Tractable stochastic analysis in high dimensions via robust optimization

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 201-207).Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory, in contrast to optimization, has not been developed with computational tractability as an objective when the dimension increases. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, auction design in multi-item, multi-bidder auctions, network information theory, pricing multi-dimensional financial contracts, among others. We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms and the concept of random variables as primitives of probability theory, with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem. In addition, we observe that several desired system properties such as incentive compatibility and individual rationality in auction design and correct decoding in information theory are naturally expressed in the language of robust optimization. In this way, the performance analysis questions become highly structured optimization problems (linear, semidefinite, mixed integer) for which there exist efficient, practical algorithms that are capable of solving problems in high dimensions. We demonstrate that the proposed approach achieves computationally tractable methods for (a) analyzing queueing networks (Chapter 2) (b) designing multi-item, multi-bidder auctions with budget constraints, (Chapter 3) (c) characterizing the capacity region and designing optimal coding and decoding methods in multi-sender, multi-receiver communication channels (Chapter 4).by Chaithanya Bandi.Ph.D

Dynamics of Stop-codon Recognition by Release Factor 1

Translation of an mRNA template into its corresponding protein is necessarily a highly accurate process. In all organisms, this translation is performed by the universally conserved macromolecular machine, the ribosome. However, the mechanisms through which the ribosome is able to regulate translation, and therefore ensure its fidelity, are not well understood. Often these types of mechanisms, which ensure molecular fidelity, utilize multiple, transient states over which cognate and non-cognate substrates are discriminated multiple times. However, such transient and/or rarely populated states are difficult to study by conventional, ensemble experimental techniques. In this thesis, single-molecule fluorescence resonance energy transfer (smFRET), which alleviates many of these limitations, is used in order to interrogate the dynamics of a translation factor, release factor 1 (RF1), and how they are organized to ensure accurate and efficient recognition of stop-codons during the termination stage of translation. In order to observe the dynamics of the RF1 binding and codon discrimination processes with smFRET, a relatively high concentration of fluorophore-labeled RF1 must be used in order to observe significant binding to sense-codons; however, such high concentrations are not accessible with traditional smFRET total internal fluorescence microscopy. Therefore, in Chapter 2 a novel approach to breaking this concentration barrier is presented, in which robustly-passivated gold-based nanoaperture arrays are developed to limit the excitation volume used in smFRET measurements of RF1. Unfortunately, as in the case of RF1 binding to sense-codon programmed ribosomes, many of the ribosomal dynamics that are in principal observable using smFRET are too fast to observe using current wide-field detectors. Therefore, Chapter 3 investigates the precision and accuracy with which transient conformational dynamics can be quantified using single-molecule techniques such as smFRET. As a case study, these approaches were used to analyze the dynamics of the GS1-GS2 equilibrium of the pretranslocation (PRE) ribosome--a situation where transient intermediate states that can be observed using single-particle cryo-electron microscopy are not seen using smFRET. In Chapter 4, a novel computational method is developed to address such temporally-limited single-molecule data, and in doing so, it is used to analyze the structural contributions of tRNA to ribosomal transition state energy barriers using temperature-dependent smFRET with temporal super-resolution. The temperature-dependence of reaction rate constants is governed by the underlying thermodynamic landscape of the molecular system. To investigate the energy landscape over which the PRE ribosome operates, temperature-dependent smFRET experiments were performed on PRE complexes containing different tRNAs. By investigating the relative temperature-dependence of the rate constants involved in the GS1 - GS2 equilibrium as a function of tRNA identity, nascent polypeptide chain presence, and A and P site occupation, relative thermodynamic contributions of the different structural elements were quantified. Unfortunately, this investigation was complicated by fast rate constants which approach the time resolution limitations of smFRET TIRF experiments, especially with the increased temperatures used in these experiments. Additionally, it is complicated by the heterogeneity within the ensemble of ribosomes that is created when some of the enzymatically-prepared ribosomal complexes fail to undergo, or undergo additional rounds of translation. To overcome these complications, a novel computational method to achieve temporal super-resolution. This method uses Bayesian inference for the analysis of sub-temporal resolution data (BIASD). By integrating this approach with a Bayesian variational mixture model, the fast dynamics of heterogenous populations can be accurately and precisely quantified. This then allowed the contributions of the structural differences that the various tRNA make to the underlying PRE complex energy landscape to be determined. The conformational dynamics that regulate the binding affinity and codon discrimination ability of RF1 are investigated in Chapter 5. During the elongation stage of translation, class I release factors compete with aminoacyl-tRNAs to interrogate the mRNA triplet-nucleotide codon that is located in the ribosomal aminoacyl-tRNA binding (A) site. To avoid deleterious effects, class I RFs must be able to accurately discriminate stop-codons from sense-codons, only triggering the termination stage of translation and catalyzing the release of the nascent polypeptide chain from the peptidyl-tRNA located in the ribosomal peptidyl-tRNA binding (P) site upon recognition of a stop-codon. Despite its importance for ensuring the accuracy of gene expression, the high fidelity mechanism through which class I RFs discriminate sense codons remains elusive. Using smFRET, the kinetics with which a fluorophore-labeled, bacterial RF1 binds to the A site of bacterial ribosomal release complexes carrying a fluorophore-labeled peptidyl-tRNA in the P site and either a stop-codon, or a sense-codon that differs from a stop-codon by a single nucleotide (i.e., a near-stop codon) programmed in the A-site are investigated. The results of these experiments, as well as analogous experiments performed using RF1 mutants or antibiotic inhibitors of RF1 function, reveal that RF1 binding affinity and codon discrimination occurs via a multistep process. Taken together with molecular dynamics simulations of wildtype and mutant RF1, these data demonstrate how the conformation dynamics of the switch loop modulate RF1 binding affinity and codon discrimination--enabling the elucidation of some of the molecular details through which class I RFs ensure the integrity of translation elongation and the fidelity of translation termination

Current Topics on Risk Analysis: ICRA6 and RISK2015 Conference

Artículos presentados en la International Conference on Risk Analysis ICRA 6/RISK 2015, celebrada en Barcelona del 26 al 29 de mayo de 2015.Peer ReviewedPostprint (published version

Current Topics on Risk Analysis: ICRA6 and RISK2015 Conference

Peer ReviewedPostprint (published version