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Tuesday rolls around and one or maybe both of you no longer feels up to it and you or they cancel. With this, the vicious cycle begins. A round of sexting, a promise to meet, a cancellation and repeat. All of your conversations seem to focus strictly on the here and now. What are you? Neither of you know.


LTR retrotransposons are mobile elements that are able, like retroviruses, to copy and move inside eukaryotic genomes. In the present work, we propose a branching model for studying the propagation of LTR retrotransposons in these genomes. This model allows us to take into both the positions and the degradation level of LTR retrotransposons copies. In our model, the duplication rate is also allowed to vary with the degradation level. Various functions have been implemented in order to simulate their spread and visualization tools are proposed.

Based on these simulation tools, we have developed a first method to evaluate the parameters of this propagation model.

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Our proposal has been implemented using Python software. A transposable element TE is a DNA sequence able to move from one location to another inside a genome. These sequences, discovered during the s by McClintock exist in almost all living organisms and are the source of a huge of mutations.

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They are considered as a major cause of genetic disease in human Belancio et al. DNA sequences derived from these TEs can represent a large part of a genome. TEs have two possible ways to move in a genome, according to their type Finnegan, ; Wicker et al. Two orders are identified among the retrotransposons according to the presence or absence of Long Terminal Repeat LTR sequences at their extremities.

In an assembled genome, the various sequences corresponding to TE insertions can be found using different bioinformatic approaches see Lerat et al. In this article, we focused on the important problem of inferring the history of the spreading of LTR retrotransposons. For this purpose, we modeled the evolution using a branching process where each element i.

Instances of branching processes have already been proposed in the literature, as putative models for the propagation of TEs. However, most of these studies focus on the evolution of the host population, and not on the propagation of the TEs in the host. For instance, Moody has used a branching model, where the studied variable was the of individuals owning i copies of a given TE. Sawyer et al. Kaplan et al.

When a host gives birth to its child, wild copies can mutate or be deleted, whereas mutant ones can only be removed. New copies can be additionally created.

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This of new created copies is supposed to decrease with the proportion of mutants. More recently, interesting models have been proposed that take into the location of TEs. For instance, Drakos and Wahl suggested a model of mobile promoter evolution, where the probabilities for promoters to duplicate inside or outside their region is potentially not the same.

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In the present work, the objective is to propose a new approach for the propagation of LTR retrotransposons that combines a location-dependent model with the fact that LTR retrotransposons can face degradation i. Then, we have developed a first method to evaluate the model parameters: average distance traveled by the TEs before insertion, location of the original copy, average time between two degradations mutations, recombination, etc.

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This method requires to define a distance between the of the simulations and the observed chromosome, which is based on the Hungarian method Kuhn, ; Munkres, The parameters associated to each TE are computed and a branching tree is proposed in each case. An example of branching tree is shown in Figure 1. At time 1.

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The branching tree represents only the duplications, but copies are also subject to degradations as explained in Section 2. The state of the tree i. The working principle of our estimation method is to simulate trees, in order to determine in which conditions the final states of simulated trees match well with the observed chromosome. To compare the final state of a simulated tree with the observed chromosome, a distance was build, as detailed in Section 2. The branching model is constructed as follows.

The spread starts with only one copy, called the root, at time zero in a location X 0 to be determined. Each copy can either be duplicated or undergo degradations i. The of copies increases due to duplications. When a new copy is created, it receives an index equal to the of existing copies at the time of its birth, including itself.

Each copy is also associated to its Needleman—Wunsch Needleman and Wunsch, similarity to the original state of the root. This similarity is a value between 0 and 1.

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Let us denote S i t the similarity between the original state of the root and the state of the i th copy at time t. This similarity decreases as a function of time, due to degradation effects. In other words, the time before the next duplication is longer when the copy is far from the original state of the root in terms of Needleman—Wunsch distance. Moreover, each copy is also associated to its position in the chromosome. This position is denoted by X i for the i th copy.

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This position is constant with time. Our goal is thus to estimate the parameters of this model, i. Note that the duplication speed of the non-degraded root is set to 1 and it does not need to be determined. In addition, note that the parameter L is not really informative about the mean distance traveled by the child before its insertion, due to putative relaunching processes.

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This is why we also provide the mean traveled distance in simulations, that is, the mean jump, which is denoted by J. See Part 3. As explained in Section 2. Trees are simulated according to the model defined in Section 2. The stopping criterion of these simulated trees depends on the of copies in the observed chromosome. Section 2. We can note that these parameters only affect the distribution of deterioration states. They have no direct influence on copy positions.

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Thus, the goal at this step is to minimize the differences between the distribution of states of deterioration in the simulated trees, and the states of deterioration distribution in the observed chromosome. The best of these points is selected, and a smaller grid is constructed around it. This iterative process is continued until the precision chosen by the user of the optimization method has been obtained.

This weighting by w 1 and w 2 allows us to give the same weight to positions and states of deterioration. Then, the distance between final states of two trees has been defined as the best possible adjustment between copies, using the so-called Kuhn—Munkres algorithm, also named the Hungarian method Kuhn, ; Munkres, In our case, the Hungarian method allows us to as exactly one copy of the simulated tree to each copy of the real chromosome while minimizing the sum of distances between paired copies.

Let us name D 3 this distance created by this way. Once this distance between trees has been defined, we use it to estimate X 0 and L with the same type of process as in the step. It is thus easier to estimate them. A short application programming interface is detailed thereafter. In this example, the mother of the copy located in 0.

The mother of the copy located in 0.

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Other details regarding this main function are provided thereafter. The mean jump J is not a direct output of TreeBuild, but it can be easily computed with T. The working principle of TreeBuild can be summarized as follows: it determines the next event deterioration or duplication and executes it until the stopping criterion is satisfied.

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To determine the next event means to know its nature deterioration or duplicationits time, and in which of the available copies it happens. Let j be the of available copies at time t 1. Hence, due to the first property, the time of the next event can be simulated by a single exponential law. The second property, for its part, allows us to determine the nature and the copy affected by the next event using a single uniform law. Copy positions in the chromosome are in the interval [0,1].

The distance traveled by a TE before insertion is assumed to follow an exponential law, but this latter can send the new copy outside the interval [0,1]. The solution chosen in this case is to launch again the computation of the new copy position. When TreeBuild is launched for each point of the grid of parameters, some critical situations can happen, which may induce a ificant slowdown of the program.

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Thus, TreeBuild executes an inordinate of deteriorations before reaching the desired of copies.

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The s go like this: Very few single black women — just a quarter of those surveyed — said they were looking for long-term relationships, or LTRs.


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