Circular Permutation Research Articles

Repositioning the Sm-Binding Site in Saccharomyces cerevisiae Telomerase RNA Reveals RNP Organizational Flexibility and Sm-Directed 3'-End Formation.

Telomerase RNA contains a template for synthesizing telomeric DNA and has been proposed to act as a flexible scaffold for holoenzyme protein subunits in the RNP. In Saccharomyces cerevisiae, the telomerase RNA, TLC1, is bound by the Sm7 protein complex, which is required for stabilization of the predominant, non-polyadenylated (poly(A)–) TLC1 isoform. However, it remains unclear (1) whether Sm7 retains this function when its binding site is repositioned within TLC1, as has been shown for other TLC1-binding telomerase subunits, and (2) how Sm7 stabilizes poly(A)– TLC1. Here, we first show that Sm7 can stabilize poly(A)– TLC1 even when its binding site is repositioned via circular permutation to several different positions within TLC1, further supporting the conclusion that the telomerase holoenzyme is organizationally flexible. Next, we show that when an Sm site is inserted 5′ of its native position and the native site is mutated, Sm7 stabilizes shorter forms of poly(A)– TLC1 in a manner corresponding to how far upstream the new site was inserted, providing strong evidence that Sm7 binding to TLC1 controls where the mature poly(A)– 3′ is formed by directing a 3′-to-5′ processing mechanism. In summary, our results show that Sm7 and the 3′ end of yeast telomerase RNA comprise an organizationally flexible module within the telomerase RNP and provide insights into the mechanistic role of Sm7 in telomerase RNA biogenesis.

Improved Ternary Reversible Logic Synthesis Using Group Theoretic Approach

Quantum computation relies on exploiting quantum mechanical phenomena, and has received significant attention in recent years. Higher-dimensional quantum systems increase the density of encoded information per computing element (e.g., qutrit for three-level system), resulting in less resource overhead. For instance, 63% reduction in the number of qutrits is possible for ternary quantum systems as compared to the corresponding binary systems. The proposed work exploits this fact to synthesize ternary reversible circuits employing a cycle-based technique. The method starts from the ternary reversible specification of a given function in the form of a permutation. The permutation cycles are factored into simpler three-cycles and two-cycles, which are then mapped to ternary reversible gates. Different gate libraries are used to synthesize three-cycles and two-cycles, respectively. A gate decomposition approach is also proposed to synthesize a quantum gate netlist in terms of elementary ternary quantum gates, viz. Muthukrishnan–Stroud gate and shift gate. Synthesis results on benchmark functions indicate that the proposed method results in 27% and 6% improvements in quantum cost and gate count, respectively, over existing works in the literature.

The Effect of Chain Connectivity on the Thermodynamic, Kinetic and Mechanical Properties of Azurin

Azurin, a blue-copper protein, is responsible for electron transfer in Pseudomonas aeruginosa. It has widely been studied for its stability, electronic and electron transport properties, with potential applications in biomaterials-based devices. The amino acid chain connectivity is of fundamental importance in modulating the protein stability and folding. Hence, here we studied the thermodynamic, kinetic and mechanical properties of a circular permutant of apo-azurin (Azu-CPN42), with its N-terminus at Asn42, and compared them with those of the wild-type apo-azurin (WT-Azu). While the spectroscopic and copper-binding properties of Azu-CPN42 are unaltered, we observe changes in protein stability. Equilibrium unfolding studies using GdHCl suggest a drop of ∼0.6M in Cm and ∼13 kJ/mol in free energy of unfolding for Azu-CPN42 compared to that of WT-Azu. Kinetic studies reveal increase in the spontaneous unfolding rate by two-orders of magnitude, while the spontaneous folding rate being similar. Mechanical properties probed using single-molecule atomic force microscope suggest parallel unfolding pathways via 2- and 3-states, similar to that of WT-Azu reported previously. Interestingly, the intermediate stability is lower than that of the native state of Azu-CPN42 by ∼10pN, in accord with that of WT-Azu. As anticipated, the mechanical unfolding pathways of Azu-CPN42 and WT-Azu are different, as the two proteins are pulled along different N-C termini. This resulted in different mechanical intermediates, with a broad distribution of unfolding contour lengths (∼3-25 nm) for Azu-CPN42 while those of WT-Azu are centered at 7.5 ± 1.5 nm. This huge diversity may arise due to mechanical unraveling from both C- and N- termini as opposed to only C-terminal unraveling observed in WT-Azu. Our study reveals a decreased thermodynamic and kinetic stability and altered mechanical unfolding pathway of azurin upon changing its chain connectivity through circular permutation.

Using Circular Permutation to Probe the Role of Chain Connectivity in the Co-Translational Folding Process of Halotag

Using Circular Permutation to Probe the Role of Chain Connectivity in the Co-Translational Folding Process of Halotag

Extended Barrel-Shifter for Versatile QC-LDPC Decoders

In this letter, we present a Barrel-Shifter of size n extended by an additional layer that can handle any circular permutation on a vector of size m, m ≤ n, thanks to a specific initial positioning of the data. The construction of the so-called Extended Barrel-Shifter is motivated by the hardware decoder constraint related to the Low-Density Parity-Check (LDPC) code recently adopted for the 5G mobile standard. The proposed algorithm requires 42% less multiplexers than the best state-of-the-art solution for n = 384 of the 5G LDPC standard. This proposal is also able to process several inputs in parallel without extra hardware cost.

Globally simple Heffter arrays [formula omitted] when [formula omitted

Square Heffter arrays are n×n arrays such that each row and each column contains k filled cells, each row and column sum is divisible by 2nk+1 and either x or −x appears in the array for each integer 1⩽x⩽nk. Archdeacon noted that a Heffter array, satisfying two additional conditions, yields a face 2-colourable embedding of the complete graph K2nk+1 on an orientable surface, where for each colour, the faces give a k-cycle system. Moreover, a cyclic permutation on the vertices acts as an automorphism of the embedding. These necessary conditions pertain to cyclic orderings of the entries in each row and each column of the Heffter array and are: (1) for each row and each column the sequential partial sums determined by the cyclic ordering must be distinct modulo 2nk+1; (2) the composition of the cyclic orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. We construct Heffter arrays that satisfy condition (1) whenever (a) k≡0(mod4); or (b) n≡1(mod4) and k≡3(mod4); or (c) n≡0(mod4), k≡3(mod4) and n≫k. As corollaries to the above we obtain pairs of orthogonal k-cycle decompositions of K2nk+1.

On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size

We develop a method to construct all the indecomposable involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and cyclic permutation group. Moreover, we give a complete classification of the indecomposable ones having abelian permutation group and cardinality pq (where p and q are prime numbers not necessarily distinct).

Analyzing Controllability of Bilinear Systems on Symmetric Groups: Mapping Lie Brackets to Permutations

Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the design of optimal control laws, stabilization of unstable systems, and minimal realization of input-output relations. Tools from Lie theory have been adopted to establish controllability conditions for bilinear systems, and the most notable development was the Lie algebra rank condition (LARC). However, the application of the LARC may be computationally expensive for high-dimensional systems. In this paper, we present an alternative and effective algebraic approach to investigate controllability of bilinear systems. The central idea is to map Lie bracket operations of the vector fields governing the system dynamics to permutation multiplications on a symmetric group, so that controllability and controllable submanifolds can be characterized by permutation cycles. The method is further applicable to characterize controllability of systems defined on undirected graphs, such as multi-agent systems with controlled couplings between agents and Markov chains with tunable transition rates between states, which in turn reveals a graph representation of controllability through the graph connectivity.

Feller coupling of cycles of permutations and Poisson spacings in inhomogeneous Bernoulli trials

Feller (1945) provided a coupling between the counts of cycles of various sizes in a uniform random permutation of $[n]$ and the spacings between successes in a sequence of $n$ independent Bernoulli trials with success probability $1/n$ at the $n$th trial. Arratia, Barbour and Tavaré (1992) extended Feller’s coupling, to associate cycles of random permutations governed by the Ewens $(\theta )$ distribution with spacings derived from independent Bernoulli trials with success probability $\theta /(n-1+\theta )$ at the $n$th trial, and to conclude that in an infinite sequence of such trials, the numbers of spacings of length $\ell $ are independent Poisson variables with means $\theta /\ell $. Ignatov (1978) first discovered this remarkable result in the uniform case $\theta = 1$, by constructing Bernoulli $(1/n)$ trials as the indicators of record values in a sequence of i.i.d. uniform $[0,1]$ variables. In the present article, the Poisson property of inhomogeneous Bernoulli spacings is explained by a variation of Ignatov’s approach for a general $\theta >0$. Moreover, our approach naturally provides random permutations of infinite sets whose cycle counts are exactly given by independent Poisson random variables.

Constructions of Polynomial Codes Based on Circular Permutation Over Finite Fields

As a kind of very important error-correcting codes, polynomial codes have the advantages of good performance and simple structure. Generalized R-S codes over F q as polynomial codes have the advantages described above, but their lengths n are at most q. In order to increase the length of the codes, in this paper, we apply a method similar to the construction of the generalized R-S codes over F q and develop Ling and Xing's idea to construct new q-ary linear codes. First, based on the idea of constructing polynomials codes over F q , we construct a class of polynomial functions by using the circular permutation defined over F q , and a new type of linear codes is constructed from the properties of these functions and Mobius functions. Then, we give the value of the length n, the dimension k and the lower bound of the minimum distance d of the new linear codes. It turns out that some codes from this construction have good parameters based on Brouwer's table.

Cyclic permutations in determining crossing numbers

Cyclic permutations in determining crossing numbers

Cryptanalyzing an Image Cryptosystem Based on Circular Inter-Intra Pixels Bit-Level Permutation

Recently, a new image encryption algorithm based on chaos has been proposed [Circular inter-intra pixels bit-level permutation and chaos-based image encryption, Information Sciences, 355-356: 314-327, 2016]. In this paper, this image encryption algorithm was crypt-analyzed in detail. Some defects of it, such as its row-based scrambling being invalid for the special images and the lacking of diffusion operations in its processes, were pointed out. Meanwhile, two crack methods were presented in this paper. They are using only a pair of chosen plain-cipher images or a pair of known plain-cipher images to crack the image encryption algorithm. That is enough to demonstrate the image cryptosystem using this image encryption algorithm is insecure.

Determining crossing numbers of the join products of two specific graphs of order six with the discrete graph

The main aim of the paper is to give the crossing number of the join product G* + Dn for the connected graph G* of order six consisting of P4 + D1 and of one leaf incident with some inner vertex of the path P4 on four vertices, and where Dn consists of n isolated vertices. In the proofs, it will be extend the idea of the minimum numbers of crossings between two different subgraphs from the set of subgraphs which do not cross the edges of the graph G* onto the set of subgraphs by which the edges of G* are crossed exactly once. Due to the mentioned algebraic topological approach, we are able to extend known results concerning crossing numbers for join products of new graphs. The proofs are done with the help of software that generates all cyclic permutations for a given number k, and creates a new graph COG for calculating the distances between all (k-1)! vertices of the graph. Finally, by adding one edge to the graph G*, we are able to obtain the crossing number of the join product of one other graph with the discrete graph Dn.

Avoiding conjugacy classes on the 5-letter alphabet

We construct an infinite word w over the 5-letter alphabet such that for every factor f of w of length at least two, there exists a cyclic permutation of f that is not a factor of w. In other words, w does not contain a non-trivial conjugacy class. This proves the conjecture in Gamard et al. [Theoret. Comput. Sci. 726 (2018) 1–4].

Метод тиражирования точных решений уравнений Эйлера для несжимаемых течений Бельтрами

Течениями Бельтрами или винтовыми течениями в статье называются течения, в которых векторы завихренности и скорости коллинеарны, а коэффициент пропорциональности между этими векторами отличен от нуля и одинаков во всех точках течения. Предлагается метод, позволяющий с использованием известных винтовых решений получать новые винтовые решения уравнений Эйлера для несжимаемой жидкости. Некоторые из этих новых решений не могут быть получены известными методами тиражирования решений путем сдвига и поворота системы координат, симметрии, масштабирования, циклической перестановки компонент скорости и координат, векторного суммирования. Новый метод тиражирования применяется к таким параметрическим семействам точных решений, в которых коэффициент пропорциональности между скоростью и завихренностью остается неизменным при различных значениях параметра. Суть метода состоит в том, что для таких семейств производная скорости по параметру также является винтовой скоростью. Последовательное дифференцирование скорости нового решения по параметру дает бесконечную цепочку новых точных решений.

Protein tolerance to random circular permutation correlates with thermostability and local energetics of residue-residue contacts.

Adenylate kinase (AK) orthologs with a range of thermostabilities were subjected to random circular permutation, and deep mutational scanning was used to evaluate where new protein termini were nondisruptive to activity. The fraction of circularly permuted variants that retained function in each library correlated with AK thermostability. In addition, analysis of the positional tolerance to new termini, which increase local conformational flexibility, showed that bonds were either functionally sensitive to cleavage across all homologs, differentially sensitive, or uniformly tolerant. The mobile AMP-binding domain, which displays the highest calculated contact energies, presented the greatest tolerance to new termini across all AKs. In contrast, retention of function in the lid and core domains was more dependent upon AK melting temperature. These results show that family permutation profiling identifies primary structure that has been selected by evolution for dynamics that are critical to activity within an enzyme family. These findings also illustrate how deep mutational scanning can be applied to protein homologs in parallel to differentiate how topology, stability, and local energetics govern mutational tolerance.

Intrinsic Disorder-Based Design of Stable Globular Proteins.

Directed stabilization of globular proteins via substitution of a minimal number of amino acid residues is one of the most complicated experimental tasks. This work summarizes our research on the effect of amino acid substitutions on the protein stability utilizing the outputs of the analysis of intrinsic disorder predisposition of target proteins. This allowed us to formulate the basis of one of the possible approaches to the stabilization of globular proteins. The idea is quite simple. To stabilize a protein as a whole, one needs to find its "weakest spot" and stabilize it, but the question is how this weak spot can be found in a query protein. Our approach is based on the utilization of the computational tools for the per-residue evaluation of intrinsic disorder predisposition to search for the "weakest spot" of a query protein (i.e., the region(s) with the highest local predisposition for intrinsic disorder). When such "weakest spot" is found, it can be stabilized through a limited number of point mutations by introducing order-promoting residues at hot spots, thereby increasing structural stability of a protein as a whole. Using this approach, we were able to obtain stable mutant forms of several globular proteins, such as Gαo, GFP, ribosome protein L1, and circular permutant of apical domain of GroEL.

New refinements of the discrete Jensen\u2019s inequality generated by finite or infinite permutations

In this paper some new refinements of the discrete Jensen’s inequality are obtained in real vector spaces. The idea comes from some former refinements determined by cyclic permutations. We essentially generalize and extend these results by using permutations of finite sets and bijections of the set of positive numbers. We get refinements of the discrete Jensen’s inequality for infinite convex combinations in Banach spaces. Similar results are rare. Finally, some applications are given on different topics.

Structural Basis of Design and Engineering for Advanced Plant Optogenetics.

In optogenetics, light-sensitive proteins are specifically expressed in target cells and light is used to precisely control the activity of these proteins at high spatiotemporal resolution. Optogenetics initially used naturally occurring photoreceptors to control neural circuits, but has expanded to include carefully designed and engineered photoreceptors. Several optogenetic constructs are based on plant photoreceptors, but their application to plant systems has been limited. Here, we present perspectives on the development of plant optogenetics, considering different levels of design complexity. We discuss how general principles of light-driven signal transduction can be coupled with approaches for engineering protein folding to develop novel optogenetic tools. Finally, we explore how the use of computation, networks, circular permutation, and directed evolution could enrich optogenetics.

On Enumeration of Families of Genus Zero Permutations

The genus of a permutation $$\sigma $$ of length n is the nonnegative integer $$g_{\sigma }$$ given by $$n+1-2g_{\sigma }={\textsf {cyc}}(\sigma )+{\textsf {cyc}}(\sigma ^{-1}\zeta _n)$$, where $${\textsf {cyc}}(\sigma )$$ is the number of cycles of $$\sigma $$ and $$\zeta _n$$ is the cyclic permutation $$(1,2,\ldots ,n)$$. On the basis of a connection between genus zero permutations and noncrossing partitions, we enumerate the genus zero permutations with various restrictions, including Andre permutations, simsun permutations, and smooth permutations. Moreover, we present refined sign-balance results on genus zero permutations and their analogues restricted to connected permutations.