On the evolution of codon usage bias

The genetic code is redundant, with most amino acids coded by multiple codons. In many organisms, codon usage is biased towards particular codons. A variety of adaptive and non-adaptive explanations have been proposed to explain these patterns of codon usage bias. Using mechanistic models of protein translation and population genetics, I explore the relative importance of various evolutionary forces in shaping these patterns. This work challenges one of the fundamental assumptions made in over 30 years of research: codons with higher tRNA abundances leads to lower error rates. I show that observed patterns of codon usage are inconsistent with selection for translation accuracy. I also show that almost all the variation in patterns of codon usage in S. cerevisiae can be explained by a model taking into account the effects of mutational biases and selection for efficient ribosome usage. In addition, by sampling suboptimal mRNA secondary structures at various temperatures, I show that melting of ribosomal binding sites in a special class of mRNAs known as RNA thermometers is a more general phenomenon

alpha -Lactalbumin (LA) Stimulates Milk beta-1,4-Galactosyltransferase I (beta 4Gal-T1) to Transfer Glucose from UDP-glucose to N-Acetylglucosamine: CRYSTAL STRUCTURE OF beta 4Gal-T1·LA COMPLEX WITH UDP-Glc*

beta-1,4-Galactosyltransferase 1 (Gal-T1) transfers galactose (Gal) from UDP-Gal to N-acetylglucosamine (GlcNAc), which constitutes its normal galactosyltransferase (Gal-T) activity. In the presence of alpha -lactalbumin (LA), it transfers Gal to Glc, which is its lactose synthase (LS) activity. It also transfers glucose (Glc) from UDP-Glc to GlcNAc, constituting the glucosyltransferase (Glc-T) activity, albeit at an efficiency of only 0.3-0.4% of Gal-T activity. In the present study, we show that LA increases this activity almost 30-fold. It also enhances the Glc-T activity toward various N-acyl substituted glucosamine acceptors. Steady state kinetic studies of Glc-T reaction show that the Km for the donor and acceptor substrates are high in the absence of LA. In the presence of LA, the Km for the acceptor substrate is reduced 30-fold, whereas for UDP-Glc it is reduced only 5-fold. In order to understand this property, we have determined the crystal structures of the Gal-T1·LA complex with UDP-Glc·Mn2+ and with N-butanoyl-glucosamine (N-butanoyl-GlcN), a preferred sugar acceptor in the Glc-T activity. The crystal structures reveal that although the binding of UDP-Glc is quite similar to UDP-Gal, there are few significant differences observed in the hydrogen bonding interactions between UDP-Glc and Gal-T1. Based on the present kinetic and crystal structural studies, a possible explanation for the role of LA in the Glc-T activity has been proposed

Historical contingency and entrenchment in protein evolution under purifying selection

The fitness contribution of an allele at one genetic site may depend on alleles at other sites, a phenomenon known as epistasis. Epistasis can profoundly influence the process of evolution in populations under selection, and can shape the course of protein evolution across divergent species. Whereas epistasis between adaptive substitutions has been the subject of extensive study, relatively little is known about epistasis under purifying selection. Here we use mechanistic models of thermodynamic stability in a ligand-binding protein to explore the structure of epistatic interactions between substitutions that fix in protein sequences under purifying selection. We find that the selection coefficients of mutations that are nearly-neutral when they fix are highly contingent on the presence of preceding mutations. Conversely, mutations that are nearly-neutral when they fix are subsequently entrenched due to epistasis with later substitutions. Our evolutionary model includes insertions and deletions, as well as point mutations, and so it allows us to quantify epistasis within each of these classes of mutations, and also to study the evolution of protein length. We find that protein length remains largely constant over time, because indels are more deleterious than point mutations. Our results imply that, even under purifying selection, protein sequence evolution is highly contingent on history and so it cannot be predicted by the phenotypic effects of mutations assayed in the wild-type sequence.Comment: 42 pages, 13 figure

Analysis of employee stock options and guaranteed withdrawal benefits for life

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 215-224).In this thesis we study three problems related to financial modeling. First, we study the problem of pricing Employee Stock Options (ESOs) from the point of view of the issuing company. Since an employee cannot trade or eectively hedge ESOs, she exercises them to maximize a subjective criterion of value. Modeling this exercise behavior is key to pricing ESOs. We argue that ESO exercises should not be modeled on a one by one basis, as is commonly done, but at a portfolio level because exercises related to different ESOs that an employee holds would be coupled. Using utility based models we also show that such coupled exercise behavior leads to lower average ESO costs for the commonly used utility functions such as power and exponential utilities. Unfortunately, utility based models do not lead to tractable solutions for finding costs associated with ESOs. We propose a new risk management based approach to model exercise behavior based on mean-variance portfolio maximization. The resulting exercise behavior is both intuitive and leads to a computationally tractable model for finding ESO exercises and pricing ESOs as a portfolio. We also study a special variant of this risk-management based exercise model, which leads to a decoupling of the ESO exercises and then obtain analytical bounds on the implied cost of an ESO for the employer in this case. Next, we study Guaranteed Withdrawal Benefits (GWB) for life, a recent and popular product that many insurance companies have offered for retirement planning. The GWB feature promises to the investor increasing withdrawals over her lifetime and is an exotic option that bears financial and mortality related risks for the insurance company.(cont.) The GWB feature promises to the investor increasing withdrawals over her lifetime and is an exotic option that bears financial and mortality related risks for the insurance company. We first analyze a continuous time version of this product in a Black Scholes economy with simplifying assumptions on population mortality and obtain an analytical solution for the product value. This simple analysis reveals the high sensitivity the product bears to several risk factors. We then further investigate the pricing of GWB in a more realistic setting using different asset pricing models, including those that allow the interest rates and the volatility of returns to be stochastic. Our analysis reveals that 1) GWB has insufficient price discrimination and is susceptible to adverse selection and 2) valuations can vary substantially depending on which class of models is used for accounting. We believe that the ambiguity in value and the presence of significant risks, which can be challenging to hedge, should create concerns to the GWB underwriters, their clients as well as the regulators. Finally, many problems in finance are Sequential Decision Problems (SDPs) under uncertainty. We nd that SDP formulations using commonly used financial metrics or acceptability criteria can lead to dynamically inconsistent strategies. We study the link between objective functions used in SDPs, dynamic consistency and dynamic programming. We then propose ways to create dynamically consistent formulations.by Premal Shah.Ph.D

No-arbitrage bounds on American Put Options with a single maturity

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2006.Includes bibliographical references (p. 63-64).We consider in this thesis the problem of pricing American Put Options in a model-free framework where we do not make any assumptions about the price dynamics of the underlying except those implied by the no-arbitrage conditions. Our goal is to obtain bounds on the price of an American put option with a given strike and maturity directly from the prices of other American put options with the same maturity but different strikes and the current price of the underlying. We proceed by first investigating the structural properties of the price curve of American Put Options of a fixed maturity and derive necessary and sufficient conditions that strike - price pairs of these options must satisfy in order to exclude arbitrage. Using these conditions, we can find tight bounds on the price of the option of interest by solving a very tractable Linear Programming Problem. We then apply the methods developed to real market data. We observe that the quality of bounds that we obtain compares well with the quoted bid-ask spreads in most cases.by Premal Shah.S.M

Effect of Correlated TRAN Abundances on Translation Errors and Evolution of Codon Usage Bias

Abstract Despite the fact that tRNA abundances are thought to play a major role in determining translation error rates, their distribution across the genetic code and the resulting implications have received little attention. In general, studies of codon usage bias (CUB) assume that codons with higher tRNA abundance have lower missense error rates. Using a model of protein translation based on tRNA competition and intra-ribosomal kinetics, we show that this assumption can be violated when tRNA abundances are positively correlated across the genetic code. Examining the distribution of tRNA abundances across 73 bacterial genomes from 20 different genera, we find a consistent positive correlation between tRNA abundances across the genetic code. This work challenges one of the fundamental assumptions made in over 30 years of research on CUB that codons with higher tRNA abundances have lower missense error rates and that missense errors are the primary selective force responsible for CUB. Author Summary Codon usage bias (CUB) is a ubiquitous and important phenomenon. CUB is thought to be driven primarily due to selection against missense errors. For over 30 years, the standard model of translation errors has implicitly assumed that the relationship between translation errors and tRNA abundances are inversely related. This is based on an implicit and unstated assumption that the distribution of tRNA abundances across the genetic code are uncorrelated. Examining these abundance distributions across 73 bacterial genomes from 20 different genera, we find a consistent positive correlation between tRNA abundances across the genetic code. We further show that codons with higher tRNA abundances are not always “optimal” with respect to reducing the missense error rate and hence cannot explain the observed patterns of CUB. DOI: 10.1371/journal.pgen.100112

iteRates: An R Package for Implementing a Parametric Rate Comparison on Phylogenetic Trees

Patterns of diversification rate variation detected in phylogenetic hypotheses are frequently used to infer historical, ecological, and evolutionary processes. The parametric rate comparison (PRC) is a method for detecting rate variation in trees that models branch lengths as random variables drawn from familiar statistical distributions. iteRates is a library of functions for the R statistical computing environment for implementing PRC on phylogenetic trees. Here, we describe some of the functions in iteRates for subtree identification, tree manipulation, applying the PRC and K-clades PRC analyses, and conducting a whole-tree randomization test

Surgically inverting an incidentally detected Meckel's diverticulum – Wrong method

AbstractINTRODUCTIONIntusussception leading to intestinal obstruction is a known complication of Meckel's diverticulum. Inverting of Meckel's acts as a lead point for intussusception. Causes of inversion are many but surgical inversion leading to intusussception is extremely rare.PRESENTATION OF CASEWe hereby report a case of a 14 year adolescent boy operated previously for open appendicetomy presenting to us with intestinal obstruction who on exploration was found to have an surgically inverted Meckel's diverticulum acting as a lead point for ileo-colic intusussception.DISCUSSIONTo the best of our knowledge, surgically inverting any Meckel's diverticulum is never a treatment option even when the diverticulum is incidentally detected. Diverticulectomy or segmental resection is the procedure of choice for Meckel's diverticulum.CONCLUSIONMeckel's divereticulum should never be inverted surgically. Not only it is a wrong method but also increases the risk of complications