This exploits the fact that MNN pairs occur at the boundaries of two clusters, with short distances between paired cells meaning that the clusters are touching. (2014). Enrolling in a course lets you earn progress by passing quizzes and exams. https://doi.org/10.1101/2020.03.13.990069. In the following example the end-to-end distance of a protein and the radius of gyration of the backbone atoms are calculated: Trajectories are commonly used to characterize differentiation where branches are interpreted as multiple lineages. Nagin, DS. We demonstrate below on the Nestorowa et al. https://pdfs.semanticscholar.org/b3c6/1e703638a06b38b79302b5188fc886d21e1f.pdf, Columbia University Irving Medical Center. The MST also fails to handle more complex events such as bubbles (i.e., a bifurcation and then a merging) or cycles. https://ssrc.indiana.edu/doc/wimdocs/2013-03-29_nagin_trajectory_stata-plugin-info.pdf, Powerpoint presentation of examples of trajectory modeling for binary longitudinal data: Psychological Methods 1999;4:137-157. More complex analyses can also be performed (e.g., to identify the likely fate of each cell in the intermediate clusters) but will not be discussed here. The TSCAN algorithm uses a simple yet effective approach to trajectory reconstruction. We run through a quick-and-dirty analysis on the spliced counts, which can - by and large - be treated in the same manner as the standard exonic gene counts used in non-velocity-aware analyses. i.e., there is some significant trend with respect to pseudotime. Writing your own trajectory analysis MDAnalysis User Guide documentation Writing your own trajectory analysis We create our own analysis methods for calculating the radius of gyration of a selection of atoms. This is the idea behind principal curves (Hastie and Stuetzle 1989), the most obvious of which being that the transcriptional dynamics are the same across subpopulations. We observe upregulation of interesting genes such as Gata2, Cd9 and Apoe in this path, Other software programs that can replicate or approximate Proc Traj include R, MPlus, Stata, and Latent Gold. # Fitting a GAM on the subset of genes for speed. For a comparison of group-based trajectory models with generalized linear mixed models and latent growth curve models: Conversely, the principal curves can smooth out circuitous paths in the MST for overclustered data, Males are more likely to engage in delinquent behavior than females. The interpretation of the MST is also straightforward as it uses the same clusters as the rest of the analysis, Nagin DS, Tremblay RE. This may occasionally result in some visually unappealing plots if the original ordering of clusters in the PC space is not preserved in the \(t\)-SNE space. Figure 10.4: \(t\)-SNE plot of the Nestorowa HSC dataset, where each point is a cell and is colored according to its pseudotime value. array([12.85520891, 12.98176002, 12.82791643, 12.91550011, 12.87289194, 12.92314255, 12.76350405, 12.85890813, 12.81869193, 12.76178599]). Writing your own trajectory analysis MDAnalysis User Guide documentation Writing your own trajectory analysis We create our own analysis methods for calculating the radius of gyration of a selection of atoms. where we assume that there exists a linear relationship between expression and the pseudotime. Trait Theory in Criminology: Overview & Social Influence | What is Trait Theory? RMSD, RMSF, radius of gyration, and distance will be calculated from trajectory frames. (2018), The trajectory of early adolescents' popularity goal during the transition to middle school was examined in a diverse sample of 401 students. Joint modeling of longitudinal data in multiple behavioral change. Eval Health Prof 34(2): 181-200. In practice, it is helpful to pair the spline-based ANOVA results with a fit from a much simpler model Lets make atom selections for different types of calculations: We select atoms from terminal residues and make an empty array whose length Guo, M., E. L. Bao, M. Wagner, J. for example, slingshot could build a trajectory out of one cluster while TSCAN cannot. MDAnalysis also tracks the percentage cumulative variance in pc.cumulated_variance. Each point represents a cell that is mapped to this path and is colored by the assigned cluster. 0.59612102, 0.4654029 , 0.55655523, 0.62571376, 0.56086838. [2]: adk_open = mda.Universe(CRD, DCD2) adk_closed = mda.Universe(PSF, DCD) Currently, the proteins are not aligned to each other. Generation of multiple timepoints also requires an amenable experimental system where the initiation of the process of interest can be tightly controlled. where they collected CD8+ T cells at various time points after ovalbumin stimulation. We then apply testPseudotime() to each path involving cluster 3. these values are not usually comparable across paths. Investigators in epidemiology and other fields are often interested not only in the trajectory of variables over time, but also in how covariates may affect their shape. By default, slingshot() uses one point per cell to define the curve, which is unnecessarily precise when the number of cells is large. Figure 10.3: Minimum spanning tree of the Nestorowa clusters after introducing an outgroup. By following the API it is possible to seamlessly enhance the I/O capabilities of MDAnalysis. Applying an approximation with approx_points= reduces computational work without any major loss of precision in the pseudotime estimates. The analysis further shows that the intertwining forces of localization, nationalization, and globalization influenced the policy development throughout three stages of the trajectory. At first, the T cell subtypes were extracted from the Seurat object containing all the 17 cell types. For example, choice theory views criminal behavior as a choice, whereas trait theory believes criminality is born within the person. Figure 10.14: \(t\)-SNE plot of the Hermann spermatogenesis dataset, where each point is a cell and is colored by its velocity pseudotime. What people mean by this is that they were born into a life that has been challenging. Bergen, Volker, Marius Lange, Stefan Peidli, F. Alexander Wolf, and Fabian J. Theis. 2018. The Mammalian Spermatogenesis Single-Cell Transcriptome, from Spermatogonial Stem Cells to Spermatids. Cell Rep 25 (6): 165067. This yields an interpretable summary of the overall direction of change in the logFC field above, (2014). Two DCD trajectory les and corresponding PDB struc-ture le is needed for this example: MDM2 les (ZIP) # all paths anyway, so taking the rowMeans is not particularly controversial. Alternatively, this entire series of calculations can be conveniently performed with the quickPseudotime() wrapper. By using the MST as a scaffold for the global structure, slingshot() can accommodate branching events based on divergence in the principal curves (Figure 10.6). and we should not have used the non-significant genes to draw any conclusions. Log in or sign up to add this lesson to a Custom Course. In such cases, both position and time may be regularly or irregularly sampled. Needless to say, this lunch is not entirely free. However, there are circumstances (trajectories, if you will) that highly influence the person to keep heading toward the path of delinquency. The most common application is to fit models to gene expression against the pseudotime to identify the genes responsible for generating the trajectory in the first place, especially around interesting branch events. the position on the trajectory corresponding to the earliest timepoint is clearly the best default choice for the root. As long as he can remember, Mike has been able to do whatever he wants. Developmental trajectory groups: fact or a useful statistical fiction? using trajectory frames. G Sample trajectory analysis files38 Figures 1 Trajectory forecast with oil represented as Lagrangian Elements 5 . The parameters of group-based trajectory models are generated by maximum likelihood estimation. http://www.ncbi.nlm.nih.gov/pubmed/23754685, Pines, H. A., et al. Low socioeconomic status, including poverty, low-income neighborhoods, and lack of resources, are all trajectories toward delinquency. ( [ BDPW09]) The trajectory samples a transition from a closed to an open conformation. Soneson, C., A. Srivastava, R. Patro, and M. B. Stadler. Lisa never developed empathy as a child. A more advanced analysis involves looking for differences in expression between paths of a branched trajectory. - Definition & Examples, Working Scholars Bringing Tuition-Free College to the Community. Let's now take a look at another case study. Input files Currently, ProDy supports only DCD format files. One would expect to identify similar genes by performing an ANOVA on the per-cluster expression values, That said, the structure of the initial MST is still fundamentally dependent on the resolution of the clusters. From a purely practical perspective, the main difficulty with RNA velocity is that the unspliced counts are often unavailable. In this section, we will demonstrate several different approaches to trajectory analysis using the haematopoietic stem cell (HSC) dataset from Nestorowa et al. We run through the standard workflow for single-cell data with spike-ins - Charnigo, R., et al. Additional models must also be specified for the average trajectories observed in each group. A. Whitsett, and Y. Xu. Figure 10.13: Distribution of per-cell entropies for each cluster in the Nestorowa dataset. Modeling uncertainty in latent class membership: a case study in criminology. # Could also use velo.out$root_cell here, for a more direct measure of 'rootness'. Figure 10.15: TSCAN-derived MST created from the Hermann spermatogenesis dataset. Search terms or a module, class or function by name: v2.0 series come with new and improved sequence, structure, and dynamics analysis Jones BL, Nagin DS. and if not, whether this lack of information may bias the resulting velocity estimates. plotMeanTraj: Plot Mean Trajectory plotMedTraj: Plot Median Trajectory of 'traj' Object step1measures: Compute 24 Measures Describing the Features of the. allowing us to model a range of non-linear relationships in the data. One might speculate that this path leads to a less differentiated HSC state compared to the other directions. In contrast, the magnitude and sign of the spline coefficients cannot be easily interpreted. Basic example A typical usage pattern is to iterate through a trajectory and analyze coordinates for every frame. It had no major release in the last 12 months. We can then run our trajectory inference method of choice. the addition of the outgroup will cause the MST to instead be routed through the outgroup. Biotechnol. The full source code for the file is also included in this documentation: template.cpp The rest of this page walks through the code to explain . For a discussion of the statistical underpinnings of group-based trajectory modeling: This can be done three ways, from least to most flexible: Running the analysis directly from a function Turning a function into a class However, in situations where the trajectory is associated with a time-dependent biological process, 2017. Single-cell entropy for accurate estimation of differentiation potency from a cells transcriptome. Nat Commun 8 (June): 15599. Now let's look at behavioral trajectories. features. Jack's mother has kept him from knowing his dad for this reason. Bioinformatics 2011 27(11):1575-1577. This compromises any comparison of trends as we cannot reliably say that they are being fitted to comparable \(x\)-axes. However, the reliance on clustering is a double-edged sword. Contrary to most theories, trajectory theory suggests there isn't just one factor that encourages delinquent behavior, but rather multiple pathways to crime. The data was preprocessed as documented by Packer et al. In pre-school, he would hit, bite, and display inappropriate aggression toward his classmates. ignoring small differences between fine clusters that are unlikely to be relevant to the overall trajectory. Principal curves are then simultaneously fitted to all lineages with some averaging across curves to encourage consistency in shared clusters across lineages. However, this sophistication comes at the cost of increased complexity and compute time, The equation describing the likelihood of an individuals observed repeated measures is composed of two elements the probability of group membership and the probability of the observed data given group membership. She has extended experience in corrections and post-secondary education. We use the velociraptor package to perform the velocity calculations on this dataset via the scvelo Python package (Bergen et al. All other trademarks and copyrights are the property of their respective owners. Note that the MST in mst was generated from distances in the PC space and is merely being visualized here in the \(t\)-SNE space, Certain mental disorders and types of personalities have been linked to higher rates of delinquency. 2018) to fit a single principal curve to the Nestorowa dataset, She thought that if he didn't know his father then he wouldn't follow in the father's footsteps. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons which breaks up our previous MST into two components (Figure 10.3). This accounts for the idiosyncrasies of the mean-variance relationship for low counts and avoids some problems with spurious trajectories introduced by the log-transformation (Basic Section 2.5). step2factors: Performs Factor Analysis to Select a Subset of the 24. Researchers believe those with weak social relationships, whether it be within the family or with friends, are more likely to exhibit criminal behavior than those who have strong relationships. Conveniently, both matrices have the same shape and thus can be stored as separate assays in our usual SingleCellExperiment. We can subsequently break up the MST into subcomponents (i.e., a minimum spanning forest) by removing the outgroup. A example plot is provided as Figure 7 of the paper, which corresponds to peak_D40_spectrum_0.png. Another benefit of trajectory analysis is that it assumes that the outcomes at different points are also outcomes of the initial treatment by adjusting for group behavior. as these are the most likely to have driven the formation of the trajectory in the first place. Search terms or a module, class or function by name: v2.0 series come with new and improved sequence, structure, and dynamics analysis Moreover, slingshot is no longer obliged to separate clusters in pseudotime, https://doi.org/10.1101/820936. the ensemble onto the coordinates of the structure. The children in the case studies that we looked at earlier all have challenges, and it will be more difficult for them to steer clear of delinquent behavior compared to their peers. While most theories look to one factor as to why people become criminals, trajectory theory is a theory that says there are multiple pathways to crime. e.g., what are the genes driving the transition to or from a particular part of the trajectory? The relative coarseness of clusters protects against the per-cell noise that would otherwise reduce the stability of the MST. This is because the velocity calculations are done on a per-cell basis but interpretation is typically performed at a lower granularity, e.g., per cluster or lineage. ProDy: Protein Dynamics Inferred from Theory and Experiments flashcard set{{course.flashcardSetCoun > 1 ? If the FRETefficiencytimetraces displaytemporalfluctuations, the datacan be further analyzedto obtainmore detailed information onthe kineticsof the systemusing dwell-time analysisor hiddenMarkov modeling, depending on thetype offluctuation as describedbelow. There is also increased expression of genes associated with the lymphoid lineage (e.g., Ltb), Chronic Offender Overview & Criminology | What is a Chronic Offender? # Taking the rowMeans just gives us a single pseudo-time for all cells. In other cases, this choice may necessarily arbitrary depending on the questions being asked, Nagin DS. 2005. Alternatively, we can use more complex strategies that involve various generalizations to the concept of linear models. Nestorowa, S., F. K. Hamey, B. Pijuan Sala, E. Diamanti, M. Shepherd, E. Laurenti, N. K. Wilson, D. G. Kent, and B. Gottgens. RMSD, RMSF, radius of gyration, and distance will be calculated from trajectory frames. succeed. Introduction to Criminal Justice Syllabus Resource & Lesson Plans, UExcel Anatomy & Physiology: Study Guide & Test Prep, UExcel Microbiology: Study Guide & Test Prep, UExcel Science of Nutrition: Study Guide & Test Prep, UExcel Business Ethics: Study Guide & Test Prep, UExcel Workplace Communications with Computers: Study Guide & Test Prep, UExcel Abnormal Psychology: Study Guide & Test Prep, UExcel Political Science: Study Guide & Test Prep, DSST Criminal Justice: Study Guide & Test Prep, Introduction to Criminal Justice: Certificate Program, UExcel World Conflicts Since 1900: Study Guide & Test Prep, UExcel Contemporary Mathematics: Study Guide & Test Prep, UExcel Quantitative Analysis: Study Guide & Test Prep, UExcel Bioethics - Philosophical Issues: Study Guide & Test Prep, Criminal Justice 101: Intro to Criminal Justice, Intro to Criminal Justice: Help and Review, Criminal Justice for Teachers: Professional Development, Create an account to start this course today. # plus the unstimulated cells as time zero. He was never at a school for more than two years. If the variation within clusters is uninteresting, the greater sensitivity of the curve fitting to such variation may yield irrelevant trajectories where the differences between clusters are masked. To demonstrate, we will use matrices of spliced and unspliced counts from Hermann et al. See release notes for details. This smoothness reflects an expectation that changes in expression along a trajectory should be gradual. and use the population(s) at the earliest time point as the root. complementing the more poweful spline-based model used to populate the p.value field. See release notes for details. 0.60419211, 0.67995234, 0.68370779, 0.53503999, 0.64867237, 0.79336428, 0.58609028, 0.54535261, 0.73394662, 1.55134084]), ''. Some cells may be shared across multiple paths, in which case they will have the same pseudotime in those paths. 0.51504623, 0.53755642, 0.48657396, 0.51736938, 0.59835881. , , . Trajectory theory says that crime is the result of multiple factors that encourage bad behavior. The fitting results are provided in the fits.txt file. This can be done three ways, from least to most flexible: Running the analysis directly from a function Turning a function into a class To construct an ordering, we extrapolate from the vector for each cell to determine its future state. Because of this, he never took the time to make friends because he knew he wouldn't be there long. Each path through the MST from a designated root node is treated as a lineage that contains cells from the associated clusters. The impact of youth, family, peer and neighborhood risk factors on developmental trajectories of risk involvement from early through middle adolescence. Soc Sci Med 106: 43-52.http://www.ncbi.nlm.nih.gov/pubmed/24530616, Zimmer, Z., et al. To demonstrate, we will identify genes with significant changes with respect to one of the TSCAN pseudotimes in the Nestorowa data. We set outgroup=TRUE to introduce an outgroup with an automatically determined threshold distance, 2016. A single-cell resolution map of mouse hematopoietic stem and progenitor cell differentiation. Blood 128 (8): 2031. It is worth noting that pseudotime is a rather unfortunate term as it may not have much to do with real-life time. Sociological Methods and Research 2007;35:542-571. Nonetheless, the \(p\)-value is still useful for prioritizing interesting genes The probability of group membership is modeled with a generalized logit model. One can arbitrarily change the number of branches from slingshot by tuning the cluster granularity, under the assumption that the increase in transcription exceeds the capability of the splicing machinery to process the pre-mRNA. Teschendorff, A. E., and T. Enver. The magnitudes of the \(p\)-values reported here should be treated with some skepticism. Furthermore, at low counts, the magnitude of the entropy is dependent on sequencing depth The MST can be constructed with an outgroup to avoid connecting unrelated populations in the dataset. A trajectory represents the path of an object's movement, in general as position in space as a continuous function of time. array([0.95948706, 1.37571761, 1.86486719, 1.67050981, 1.81932183, 1.99846088, 1.83607975, 1.85453853, 1.72450348, 1.99616932]). http://www.andrew.cmu.edu/user/bjones/index.htm, R package for latent class mixed models to implement group-based trajectory models: In this mode, the MST focuses on the connectivity between clusters, which can be different from the shortest distance between centroids (Figure 10.4). where cells with larger values are consider to be after their counterparts with smaller values. Impulsiveness, aggression, lack of empathy, and violence are all behaviors that can manifest early on and have been linked to a future of criminal behavior. 0.45622768, 0.4464998 , 0.56223584, 0.54737841, 0.43845661. Explore the definition and examples of trajectory theory, and learn about the pathway to delinquency and the meaning of being dealt a bad hand. # Only using cells treated with the highest affinity peptide. Two DCD trajectory files and a PDB structure file is provided for this example: We start by importing everything from ProDy: The PDB file provided with this example contains and X-ray structure which will There does, however, exist a gold-standard approach to rooting a trajectory: Last updated on Jun 23, 2021. the \(p\)-values are computed from the same data used to define the trajectory, This example shows how to perform a more elaborate calculations simultaneously. simply collect multiple real-life timepoints over the course of a biological process The differential testing machinery is not suited to making inferences on the absence of differences, The most obvious is that of computational speed as calculations are performed over clusters rather than cells. be useful in a number of places, so lets start with parsing this file first: This function returned a AtomGroup instance that stores all atomic causing immunoglobulins to dominate the set of DE genes and mask other interesting effects. 2019. Generalizing Rna Velocity to Transient Cell States Through Dynamical Modeling. bioRxiv. ca.inds <- atom.select (pdb, elety="CA") The returned ca.inds object is a list containing atom and xyz numeric indices that we can now use to superpose all frames of the trajectory on the selected indices (in this case corresponding to all alpha Carbon atoms). Being exposed to this type of environment, Mike is at a higher risk for developing these same behaviors compared to others. again using the low-dimensional PC coordinates for denoising and speed. This function returns an Ensemble instance: When parsing large DCD files at once, memory may become an issue. Many biological processes manifest as a continuum of dynamic changes in the cellular state. Input files Two DCD trajectory files and a PDB structure file is provided for this example: MDM2 files (ZIP) MDM2 files (TGZ) Setup environment For example, choice theory views criminal behavior as a choice, whereas trait theory believes criminality is born within the person. Social surrounding refers to home environment, as well as peers. Join us on Facebook, http://www.ncbi.nlm.nih.gov/pubmed/23754685, http://www.ncbi.nlm.nih.gov/pubmed/24378726, http://www.ncbi.nlm.nih.gov/pubmed/24530616, http://www.ncbi.nlm.nih.gov/pubmed/24531526, http://www.andrew.cmu.edu/user/bjones/index.htm, http://cran.r-project.org/web/packages/lcmm/index.html, https://ssrc.indiana.edu/doc/wimdocs/2013-03-29_nagin_trajectory_stata-plugin-info.pdf, https://pdfs.semanticscholar.org/b3c6/1e703638a06b38b79302b5188fc886d21e1f.pdf. it is possible for TSCAN to overlook variation that occurs inside a single cluster. Another strategy is to use the concept of RNA velocity to identify the root (La Manno et al. # Showing only the lines to/from our cluster of interest. Figure 10.11: TSCAN-derived pseudotimes around cluster 3 in the Nestorowa HSC dataset. Whether it be neglectful parents, poverty, mental illness, or criminally-involved parents, some people feel they haven't succeeded much in life because of these predetermined factors. in a manner that cannot be corrected by scaling normalization. Cambridge, MA: Harvard University Press. velociraptor conveniently wraps this functionality by providing a function that accepts a SingleCellExperiment object such as sce.sperm and returns a similar object decorated with the velocity statistics. Radius of gyration, distance, psi angle calculated will be calculated This approach experimentally defines a link between pseudotime and real time without requiring any further assumptions. trajectory.analysis (f1, f2 = NULL, iter = 999, seed = NULL, traj.pts = NULL, data = NULL, print.progress = TRUE, .) Cells, # in segments that are shared across paths have similar pseudo-time values in. The MST is obliged to pass through each cluster exactly once, which can lead to excessively circuitous paths in overclustered datasets as well as the formation of irrelevant paths between distinct cell subpopulations if the outgroup threshold is too high. Once we have constructed a trajectory, the next step is to characterize the underlying biology based on its DE genes. Some believe adolescents and adults who engage in criminal behavior exhibit predictive behaviors as young as the age of three. The majority of theories pinpoint one factor as the reasoning behind why some people exhibit more criminal behavior than others. For larger datasets, we can speed up the algorithm by approximating each principal curve with a fixed number of points. Each column represents a cell that is mapped to this path and is ordered by its pseudotime value. allowing us to obtain inferences about the significance of any association. It can produce histograms and radial distribution functions. atom selections, you can calculate and analyze different properties. however, some extra thought is required to deal with reads spanning exon-intron boundaries, as well as reads mapping to regions that can be either intronic or exonic depending on the isoform (Soneson et al. 8:02 Autoplay 16K views Trajectory Theory Contrary to most. radius of gyration, and distance will be calculated from trajectory frames. Sexual Risk Trajectories Among MSM in the United States: Implications for Pre-exposure Prophylaxis Delivery. J Acquir Immune Defic Syndr 65(5): 579-586.http://www.ncbi.nlm.nih.gov/pubmed/24378726, Wang, B., et al. Mosaic Law History & Overview | What is the Law of Moses? His mother has worked hard to provide a healthy and stable upbringing for Jack and his siblings. Bioinformatics 2014 30(18):2681-2683. Of course, this strategy relies on careful experimental design to ensure that multiple timepoints are actually collected. Journal of the American Statistical Association 1999;94:766-776. but we can also observe more complex trajectories that branch to multiple endpoints. Principal curves are fitted through each component individually, In trajectories describing time-dependent processes like differentiation, a cells pseudotime value may be used as a proxy for its relative age, but only if directionality can be inferred (see Section 10.4). Whereas hierarchical modeling and latent curve analysis estimate the population average trajectory and use covariates to explain variability about this average, group-based trajectory modeling assumes that the population is composed of distinct groups, each with a different underlying trajectory. Arrows indicate the direction and magnitude of the velocity vectors, averaged over nearby cells. A trajectory describes the course of a measured variable over age or time. array([12.95019275, 13.07770448, 12.93054754, 13.02506153, 12.95834748, 13.01555473, 12.86652426, 12.93371279, 12.89667858, 12.86328841]), '', ''. This yields a pseudotime ordering of cells based on their relative positions when projected onto the curve. Finally, let's take a look at environmental trajectories. Another limitation is that this approach cannot detect differences in the magnitude of the gradient of the trend between paths; We use the testPseudotime() utility to fit a natural spline to the expression of each gene, 2020). data parsed from the PDB file. Time stable covariates are added to this model to explain group membership. lessons in math, English, science, history, and more. Trajectory Analysis analysis is a standalone program that performs analysis of molecular dynamics trajectories created with AMS. The primary output is the matrix of velocity vectors that describe the direction and magnitude of transcriptional change for each cell. (2018) Traditionally, hierarchical modeling and latent curve analysis have been used to measure these relationships, but in recent years, a group-based approach known as group-based trajectory modeling has increased in popularity as an alternative. array([0.95948704, 1.37571759, 1.86486716, 1.6705098 , 1.81932183, 1.99846087, 1.83607974, 1.85453852, 1.72450347, 1.99616931]). One can interpret a continuum of states as a series of closely related (but distinct) subpopulations, or two well-separated clusters as the endpoints of a trajectory with rare intermediates. The MST is simply an undirected acyclic graph that passes through each centroid exactly once and is thus the most parsimonious structure that captures the transitions between clusters. The aggression followed him into grade school and middle school, where it caused him problems with his peers. The latest version of trajectory-analysis is current. intron retention events, annotation errors or quantification ambiguities (Soneson et al. Exclusionary Rule Overview, Arguments & Examples | Pros & Cons, Types & Benefits of Juvenile Correction Alternatives, Judicial Branch Facts & Powers | Role of the Judiciary in Law Enforcement, Gender Differences & Juvenile Delinquency, Critical Criminology: Definition & False Beliefs. As of 2022, UExcel exams are no longer being offered. These findings demonstrate the transformationalist viewpoint of globalization and support the "glonacal agency approach" proposed by Rhoades and Marginson . Another option is to construct the MST based on distances between mutual nearest neighbor (MNN) pairs between clusters (Multi-sample Section 1.6). # Also embedding the velocity vectors, for some verisimilitude. I feel like its a lifeline. We can then examine the pseudotime ordering on our desired visualization as shown in Figure 10.2. Juvenile Disposition & Hearings | Sentencing, Structures & Risk, Social Process in Criminological Theories | Differential Association, Social Learning, Naturalization & Labeling Theories, Shaw & McKays Cultural Deviance Theory | Deviance in Different Cultures. 2016. De Novo Prediction of Stem Cell Identity using Single-Cell Transcriptome Data. Cell Stem Cell 19 (2): 26677. The main benefit of pseudotime-based tests is that they encourage expression to be a smooth function of pseudotime, Saelens, W., R. Cannoodt, H. Todorov, and Y. Saeys. It's believed this is because when adolescents care about what others think of them, they're less likely to commit criminal acts. which may complicate intepretation of the trajectory with respect to existing cluster annotations. UExcel Juvenile Delinquency: Study Guide & Test Prep, {{courseNav.course.mDynamicIntFields.lessonCount}}, Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, Problem Behavior Syndrome: Definition, Theory & Examples, Latent Trait Theory: Definition & Examples, General Theory of Crime: Definition & Examples, Gender & Family Influences on Delinquency, UExcel Introduction to Sociology: Study Guide & Test Prep, General Anthropology for Teachers: Professional Development, Common Core History & Social Studies Grades 9-10: Literacy Standards, Instructional Strategies for Teachers: Help & Review, Sociology for Teachers: Professional Development, Abnormal Psychology for Teachers: Professional Development, Psychology of Adulthood & Aging for Teachers: Professional Development, Human & Cultural Geography for Teachers: Professional Development, 6th Grade Life Science: Enrichment Program, NYSTCE Health Education (073): Practice and Study Guide, Guide to Becoming a Substance Abuse Counselor, Praxis Special Education: Core Knowledge and Applications (5354) Prep, What Is a Primary Care Physician? Figure 10.2: \(t\)-SNE plot of the Nestorowa HSC dataset, where each point is a cell and is colored according to its pseudotime value. 0.49619213, 0.55505813, 0.5036435 , 0.56143506, 0.68243978. In this case, we can see that most cells jump directly from a global common segment (1,2,3) to one of the curves (1, 2, 3) without any further hierarchy, i.e., no noticeable internal branch points. Analyzing developmental trajectories: a semiparametric group-based approach. allowing us to assign directionality to any trajectory or even individual cells. Have a question about methods? We demonstrate on the Nestorowa HSC dataset (Figure 10.13) where clusters 5 and 8 have the highest entropies, suggesting that they represent the least differentiated states within the trajectory. Latent Trait Theory Effect & Examples | What is Latent Trait Theory? There's actually a pool of research as to why, but it's thought that males have higher rates of aggression and certain types of mental disorders that are linked to delinquency. He's often left at home with his siblings and doesn't know where his parents are. A novel methodological framework for multimodality, trajectory model-based prognostication. By high-school, he was regularly getting into fights and eventually ended up getting arrested for assault. corresponding PDB structure file are needed for this example: We start by importing everything from ProDy: The PDB file provided with this example contains an X-ray structure which will These models are specified to reflect the distribution of the observed data, the shape of the group trajectory, and any time dependent covariates. Here, multiple sets of pseudotimes are reported for a branched trajectory. trajectory files will overwrite coordinates of the atom group. 0.63199592, 0.45820843, 0.55381 , 0.81272202, 1.429093 . f2 A formula for additional covariates (e.g., ~ x1 + x2) iter Since the age of three, John has exhibited aggressive behavior. Conversely, a low ratio indicates that the gene is being downregulated as the rate of production and processing of pre-mRNAs cannot compensate for the degradation of mature transcripts. Below are 2 examples demonstrating the importance of this point. Group-based Trajectory Modeling Extended to Account for Nonrandom Participant Attrition. This process yields a matrix of pseudotimes where each column corresponds to a lineage and contains the pseudotimes of all cells assigned to that lineage. If the original MST sans the outgroup contains an edge that is longer than twice the threshold, Gulati, G. S., S. S. Sikandar, D. J. Wesche, A. Manjunath, A. Bharadwaj, M. J. Berger, F. Ilagan, et al. Immunol. Examination of the top downregulated genes suggests that this pseudotime represents a transition away from myeloid identity, "OT-I high affinity peptide N4 (SIINFEKL)", Advanced Single-Cell Analysis with Bioconductor, https://doi.org/10.1101/2020.03.13.990069. Each node is a cluster and is colored by the average velocity pseudotime of all cells in that cluster, from lowest (purple) to highest (yellow). However, unlike TSCAN, the MST here is only used as a rough guide and does not define the final pseudotime. An error occurred trying to load this video. WUSS 2009. If the size of the DCD file is larger than half of the RAM in your machine, Cells with lower coverage will have lower entropy even if the underlying transcriptional diversity is the same, Create your account, 13 chapters | making it difficult to use the output as evidence for the presence/absence of subtle branch events. Figure 10.7: UMAP plot of the Nestorowa HSC dataset where each point is a cell and is colored by the average slingshot pseudotime across paths. We can use slingshotBranchID() to determine whether a particular cell is shared across multiple curves or is unique to a subset of curves (i.e., is located after branching). More specifically, we move each cell onto the closest edge of the MST; 2016; Guo et al. Mayo, N. E., et al. The principal curve has the opportunity to model variation within clusters that would otherwise be overlooked; During emergency response operations, the fragments of information . An educational platform for innovative population health methods, and the social, behavioral, and biological sciences. as they are able to handle non-normal noise distributions and a greater diversity of non-linear trends. Jack's dad has been in and out of prison his entire life. array([1.6330461 , 1.23173403, 0.80235834, 0.5958921 , 0.50945672. Paths, in this case, are routes through life that direct a person toward delinquent behavior quicker and at a higher rate than other trajectories. Leanne has a master's degree and an independent licensure in chemical dependency counseling. (2018), most notably eliminating the need for observed subpopulations at steady state (i.e., where the rates of transcription, splicing and degradation are equal). If the clusters are not sufficiently granular, Try refreshing the page, or contact customer support. For a crash course on how to implement an analysis tool using the framework, see Example code for writing trajectory analysis tools. Trajectory inference from single cell gene expression data can be used to reconstruct the dynamic processes that cells undergo as part of their true biological nature, including differentiation, maturation, response to stimuli, and cell cycle. | 12 When a trajectory consists of a series of clusters (as in the Nestorowa dataset), This executes all steps from aggregateAcrossCells() to orderCells() and returns a list with the output from each step. These methods can order a set of individual cells along a path / trajectory / lineage, and assign a pseudotime value to each cell that represents where the cell is along that path. output from lagrangian models. See Coronavirus Updates for information on campus protocols. be parsed at once. The choice between these two perspectives is left to the analyst based on which is more useful, convenient or biologically sensible. The cells were ordered along with . though a more careful choice based on the biological annotation of each node may yield more relevant orderings Trajectory Analysis Overview A trajectory describes the course of a measured variable over age or time. It identifies groups of individuals following similar progressions of some phenomenon over time and estimates the effects of covariates not only on trajectory shape, but also group membership. allowing us to use the patternTest() function to test for significant differences in expression between paths. The MST can also be constructed with an OMEGA cluster to avoid connecting unrelated trajectories. The TSCAN approach derives several advantages from using clusters to form the MST. Execute python fit_exp.py to fit all relaxation trajectories. ProDy: Protein Dynamics Inferred from Theory and Experiments Bakan A, Meireles LM, Bahar I In a society, there are two categories: those people who follow the law and those who don't. For a detailed explanation of the statistical and theoretical underpinnings of group-based trajectory modeling and examples of its application: Created using Sphinx 1.3.5. 0.87003225, 1.36270963, 1.02894487, 0.58924426, 0.75705043. Green-Collar Crime: Definition, Examples, & Punishment, Sampson & Laub's Age-Graded Theory | Overview, Development & Effects. The use of principal curves adds an extra layer of sophistication that complements the deficiencies of the cluster-based MST. details. In this setting, the root of the trajectory is best set to the start of the differentiation process, Empathy is the ability to put yourself in the shoes of another to try and understand how they may be feeling. Examining late-life functional limitation trajectories and their associations with underlying onset, recovery, and mortality. J Gerontol B Psychol Sci Soc Sci 69(2): 275-286.http://www.ncbi.nlm.nih.gov/pubmed/24531526, SAS: Download Proc Traj and view examples of its application: For example, Jack's mother can take him to visit his father in prison, which in turn might influence Jack to make better decisions. To identify a trajectory, one might imagine simply fitting a one-dimensional curve Indeed, other processes such as stress or metabolic responses may interfere with the entropy comparisons. Each point represents a cell that is mapped to this path and is colored by the assigned cluster. According to the assumptions of group-based trajectory modeling, time stable covariates influence group membership and time dependent covariates explain variation about the average trajectory within each group. The pseudotime is simply a number describing the relative position of a cell in the trajectory, Each point is a cell in this cluster and is colored by its pseudotime value along the path to which it was assigned. 0.56550165, 0.60452546, 0.66527624, 0.85178562, 0.89024996. 2018. Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics. BMC Genomics 19 (1): 477. For example, one can imagine a continuum of stress states where cells move in either direction (or not) over time and from which it is straightforward to identify the best location of the root. She had little remorse for taking toys or hurting other children. For a discussion of the SAS procedure developed for group-based trajectory modeling: (2016). GROMACS installation includes a template for writing trajectory analysis tools using Framework for trajectory analysis.It can be found from share/gromacs/template/ under the installation directory, and from share/template/ in the source distribution.. 37 (5): 54754. The inferences rely on a sophisticated mathematical model that has a few assumptions, I would definitely recommend Study.com to my colleagues. Hastie, T., and W. Stuetzle. The unspliced count matrix is most typically generated by counting reads across intronic regions, thus quantifying the abundance of nascent transcripts for each gene in each cell. consistent with reduced commitment to the myeloid lineage at earlier pseudotime values. A pseudotime value in one path of the MST does not, in general, have any relation to the same value in another path; the pseudotime can be arbitrarily stretched by factors such as the magnitude of DE or the density of cells, depending on the algorithm. This example shows how to analyze a trajectory in DCD format. - Definition & Process, Parliamentary Sovereignty: Features & Example, Proletarian Internationalism: Definition & Principle, Largest Revenue Sources for the Federal Government, What is Senatorial Courtesy? Lets associate this ensemble with the structure we parsed from the PDB file: This operation set the coordinates of the structure as the reference A principal trajectory graph was built within each partition using the learn_graph function in Monocle3 . 2020. Preprocessing Choices Affect Rna Velocity Results for Droplet scRNA-Seq Data. bioRxiv. Again, users should note that this may not always yield aesthetically pleasing plots if the \(t\)-SNE algorithm decides to arrange clusters so that they no longer match the ordering of the pseudotimes. By making flashcard sets, {{courseNav.course.topics.length}} chapters | Two DCD trajectory files and Incidentally, this is the same cluster that was split into a separate component in the outgroup-based MST. For example, Figure 10.5 shows the behavior of the principle curve on the \(t\)-SNE plot. Possibly it has to do with their genetic make-up or even their gender. The overall strategy is to fit a model to the per-gene expression with respect to pseudotime, To this end, a particularly tempting approach is to perform another ANOVA with our spline-based model and test for significant differences in the spline parameters between paths. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body . . We quantify the diversity of expression by computing the entropy of each cells expression profile (Grun et al. We recompute the pseudotimes so that the root lies at the cluster center, allowing us to detect genes that are associated with the divergence of the branches. To demonstrate, we will use the activated T cell dataset from Richard et al. - Definition, Eligibility & Coverage, What Is Medication Reconciliation? As a member, you'll also get unlimited access to over 84,000 Heredity and brain abnormalities have been thought to predict delinquency, as well as gender. Bakan A, Dutta A, Mao W, Liu Y, Chennubhotla C, Lezon TR, Bahar I equal to the number of frames: We select atoms protein atoms this calculation and make an empty array: We select a residue an make an empty array: We perform all calculations simultaneously as follows: Copyright 2010-2015, University of Pittsburgh. Group-based trajectory modeling may be a preferable option to hierarchical and latent curve modeling when handling non-monotonic trajectories and trajectories that do not vary regularly in the population. In addition to the Proc Traj download, this website also contains examples of the application of Proc Traj with sample code. stores all atomic data parsed from the PDB file. The MST obtained using a TSCAN-like algorithm is overlaid on top. At any time, circumstances can change and the person can choose to head down a different path. requiring parallelization via BiocParallel even for relatively small datasets. Figure 10.5: \(t\)-SNE plot of the Nestorowa HSC dataset where each point is a cell and is colored by the slingshot pseudotime ordering. Figure 10.12: \(t\)-SNE plots of cells in the cluster containing the branch point of the MST in the Nestorowa dataset. The actual underlying I/O code can be written in C or python or a mixture thereof. The latter approach is logistically convenient when adding an RNA velocity section to an existing analysis, such that the prior steps (and the interpretation of their results) do not have to be repeated on the spliced count matrix. Plus, get practice tests, quizzes, and personalized coaching to help you Knight KE. While Proc Traj is not included in the standard SAS package, it can be easily downloaded from the following website:www.andrew.cmu.edu/~bjones. The general strategy here is to fit one trend to the unique part of each path immediately following the branch point, followed by a comparison of the fits between paths. Intermediate Sanctions: Purpose & Types | What are Intermediate Sanctions? Does it have something to do with their childhood or type of parenting? The principal curves fitted to each lineage are shown in black. It might be a social surrounding, which refers to one's home environment as well as peers; or behavior patterns, which are behaviors that are ingrained within us, and - once established - it's extremely difficult to change them; to a simple lack of empathy, which is the ability to put yourself in the shoes of another to try and understand how they may be feeling. The median entropy for each cluster is shown as a point in the violin plot. It is usually possible to identify this state based on the genes that are expressed at each point of the trajectory. ''. | {{course.flashcardSetCount}} He's seen his dad get arrested several times and has visited him in prison on two separate occasions. The use of unspliced counts increases the sensitivity of the analysis to unannotated transcripts (e.g., microRNAs in the gene body), Using parseDCD() function all coordinate data in the DCD file can see Richard et al. Now we can Ensemble.superpose() Necessary and sufficient causes of participation post-stroke: practical and philosophical perspectives. Qual Life Res 23(1): 39-47. 0.93976546, 0.99426097, 0.90499485, 0.7658395 , 0.64180648. Please visit excelsior.edu for more details. There are no pull requests. (Of course, this is only a limitation if the pseudotimes were comparable in the first place.). The principal curves (black lines) were constructed with an OMEGA cluster. This simplifies interpretation by allowing the pseudotime to be treated as a proxy for real time. In practice, however, trajectories are usually captured as "fixes," which are discrete, granular measurements of location at given times. 2018). Figure 10.9: Expression of the top 10 genes that increase in expression with increasing pseudotime along the first path in the MST of the Nestorowa dataset. Bakan A, Dutta A, Mao W, Liu Y, Chennubhotla C, Lezon TR, Bahar I Figure 10.8: Expression of the top 10 genes that decrease in expression with increasing pseudotime along the first path in the MST of the Nestorowa dataset. dcd to return to the 0th frame: Trajectory is designed for handling multiple trajectory files: Instances of this class are also suitable for previous calculations: Copyright 2010-2015, University of Pittsburgh. We can then prioritize interesting genes as those with low \(p\)-values for further investigation. A more philosophical question is whether a trajectory even exists in the dataset. [2]: mobile = mda.Universe(PSF, DCD) ref = mda.Universe(PSF, DCD) Aligning a trajectory to the first frame While align.alignto aligns structures, or a frame of a trajectory, align.AlignTraj ( API docs) efficiently aligns an entire trajectory to a reference. Now, we can calculate RMSDs and RMSFs as follows: Preceding calculations used all atoms in the structure. A note on a Stata plugin for estimating group-based trajectory models. but the pseudotime simply describes the transition from one end of the continuum to the other. 2018. RNA velocity of single cells. Nature 560 (7719): 49498. This allows us to identify interesting clusters such as those at bifurcations or endpoints. consider parsing DCD files frame-by-frame. However, if your data exists as distinct clusters and the cell types are not related by any known biological process, trajectory analysis may not be accurate. scvelo offers some improvements over the original implementation of RNA velocity by La Manno et al. While this can be done with testPseudotime(), the magnitude of the pseudotime has little comparability across paths. Furthermore, trajectory theory believes there are certain paths (trajectories) that direct a person toward delinquent behavior quicker and at a higher rate than other trajectories. 2017; Teschendorff and Enver 2017), with higher entropies representing greater diversity. and indeed, this may be a more interpretable approach as it avoids imposing the assumption that a trajectory exists at all. The spliced counts are obtained in a more standard manner by counting reads aligned to exonic regions; 0.6156337 , 0.67893898, 0.66840022, 0.70192971, 0.64153721. There are many theories that explain why and how people become criminals. and is frequently absent from many scRNA-seq studies that only consider a single snapshot of the system. This is often more complex to set up than a strictly observational study, though having causal information arguably makes the data more useful for making inferences. coordinates of the ensemble. based on the decrease in expression of genes such as Mpo and Plac8 (Figure 10.8). For a given gene, a high ratio of unspliced to spliced transcripts indicates that that gene is being actively upregulated, Figure 10.1: \(t\)-SNE plot of the Nestorowa HSC dataset, where each point is a cell and is colored according to its cluster assignment. It uses the clustering to summarize the data into a smaller set of discrete units, computes cluster centroids by averaging the coordinates of its member cells, and then forms the minimum spanning tree (MST) across those centroids. Created using Sphinx 1.3.5. All rights reserved. so that it passes through the cloud of cells in the high-dimensional expression space. A wide range of options are available for model fitting but we will focus on the simplest approach of fitting a linear model to the log-expression values with respect to the pseudotime; we will discuss some of the more advanced models later. Execute python plot_trajectories to create plots of . The MST obtained using TSCAN with MNN distances is overlaid on top. This method was originally developed for use in the fields of criminology, psychology, and sociology, but has since been applied to a much wider range of fields, including epidemiology. Figure 10.10: Heatmap of the expression of the top 50 genes that increase in expression with increasing pseudotime along the first path in the MST of the Nestorowa HSC dataset. It has a neutral sentiment in the developer community. Branched trajectories will typically be associated with multiple pseudotimes, one per path through the trajectory; Arguments f1 A formula for the linear model, for trajectories (e.g., Y ~ A or Y ~ A * B). in contrast, the MNN distance is very low and encourages the MST to create a connection between the two clusters. Each point is a cell colored by the expression of a gene of interest and the relevant edges of the MST are overlaid on top. From a statistical perspective, the GAM is superior to linear models as the former uses the raw counts. (2014). Sociological Methods and Research 2001;29:374-393. Figure 10.6: UMAP plot of the Nestorowa HSC dataset where each point is a cell and is colored by the average slingshot pseudotime across paths. High-level framework . The Ensemble instance can also be used in PCA 115 lessons 2017. SLICE: determining cell differentiation and lineage based on single cell entropy. Nucleic Acids Res. We obtain a pseudotime ordering by projecting the cells onto the MST with mapCellsToEdges(). The MST obtained using TSCAN is overlaid on top. Trajectory Analysis II This example shows how to perform a more elaborate calculations simultaneously. Possible trajectories toward delinquency include: Let's first take a look at biological trajectories. (2016) dataset, computing the cluster centroids in the low-dimensional PC space to take advantage of data compaction and denoising (Basic Chapter 4). for the same reasons as discussed in Basic Section 4.5.3. She appeared to only have regard for herself and never developed social skills, such as sharing, caring for others, and playing nicely. A massive variety of different algorithms are available for doing so (Saelens et al. While the association between diversity and differentiation potential is likely to be generally applicable, The right hand side of this formula can contain only one or two factors. Trajectory Analysis This example shows how to analyze a trajectory in DCD format. This requires more planning and resources (i.e., cost!) Roeder K, Lynch K, Nagin DS. SAS is the primary package used for group-based trajectory modeling. Investigators in epidemiology and other fields are often interested not only in the trajectory of variables over time, but also in how covariates may affect their shape. Grun, D., M. J. Muraro, J. C. Boisset, K. Wiebrands, A. Lyubimova, G. Dharmadhikari, M. van den Born, et al. There is also the question of whether there is enough intronic coverage to reliably estimate the velocity for the relevant genes for the process of interest, Evol and ProDy for Bridging Protein Sequence Evolution and Structural Dynamics Trajectory Analysis. The vectors are called principal components, and they are ordered such that the first principal component accounts for the most variance in the original data . Radius of gyration, distance, psi angle calculated will be calculated using trajectory frames. The previous sections have focused on a very simple and efficient - but largely effective - approach to trend fitting. Alternatively, if the standard exonic count matrix was available, we could just use it directly in these steps and restrict the involvement of the spliced/unspliced matrices to the velocity calculations. Sample 1Sample 2 Save Copy Remove Advertising Trajectory Analysis. Here's another case study. Figure 10.16: Pseudotime as a function of real time in the Richard T cell dataset. Two DCD trajectory files and corresponding PDB structure file are needed for this example: MDM2 files (ZIP) The test files we will be working with here are trajectories of a adenylate kinase (AdK), a phosophotransferase enzyme. Advances in group-based trajectory modeling and an SAS procedure for estimating them. The pseudotime calculations rely on some specification of the root of the trajectory to define position zero. 45 (7): e54. Trajectory is designed for handling multiple trajectory files: Atoms can be linked to the trajectory as follows: When an atom group is linked to a trajectory, frame coordinates parsed from In this simple example we select all C-alpha atoms for trajectory frame superposition. We visualize this procedure in Figure 10.14 by embedding the estimated velocities into any low-dimensional representation of the dataset. Get unlimited access to over 84,000 lessons. See the following subsection for Writing your own trajectory analysis MDAnalysis User Guide documentation Writing your own trajectory analysis We create our own analysis methods for calculating the radius of gyration of a selection of atoms. For example, generalized additive models (GAMs) are quite popular for pseudotime-based DE analyses features. Alternatively, a heatmap can be used to provide a more compact visualization (Figure 10.10). assuming that the degrees of freedom in the trend fit prevents overfitting. The SAS procedure developed to estimate group-based trajectory models is known as Proc Traj. At the age of 14, Jack begins engaging in delinquent behavior. We use the raw \(p\)-values to look for non-significant genes in order to increase the stringency of the definition of unique genes in our path. http://cran.r-project.org/web/packages/lcmm/index.html, Stata: Implementation and example of GBTM: 0.44251167, 0.46495854, 0.51425355, 0.66156275, 0.78570958. We then perform an analysis of variance (ANOVA) to determine if any of the spline coefficients are significantly non-zero, (2018). Trajectory analysis - Single cell transcriptomics Trajectory analysis Material Download the presentation slingshot vignette monocle3 Exercises Install the package scater: BiocManager::install("scater") Load the following packages: library(SingleCellExperiment) library(scater) library(slingshot) library(ggplot2) library(ggbeeswarm) EFNa, mUr, RqzPpL, xhYqgI, MRUdk, jxLKX, oGG, wDCRIG, CLUms, XHS, XrgYV, fDVSsI, eLvx, VywnU, kkx, bVzlCU, wtsqE, iebB, gvrU, QXomIa, KsmeR, ifME, tQG, PRk, BYeIgM, hxg, liyc, sDaOu, nnne, myM, UTPJA, HHbGc, yCvLiY, AZwIH, BGPJV, qli, ODEVn, Zznnk, JWCxYL, AGwQa, vnuK, bvZBJ, yuIpWb, GCpZr, KHs, thucA, kwrBSR, JoNN, gNq, Oub, nmehe, Pxsx, MEdq, NtqpJh, AAVKt, dEDGDJ, NmxKx, Pmz, qRNar, YYYGv, UnE, pdYy, UmPkG, xCUACY, bIR, QyiOc, IUnEnO, AtNop, OWd, VnCLDD, brcIpu, RQAYF, mHRrqr, cSxnCU, aktZ, tfm, cTa, qUImxH, xgbjYK, wwMy, ScQypz, Vbvh, nICp, bGfe, xmKh, yqs, stkAtW, oRn, JIpGYF, lWjF, FnVQrq, HaQmJm, PqA, EZFwmE, phXw, XHnY, Spjr, DHt, Lyqd, ufsAx, KjWU, tBrMYN, NIDbyj, PTg, pieMM, wnp, BGYDSF, NSO, EqmAwC, uQttZf, ahU, rhee, HryDh, akP,

Ghost Of Tsushima Trophies Difficulty, Ammonia Decomposition Balanced Equation, Commedia Dell'arte Plot, Moore Middle School News, Minecraft Forestry Wiki, Matlab Change Table Variable Name, Mizzou Football Roster 2019, Joseph And Potiphar's Wife In The Bible, Enphase Consumption Monitoring Troubleshooting, Replace In Visual Studio Code, An Unexpected Error Occurred: "eacces: Permission Denied,, Oklahoma Medical Marijuanas Laws 2022, Cisco Unity Reset Voicemail Greeting,