multibridge: An R Package To Evaluate Informed Hypotheses in Binomial and Multinomial Models

The multibridge R package allows a Bayesian evaluation of informed hypotheses H_r applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions theta: (a) hypotheses that postulate equality constraints (e.g., theta_1 = theta_2 = theta_3); (b) hypotheses that postulate inequality constraints (e.g., theta_1 < theta_2 < theta_3) or (theta_1 > theta_2 > theta_3); (c) hypotheses that postulate mixtures of inequality constraints and equality constraints (e.g., theta_1 < theta_2 = theta_3); and (d) hypotheses that postulate mixtures of (a)--(c) (e.g., theta_1 < theta_2 = theta_3, theta_4). Any informed hypothesis H_r may be compared against the encompassing hypothesis H_e that all category proportions vary freely, or against the null hypothesis H_0 that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples.

Self-assembly–based posttranslational protein oscillators

Recent advances in synthetic posttranslational protein circuits are substantially impacting the landscape of cellular engineering and offer several advantages compared to traditional gene circuits. However, engineering dynamic phenomena such as oscillations in protein-level circuits remains an outstanding challenge. Few examples of biological posttranslational oscillators are known, necessitating theoretical progress to determine realizable oscillators. We construct mathematical models for two posttranslational oscillators, using few components that interact only through reversible binding and phosphorylation/dephosphorylation reactions. Our designed oscillators rely on the self-assembly of two protein species into multimeric functional enzymes that respectively inhibit and enhance this self-assembly. We limit our analysis to within experimental constraints, finding (i) significant portions of the restricted parameter space yielding oscillations and (ii) that oscillation periods can be tuned by several orders of magnitude using recent advances in computational protein design. Our work paves the way for the rational design and realization of protein-based dynamic systems.

Evaluating Multinomial Order Restrictions with Bridge Sampling

Hypotheses concerning the distribution of multinomial proportions typically entail exact equality constraints that can be evaluated using standard tests. Whenever researchers formulate inequality constrained hypotheses, however, they must rely on sampling-based methods that are relatively inefficient and computationally expensive. To address this problem we developed a bridge sampling routine that allows an efficient evaluation of multinomial inequality constraints. An empirical application showcases that bridge sampling outperforms current Bayesian methods, especially when relatively little posterior mass falls in the restricted parameter space. The method is extended to mixtures between equality and inequality constrained hypotheses.

Sex, fitness decline and recombination – Muller’s ratchet vs. Ohta’s ratchet

It is generally accepted that the absence of recombination reduces the efficacy of natural selection for, or against, mutations. A special case is Muller’s Ratchet (MR) whereby non-recombining genomes experience irreversible fitness decline due to the accumulation of deleterious mutations. MR has been a main hypothesis for sexual reproduction as well as many other biological phenomena. We now ask whether the fitness decline can indeed be stopped if an asexual population turns sexual to become recombining. The possible fitness decline under recombination is referred to as Ohta’s Ratchet (OR). In comparison, MR is more effective in driving fitness reduction than OR, but only in a restricted parameter space of mutation rate, population size and selection. Outside of this space, the two ratchets are equally effective or, alternatively, neither is sufficiently powerful. Furthermore, beneficial mutations can affect the population fitness, which may diverge between the two ratchets, but only in a small parameter space. Since recombination plays a limited role in driving fitness decline, the operation of MR could be far less common in nature than believed. A companion report (see Supplement) surveying the biological phenomena attributed to MR indeed suggests the alternative explanations to be generally more compelling.

The Grimus–Neufeld Model with FlexibleSUSY at One-Loop

The Grimus–Neufeld model can explain the smallness of measured neutrino masses by extending the Standard Model with a single heavy neutrino and a second Higgs doublet, using the seesaw mechanism and radiative mass generation. The Grimus–Lavoura approximation allows us to calculate the light neutrino masses analytically. By inverting these analytic expressions, we determine the neutrino Yukawa couplings from the measured neutrino mass differences and the neutrino mixing matrix. Short-cutting the full renormalization of the model, we implement the Grimus–Neufeld model in the spectrum calculator FlexibleSUSY and check the consistency of the implementation. These checks hint that FlexibleSUSY is able to do the job of numerical renormalization in a restricted parameter space. As a summary, we also comment on further steps of the implementation and the use of FlexibleSUSY for the model.