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Background Tandem repeat sequences are common in the genomes of many organisms and are known to cause important phenomena such as gene silencing and rapid morphological changes. Due to the presence of multiple copies of the same pattern in tandem repeats and their high variability, they contain a wealth of information about the mutations that have led to their formation. The ability to extract this information can enhance our understanding of evolutionary mechanisms. Results We present a stochastic model for the formation of tandem repeats via tandem duplication and substitution mutations. Based on the analysis of this model, we develop a method for estimating the relative mutation rates of duplications and substitutions, as well as the total number of mutations, in the history of a tandem repeat sequence. We validate our estimation method via Monte Carlo simulation and show that it outperforms the state-of-the-art algorithm for discovering the duplication history. We also apply our method to tandem repeat sequences in the human genome, where it demonstrates the different behaviors of micro- and mini-satellites and can be used to compare mutation rates across chromosomes. It is observed that chromosomes that exhibit the highest mutation activity in tandem repeat regions are the same as those thought to have the highest overall mutation rates. However, unlike previous works that rely on comparing human and chimpanzee genomes to measure mutation rates, the proposed method allows us to find chromosomes with the highest mutation activity based on a single genome, in essence by comparing (approximate) copies of the pattern in tandem repeats. Conclusion The prevalence of tandem repeats in most organisms and the efficiency of the proposed method enable studying various aspects of the formation of tandem repeats and the surrounding sequences in a wide range of settings. Availability The implementation of the estimation method is available at http://ips.lab.virginia.edu/smtr. Electronic supplementary material The online version of this article (10.1186/s12859-019-2603-1) contains supplementary material, which is available to authorized users.

We consider the problem of approximate sorting of a data stream (in one pass) with limited internal storage where the goal is not to rearrange data but to output a permutation that reflects the ordering of the elements of the data stream as closely as possible. Our main objective is to study the relationship between the quality of the sorting and the amount of available storage. To measure quality, we use permutation distortion metrics, namely the Kendall tau, Chebyshev, and weighted Kendall metrics, as well as mutual information, between the output permutation and the true ordering of data elements. We provide bounds on the performance of algorithms with limited storage and present a simple algorithm that asymptotically requires a constant factor as much storage as an optimal algorithm in terms of mutual information and average Kendall tau distortion. We also study the case in which only information about the most recent elements of the stream is available. This setting has applications to learning user preference rankings in services such as Netflix, where items are presented to the user one at a time.

A highly desired part of the synthetic biology toolbox is an embedded chemical microcontroller, capable of autonomously following a logic program specified by a set of instructions, and interacting with its cellular environment. Strategies for incorporating logic in aqueous chemistry have focused primarily on implementing components, such as logic gates, that are composed into larger circuits, with each logic gate in the circuit corresponding to one or more molecular species. With this paradigm, designing and producing new molecular species is necessary to perform larger computations. An alternative approach begins by noticing that chemical systems on the small scale are fundamentally discrete and stochastic. In particular, the exact molecular counts of each molecular species present, is an intrinsically available form of information. This might appear to be a very weak form of information, perhaps quite difficult for computations to utilize. Indeed, it has been shown that error-free Turing universal computation is impossible in this setting. Nevertheless, we show a design of a chemical computer that achieves fast and reliable Turing-universal computation using molecular counts. Our scheme uses only a small number of different molecular species to do computation of arbitrary complexity. The total probability of error of the computation can be made arbitrarily small (but not zero) by adjusting the initial molecular counts of certain species. While physical implementations would be difficult, these results demonstrate that molecular counts can be a useful form of information for small molecular systems such as those operating within cellular environments.

One of the challenging tasks in the deployment of dense wireless networks (like sensor networks) is in devising a routing scheme for node to node communication. Important consideration includes scalability, routing complexity, quality of communication paths and the load sharing of the routes. In this paper, we show that a compact and expressive abstraction of network connectivity by the medial axis enables efficient and localized routing. We propose MAP, a Medial Axis based naming and routing Protocol that does not require geographical locations, makes routing decisions locally, and achieves good load balancing. In its preprocessing phase, MAP constructs the medial axis of the sensor field, defined as the set of nodes with at least two closest boundary nodes. The medial axis of the network captures both the complex geometry and non-trivial topology of the sensor field. It can be represented succinctly by a graph whose size is in the order of the complexity of the geometric features (e.g., the number of holes). Each node is then given a name related to its position with respect to the medial axis. The routing scheme is derived through local decisions based on the names of the source and destination nodes and guarantees delivery with reasonable and natural routes. We show by both theoretical analysis and simulations that our medial axis based geometric routing scheme is scalable, produces short routes, achieves excellent load balancing, and is very robust to variations in the network model.

The paper by Roman Smolensky is a nice example of the art of studying mathematical structures that are, on the one hand, motivated by real computational problems but are, on the other hand, not obviously related.

The road leading from computer formalisms to explaining biological function will be difficult, but Roger Brent and Jehoshua Bruck suggest three hopeful paths that could take us closer to this goal.

Nematode sinusoidal movement has been used as a phenotype in many studies of C. elegans development, behavior and physiology. A thorough understanding of the ways in which genes control these aspects of biology depends, in part, on the accuracy of phenotypic analysis. While worms that move poorly are relatively easy to describe, description of hyperactive movement and movement modulation presents more of a challenge. An enhanced capability to analyze all the complexities of nematode movement will thus help our understanding of how genes control behavior. We have developed a user-friendly system to analyze nematode movement in an automated and quantitative manner. In this system nematodes are automatically recognized and a computer-controlled microscope stage ensures that the nematode is kept within the camera field of view while video images from the camera are stored on videotape. In a second step, the images from the videotapes are processed to recognize the worm and to extract its changing position and posture over time. From this information, a variety of movement parameters are calculated. These parameters include the velocity of the worm's centroid, the velocity of the worm along its track, the extent and frequency of body bending, the amplitude and wavelength of the sinusoidal movement, and the propagation of the contraction wave along the body. The length of the worm is also determined and used to normalize the amplitude and wavelength measurements. To demonstrate the utility of this system, we report here a comparison of movement parameters for a small set of mutants affecting the Go/Gq mediated signaling network that controls acetylcholine release at the neuromuscular junction. The system allows comparison of distinct genotypes that affect movement similarly (activation of Gq-alpha versus loss of Go-alpha function), as well as of different mutant alleles at a single locus (null and dominant negative alleles of the goa-1 gene, which encodes Go-alpha). We also demonstrate the use of this system for analyzing the effects of toxic agents. Concentration-response curves for the toxicants arsenite and aldicarb, both of which affect motility, were determined for wild-type and several mutant strains, identifying P-glycoprotein mutants as not significantly more sensitive to either compound, while cat-4 mutants are more sensitive to arsenite but not aldicarb. Automated analysis of nematode movement facilitates a broad spectrum of experiments. Detailed genetic analysis of multiple alleles and of distinct genes in a regulatory network is now possible. These studies will facilitate quantitative modeling of C. elegans movement, as well as a comparison of gene function. Concentration-response curves will allow rigorous analysis of toxic agents as well as of pharmacological agents. This type of system thus represents a powerful analytical tool that can be readily coupled with the molecular genetics of nematodes.