 2010, 114, 4432. (14) Chayen, N. E. Current Opinion in Structural Biology 2004, 14, 577. (15) He, G. W.; Bhamidi, V.; Tan, R. B. H.; Kenis, P. J. A.; Zukoski, C. F. Cryst Growth Des 2006, 6, 1175. (16) Zheng, B.; Tice, J. D.; Roach, L. S.; Ismagilov, R. F. Angew Chem Int Edit 2004, 43, 2508. (17) Li, L.; Mustafi, D.; Fu, Q.; Tereshko, V.; Chen, D. L. L.; Tice, J. D.; Ismagilov, R. F. P Natl Acad Sci USA 2006, 103, 19243. (18) Song, H.; Chen, D. L.; Ismagilov, R. F. Angew Chem Int Edit 2006, 45, 7336. (19) van der Woerd, M.; Ferree, D.; Pusey, M. Journal of Structural Biology 2003, 142, 180. (20) Ng, J. D.; Gavira, J. A.; Garcia-Ruiz, J. M. Journal of Structural Biology 2003, 142, 218. (21) Talreja, S.; Kenis, P. J. A.; Zukoski, C. F. Langmuir 2007, 23, 4516. (22) Hansen, C. L.; Quake, S. R.; Berger, J. M. US, 2007. (23) Newman, J.; Fazio, V. J.; Lawson, B.; Peat, T. S. Cryst Growth Des 2010, 10, 2785. (24) Newman, J.; Xu, J.; Willis, M. C. Acta Crystallographica Section D 2007, 63, 826. (25) Collingsworth, P. D.; Bray, T. L.; Christopher, G. K. J Cryst Growth 2000, 219, 283. (26) Durbin, S. D.; Feher, G. Annu Rev Phys Chem 1996, 47, 171. (27) Talreja, S.; Kim, D. Y.; Mirarefi, A. Y.; Zukoski, C. F.; Kenis, P. J. A. J Appl Crystallogr 2005, 38, 988. (28) Yoshizaki, I.; Nakamura, H.; Sato, T.; Igarashi, N.; Komatsu, H.; Yoda, S. J Cryst Growth 2002, 237, 295. (29) Anderson, M. J.; Hansen, C. L.; Quake, S. R. P Natl Acad Sci USA 2006, 103, 16746. (30) Hansen, C. L.; Sommer, M. O. A.; Quake, S. R. P Natl Acad Sci USA 2004, 101, 14431. (31) Lounaci, M.; Rigolet, P.; Abraham, C.; Le Berre, M.; Chen, Y. Microelectron Eng 2007, 84, 1758. (32) Zheng, B.; Roach, L. S.; Ismagilov, R. F. J Am Chem Soc 2003, 125, 11170. (33) Zhou, X.; Lau, L.; Lam, W. W. L.; Au, S. W. N.; Zheng, B. Anal. Chem. 2007. (34) Cherezov, V.; Caffrey, M. J Appl Crystallogr 2003, 36, 1372. (35) Qutub, Y.; Reviakine, I.; Maxwell, C.; Navarro, J.; Landau, E. M.; Vekilov, P. G. J Mol Biol 2004, 343, 1243. (36) Rummel, G.; Hardmeyer, A.; Widmer, C.; Chiu, M. L.; Nollert, P.; Locher, K. P.; Pedruzzi, I.; Landau, E. M.; Rosenbusch, J. P. Journal of Structural Biology 1998, 121, 82. (37) Gavira, J. A.; Toh, D.; Lopez-Jaramillo, J.; Garcia-Ruiz, J. M.; Ng, J. D. Acta Crystallogr D 2002, 58, 1147. (38) Stevens, R. C. Current Opinion in Structural Biology 2000, 10, 558. (39) Baker, M. Nat Methods 2010, 7, 429. (40) McPherson, A. In Current Topics in Membranes, Volume 63; Volume 63 ed.; DeLucas, L., Ed.; Academic Press: 2009, p 5. (41) Gabrielsen, M.; Gardiner, A. T.; Fromme, P.; Cogdell, R. J. In Current Topics in Membranes, Volume 63; Volume 63 ed.; DeLucas, L., Ed.; Academic Press: 2009, p 127. (42) Page, R. In Methods in Molecular Biology: Structural Proteomics - High Throughput Methods; Kobe, B., Guss, M., Huber, T., Eds.; Humana Press: Totowa, NJ, 2008; Vol. 426, p 345. (43) Caffrey, M. Ann Rev Biophys 2009, 38, 29. (44) Doerr, A. Nat Methods 2006, 3, 244. (45) Brostromer, E.; Nan, J.; Li, L.-F.; Su, X.-D. Biochemical and Biophysical Research Communications 2009, 386, 634. (46) Li, G.; Chen, Q.; Li, J.; Hu, X.; Zhao, J. Anal Chem 2010, 82, 4362. (47) Jia, Y.; Liu, X.-Y. The Journal of Physical Chemistry B 2006, 110, 6949. (48) RCSB Protein Data Bank. http://www.rcsb.org/ (July 11, 2010). (49) Membrane Proteins of Known 3D Structure. http://blanco.biomol.uci.edu/Membrane_Proteins_xtal.html (July 11, 2010). (50) Michel, H. Trends Biochem Sci 1983, 8, 56. (51) Rosenbusch, J. P. Journal of Structural Biology 1990, 104, 134. (52) Garavito, R. M.; Picot, D. Methods 1990, 1, 57. (53) Kulkarni, C. V. 2010; Vol. 12, p 237. (54) Landau, E. M.; Rosenbusch, J. P. P Natl Acad Sci USA 1996, 93, 14532. (55) Pebay-Peyroula, E.; Rummel, G.; Rosenbusch, J. P.; Landau, E. M. Science 1997, 277, 1676. (56) Cherezov, V.; Liu, W.; Derrick, J. P.; Luan, B.; Aksimentiev, A.; Katritch, V.; Caffrey, M. Proteins: Structure, Function, and Bioinformatics 2008, 71, 24. (57) Cherezov, V.; Rosenbaum, D. M.; Hanson, M. A.; Rasmussen, S. G. F.; Thian, F. S.; Kobilka, T. S.; Choi, H. J.; Kuhn, P.; Weis, W. I.; Kobilka, B. K.; Stevens, R. C. Science 2007, 318, 1258. (58) Cherezov, V.; Yamashita, E.; Liu, W.; Zhalnina, M.; Cramer, W. A.; Caffrey, M. J Mol Biol 2006, 364, 716. (59) Jaakola, V. P.; Griffith, M. T.; Hanson, M. A.; Cherezov, V.; Chien, E. Y. T.; Lane, J. R.; IJzerman, A. P.; Stevens, R. C. Science 2008, 322, 1211. (60) Rosenbaum, D. M.; Cherezov, V.; Hanson, M. A.; Rasmussen, S. G. F.; Thian, F. S.; Kobilka, T. S.; Choi, H. J.; Yao, X. J.; Weis, W. I.; Stevens, R. C.; Kobilka, B. K. Science 2007, 318, 1266. (61) Wacker, D.; Fenalti, G.; Brown, M. A.; Katritch, V.; Abagyan, R.; Cherezov, V.; Stevens, R. C. J Am Chem Soc 2010, 132, 11443. (62) Höfer, N.; Aragão, D.; Caffrey, M. Biophys J 2010, 99, L23. (63) Li, L.; Ismagilov, R. F. Ann Rev Biophys 2010. (64) Pal, R.; Yang, M.; Lin, R.; Johnson, B. N.; Srivastava, N.; Razzacki, S. Z.; Chomistek, K. J.; Heldsinger, D. C.; Haque, R. M.; Ugaz, V. M.; Thwar, P. K.; Chen, Z.; Alfano, K.; Yim, M. B.; Krishnan, M.; Fuller, A. O.; Larson, R. G.; Burke, D. T.; Burns, M. A. Lab Chip 2005, 5, 1024. (65) Jayashree, R. S.; Gancs, L.; Choban, E. R.; Primak, A.; Natarajan, D.; Markoski, L. J.; Kenis, P. J. A. J Am Chem Soc 2005, 127, 16758. (66) Wootton, R. C. R.; deMello, A. J. Chem Commun 2004, 266. (67) McPherson, A. J Appl Crystallogr 2000, 33, 397.