Anderson Localization, Non-linearity and Stable Genetic Diversity

In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and mutation. Mutation operates as a generalized diffusion process on genotype space. In the large time asymptotics, the replication term tends to produce a single dominant quasispecies, unless the mutation rate is too high, in which case the populations of different genotypes becomes de-localized. We introduce a more macroscopic picture of genotypic evolution wherein a random replication term in the linear model displays features analogous to Anderson localization. When coupled with non-linearities that limit the population of any given genotype, we obtain a model whose large time asymptotics display stable genotypic diversityComment: 25 pages, 8 Figure

Translocation of structured polynucleotides through nanopores

We investigate theoretically the translocation of structured RNA/DNA molecules through narrow pores which allow single but not double strands to pass. The unzipping of basepaired regions within the molecules presents significant kinetic barriers for the translocation process. We show that this circumstance may be exploited to determine the full basepairing pattern of polynucleotides, including RNA pseudoknots. The crucial requirement is that the translocation dynamics (i.e., the length of the translocated molecular segment) needs to be recorded as a function of time with a spatial resolution of a few nucleotides. This could be achieved, for instance, by applying a mechanical driving force for translocation and recording force-extension curves (FEC's) with a device such as an atomic force microscope or optical tweezers. Our analysis suggests that with this added spatial resolution, nanopores could be transformed into a powerful experimental tool to study the folding of nucleic acids.Comment: 9 pages, 5 figure

Statistical mechanics of RNA folding: importance of alphabet size

We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two kinds of bases, there are many alternate folding configurations, yielding thermodynamically stable ground-states only for a small set of structures of high designability, i.e., total number of associated sequences. In contrast, sequences made from four bases, as found in nature, or six bases have far fewer competing folding configurations, resulting in a much greater average stability of the ground state.Comment: 7 figures; uses revtex

Distribution of graph-distances in Boltzmann ensembles of RNA secondary structures

Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be separated by very long introns. Similar effects appear in the processing of RNA virus genomes. Albeit a crude measure, the distribution of spatial distances in thermodynamic equilibrium therefore provides useful information on the overall shape of the molecule can provide insights into the interplay of its functional domains. Spatial distance can be approximated by the graph-distance in RNA secondary structure. We show here that the equilibrium distribution of graph-distances between arbitrary nucleotides can be computed in polynomial time by means of dynamic programming. A naive implementation would yield recursions with a very high time complexity of O(n^11). Although we were able to reduce this to O(n^6) for many practical applications a further reduction seems difficult. We conclude, therefore, that sampling approaches, which are much easier to implement, are also theoretically favorable for most real-life applications, in particular since these primarily concern long-range interactions in very large RNA molecules.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Field theory for a reaction-diffusion model of quasispecies dynamics

RNA viruses are known to replicate with extremely high mutation rates. These rates are actually close to the so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a second-order phase transition, which has been dubbed the ``error catastrophe.'' Here we explore this phenomenon using a field theory approximation to the spatially extended Swetina-Schuster quasispecies model [J. Swetina and P. Schuster, Biophys. Chem. {\bf 16}, 329 (1982)], a single-sharp-peak landscape. In analogy with standard absorbing-state phase transitions, we develop a reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model. The field theory representation of the reaction-diffusion system is constructed. The proposed field theory belongs to the same universality class than a conserved reaction-diffusion model previously proposed [F. van Wijland {\em et al.}, Physica A {\bf 251}, 179 (1998)]. From the field theory, we obtain the full set of exponents that characterize the critical behavior at the error threshold. Our results present the error catastrophe from a new point of view and suggest that spatial degrees of freedom can modify several mean field predictions previously considered, leading to the definition of characteristic exponents that could be experimentally measurable.Comment: 13 page

Safety Profile of Upadacitinib up to 3 Years in Psoriatic Arthritis: An Integrated Analysis of Two Pivotal Phase 3 Trials

Introduction: This integrated analysis describes the safety profile of upadacitinib, an oral Janus kinase inhibitor, at 15 and 30 mg once daily for up to 3 years of exposure in patients with active psoriatic arthritis (PsA) who had a prior inadequate response or intolerance to ≥ 1 non-biologic or biologic disease-modifying antirheumatic drug. Methods: Safety data were pooled and analyzed from two randomized, placebo-controlled phase 3 trials. Both trials evaluated upadacitinib 15 mg and 30 mg once daily, and one trial also evaluated adalimumab 40 mg every other week. Treatment-emergent adverse events (TEAEs) and laboratory data were summarized for four groups: pooled placebo, pooled upadacitinib 15 mg, pooled upadacitinib 30 mg, and adalimumab. TEAEs were reported as exposure-adjusted event rates (events per 100 patient-years [E/100 PY]) up to a data cut-off of June 29, 2020. Results: A total of 2257 patients received ≥ 1 dose of upadacitinib 15 mg (N = 907) or 30 mg (N = 921) for 2504.6 PY of exposure or adalimumab (N = 429) for 549.7 PY of exposure. Upper respiratory tract infection, nasopharyngitis, and increased creatine phosphokinase (CPK) were the most common TEAEs with upadacitinib. Rates of malignancies, adjudicated major adverse cardiovascular events (MACEs) and venous thromboembolic events (VTEs), and deaths were similar across treatment groups. Rates of herpes zoster (HZ) and opportunistic infections (OI; excluding tuberculosis, HZ, and oral candidiasis) were higher with upadacitinib versus adalimumab. Serious infection, anemia, and CPK elevations were most frequent with upadacitinib 30 mg. Potentially clinically significant laboratory abnormalities were uncommon. Conclusions: Upadacitinib 15 mg and adalimumab had similar safety profiles with the exception of HZ and OIs, consistent with what was observed in rheumatoid arthritis. Rates of malignancies, MACEs, VTEs, and deaths were comparable among patients receiving upadacitinib and adalimumab. No new safety risks emerged with longer-term exposure to upadacitinib. Trial Registration Numbers: SELECT-PsA 1: NCT03104400; SELECT-PsA 2: NCT03104374

RNA secondary structure formation: a solvable model of heteropolymer folding

The statistical mechanics of heteropolymer structure formation is studied in the context of RNA secondary structures. A designed RNA sequence biased energetically towards a particular native structure (a hairpin) is used to study the transition between the native and molten phase of the RNA as a function of temperature. The transition is driven by a competition between the energy gained from the polymer's overlap with the native structure and the entropic gain of forming random contacts. A simplified Go-like model is proposed and solved exactly. The predicted critical behavior is verified via exact numerical enumeration of a large ensemble of similarly designed sequences.Comment: 4 pages including 2 figure

Statistical mechanics of RNA folding: a lattice approach

We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA consists of just one hairpin. Using exact arguments and Monte Carlo simulations we determine the phase diagram for this case. We show that the denaturation transition is first order and can either occur directly or through an intermediate molten phase.Comment: 8 pages, 9 figure

Statistical mechanics of secondary structures formed by random RNA sequences

The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical studies. First, a two-replica calculation is performed. By mapping the two-replica problem to the denaturation of a single homogeneous RNA in 6-dimensional embedding space, we show that sequence disorder is perturbatively irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten phase where many secondary structures with comparable total energy coexist. A numerical study of various models at high temperature reproduces behaviors characteristic of the molten phase. On the other hand, a scaling argument based on the extremal statistics of rare regions can be constructed to show that the low temperature phase is unstable to sequence disorder. We performed a detailed numerical study of the low temperature phase using the droplet theory as a guide, and characterized the statistics of large-scale, low-energy excitations of the secondary structures from the ground state structure. We find the excitation energy to grow very slowly (i.e., logarithmically) with the length scale of the excitation, suggesting the existence of a marginal glass phase. The transition between the low temperature glass phase and the high temperature molten phase is also characterized numerically. It is revealed by a change in the coefficient of the logarithmic excitation energy, from being disorder dominated to entropy dominated.Comment: 24 pages, 16 figure

Structural and biophysical characterization of bacillus thuringiensis insecticidal proteins Cry34Ab1 and Cry35Ab1

Bacillus thuringiensis strains are well known for the production of insecticidal proteins upon sporulation and these proteins are deposited in parasporal crystalline inclusions. The majority of these insect-specific toxins exhibit three domains in the mature toxin sequence. However, other Cry toxins are structurally and evolutionarily unrelated to this three-domain family and little is known of their three dimensional structures, limiting our understanding of their mechanisms of action and our ability to engineer the proteins to enhance their function. Among the non-three domain Cry toxins, the Cry34Ab1 and Cry35Ab1 proteins from B. thuringiensis strain PS149B1 are required to act together to produce toxicity to the western corn rootworm (WCR) Diabrotica virgifera virgifera Le Conte via a pore forming mechanism of action. Cry34Ab1 is a protein of ∼14 kDa with features of the aegerolysin family (Pfam06355) of proteins that have known membrane disrupting activity, while Cry35Ab1 is a ∼44 kDa member of the toxin_10 family (Pfam05431) that includes other insecticidal proteins such as the binary toxin BinA/BinB. The Cry34Ab1/Cry35Ab1 proteins represent an important seed trait technology having been developed as insect resistance traits in commercialized corn hybrids for control of WCR. The structures of Cry34Ab1 and Cry35Ab1 have been elucidated to 2.15 Å and 1.80 Å resolution, respectively. The solution structures of the toxins were further studied by small angle X-ray scattering and native electrospray ion mobility mass spectrometry. We present here the first published structure from the aegerolysin protein domain family and the structural comparisons of Cry34Ab1 and Cry35Ab1 with other pore forming toxins