Genome architecture mapping

In molecular biology, genome architecture mapping (GAM) is a cryosectioning method to map colocalized DNA regions in a ligation independent manner. It overcomes some limitations of Chromosome conformation capture (3C), as these methods have a reliance on digestion and ligation to capture interacting DNA segments. GAM is the first genome-wide method for capturing three-dimensional proximities between any number of genomic loci without ligation.

The sections that are found using the cryosectioning method mentioned above are referred to as “Nuclear Profiles”. The information that they provide relates to their coverage across a genome. A large set of values can be produced that represents the strength of nuclear profiles’ presence within a genome. Based on how large or small the coverage across a genome is, judgements can be made involving chromatin interactions, nuclear profile location within the nucleus being cryosectioned, and chromatin compaction levels.

To be able to visualize this information, certain methods can be implemented using the raw data given by a table that shows whether or not nuclear profiles are detected in a genomic window, the genomic windows being represented within a certain chromosome. With a 1 representing a detection within a window and a 0 representing no detection, subsets of data can be obtained and interpreted by creating graphs, charts, heatmaps, and other visualization methods that allow these subsets to be seen in ways other than binary detection methods. By using a more graphic approach to interpreting the data obtained with cryosectioning, it is possible to see interactions that would have otherwise not been seen before.

Some examples of how these visuals can be interpreted include bar graphs that show the radial position and chromatin compaction levels of nuclear profiles, they can be split into categories to give a generalization of how often nuclear profiles are detected within a genomic window. A radar chart is a circular graph that represents the percentages of occurrence within a number of variables. In the sense of genomic information, radar charts can be used to show how genomic windows are represented within “features” of the genome that are part of certain regions that make it up. These charts can be made to compare groups of nuclear profiles with each other and their differences in how they occur within these features is shown graphically. Heatmaps are another form of visual representation where individual values in a table are shown by cells that take on different colors based on their value. This allows for trends to be seen within a table by the display of groups of similar colors or the lack of.

A heatmap can be used to show the relationship between nuclear profiles based on a calculated Jaccard Index where the values ranging from 0-1 are the degree of similarity between two nuclear profiles. Showing this similarity can help to display where certain groups of nuclear profiles are more common within a genome. Bar graphs can be used to display the percentage of nuclear profiles that belong to a category of radial position (with 5 being the most equatorial and 1 being the least). Radar charts can be used to show clusters of nuclear profiles’ percentage of occurrence within certain features of the mouse genome. Comparisons can be made between the clusters and how they show up more or less in certain features in contrast to each other.

Overview

Genome architecture mapping was first developed in the laboratory of Ana Pombo, based on a theoretical approach to linkage mapping the human genome published in 1989. The purpose of GAM is to achieve a greater understanding of the 3 dimensional structure of genes within a nucleus; specifically, where genomic loci lie relative to each other.

A flowchart showing the general process of how GAM data may be analyzed

The above flowchart shows a general process of how data may be derived from GAM analysis. Circles represent processes that may be performed, and squares represent pieces of data.

The first step shown is the process of GAM itself, i.e. the action of randomly slicing frozen cells with a laser to produce thin slices of the nucleus, called nuclear profiles. Each nuclear profile contains certain pieces of DNA within it, referred to in GAM as genomic loci.

The next step in the analysis requires creating a segregation table. The segregation table is a matrix listing which genomic loci were detected in which nuclear profiles. Essentially, it is the translation of the previous step’s results into data.

Next, software such as the GAMtools suite can be used to analyze the segregation table. This analysis can provide numerous results, such as heat maps showing which nuclear profiles certain genomic loci are most likely to reside in - in essence, showing where certain pieces of DNA are most likely to physically be inside a cell. Clustering algorithms can also be applied to specific regions of the genetic code to determine which nuclear profiles those DNA pieces most likely reside in.

Another piece of data derivable from GAM consists of which genetic loci interact with each other. Linkage can be calculated between loci by determining how often two loci appear within the same nuclear profile. This data can be used to create a map showing where loci are located relative to each other in 3-dimensional space.

Finally, network analytics can be applied to the above data to detect communities of genetic loci within a nucleus. This provides more depth to the data gleaned above by showing which genomic loci a given locus interacts with most often.

Cryosection and laser microdissection

Cryosections are produced according to the Tokuyasu method, involving stringent fixation to preserve nuclear and cellular architecture, cryoprotection with a sucrose-PBS solution, before freezing in liquid nitrogen. In Genome Architecture Mapping, sectioning is a necessary step for exploring the 3D topology of the genome, before Laser Microdissection. Then laser microdissection can isolate each nuclear profile, before DNA extraction and sequencing.

Data Analysis - Bioinformatics Method

GAMtools

GAMtools is a collection of software utilities for Genome Architecture Mapping data developed by Robert Beagrie. Bowtie2 is required before running GAMtools. The input required for this program is in Fastq format. This software has a variety of features and the exact commands to use will depend on what you want to do with it, however most features require generating segregation table, so for most users the first steps to take will be to download or create input data, and perform the sequence mapping. This will generate a segregation table, which can then be used to perform various other operations which are outlined below. For further information, view the GAMtools documentation.

Flowchart

Mapping the Sequencing Data

The GAMtools command gamtools process_nps can be used to perform the mapping. It maps the raw sequence data from the nuclear profiles. GAMtools also provides the option to perform quality control checks on the NPs. This option can be enabled by adding the flag -c/--do-qc to the previous command. When the quality control check is enabled, GAMtools will try to exclude poor quality nuclear profiles.

Windows Calling and Segregation Table

After the mapping has finished, GAMtools will compute the number of reads from each nuclear profile which overlap with each window in the background genome file. The default window size is 50kb. This is all done by the same process_nps command. After this, it generates a segregation table.

Producing Proximity Matrices

The command for this process is gamtools matrix. The input file is the segregation table that was calculated from the windows calling step. GAMtools calculates these matrices using the normalized linkage disequilibrium, which means that it looks at how many times each pair of windows are detected by the same NP, and then normalizes the results based on how many times each window was detected across all NPs. The figure below shows an example of a proximity matrix heatmap produced using GAMtools.

An example of a proximity matrix produced with GAMtools.

Calculating Chromatin Compaction

The volume of genomic loci can be estimated by the number of times they are intersected. This information can be used to estimate Chromatin Compaction and Radial Position.

The GAMtools command gamtools compaction can be used to calculate an estimation of chromatin compaction. The level of compaction is inversely proportional to the locus volume. Genomic loci with a low volume are said to have a high level of compaction, and loci with a high volume have a low level of compaction. Loci with a low compaction level are expected to be intersected more often by the cryosection slices. GAMtools uses this information to assign a compaction value to each chromatid based on it's detection frequency across many nuclear profiles. The compaction rate of these loci is not static, and will continually change throughout the life of the cell. Genomic loci are thought to be de-compacted when that gene is active. This allows a researcher to make assumptions about which genes are currently active in a cell, using the results of the GAMtools data. A loci with low compaction is also thought to be related to transcriptional activity.

Calculating Radial Position

GAMtools can be used to calculate chromatin radial positioning. The command for performing this operation with GAMtools is gamtools radial_pos. This requires that you have previously generated a segregation table. The radial position is estimated from the average size of NPs that contain a given chromatin region. Chromatin that are closer to the periphery will typically be intersected by smaller, more apical NPs, whereas central chromatin will be intersected by larger, equatorial NPs.

In order to estimate the size of each NP, GAMtools looks at the number of windows each NP saw, as NPs that saw more windows can be assumed to be larger in volume. This is very similar to the method used to estimate chromatin compaction. The figure to the right illustrates how GAMtools looks at each NP's detection rate to estimate the volume, in order to determine the compaction or the radial position.

SLICE

SLICE (StatisticaL Inference of Co-sEgregation) plays a key role in GAM data analysis. It was developed in the laboratory of Mario Nicodemi to provide a math model to identify the most specific interactions among loci from GAM cosegregation data. It estimates the proportion of specific interaction for each pair loci at a given time. It is a kind of likelihood method. The first step of SLICE is to provide a function of the expected proportion of GAM nuclear profiles. Then find the best probability result to explain the experimental data.

Flow chart of SLICE

SLICE Model

The SLICE Model is based on a hypothesis that the probability of non-interacting loci falls into the same nuclear profile is predictable. The probability is dependent on the distance of these loci. The SLICE Model considers a pair of loci as two types: one is interacting, the other is non-interacting. As per the hypothesis, the proportions of nuclear profiles state can be predicted by mathematical analysis. By deriving a function of the interaction probability, these GAM data can also be used to find prominent interactions and explore the sensitivity of GAM.

Calculate distribution in a single nuclear profile

SLICE considers a pair of loci can be interaction or non-interaction across the cell population. The first step of this calculation is to describe a single locus. A pair of loci, A and B, can have two possible states: one is that A and B have no interactions with each other. The other is that they have. The first problem is that whether a single locus can be found in a nuclear profile.
The mathematical expression is:

Single locus probability: $v_{0},v_{1}$
- <$v_{1}$> probability that the locus is found in an nuclear profile.
- <$v_{0}$>$=1-$<$v_{1}$> probability that the locus is not found in a nuclear profile.
- <$v_{1}$>=$V_{NP}/V_{nucleus}$

Estimation of average nuclear radius

As the equation above, the volume of the nuclear is a necessary value for calculation. The radii of these nuclear profiles can be used to estimate the nuclear radius. The SLICE prediction for radius matches Monte Carlo simulations(more detail about this step will be updated after get the license of the figure in the original author's paper.). With the result of the estimated radius, the probability of two loci in a non-interacting state and the probability of these two loci in an interacting state can be estimated.
Here is the mathematical expression of non-interacting:
<$u_{i}$>,i = 0, 1, 2 represents: find 0, 1 or 2 loci of a pair of non-interacting loci.
Two loci in a non-interacting state:$u_{i}$
$<u_{0}>=<v_{0}^{2}>,<u_{1}>=<v_{1}v_{0}>,<u_{2}>=<v_{1}^{2}>$
Here is the mathematical expression of interacting:
Estimation of two loci interaction state: $t_{i}$ probability
$<t_{2}>$~$<v_{1}>$, $<t_{1}>$~0, $<t_{0}>$~$<v_{0}>=1-<v_{1}>$

Calculate probability of pairs of loci in single nuclear profile

With the results of previous processes, the occurrence probability of a pair of loci in one nuclear profile can be calculated by statistics method. A pair of loci can exist in three different states. Each of them has a probability of $P_{i},i=0,1,2$
Occurrence probability of pairs of loci in single nuclear profiles:$P_{2},P_{1},P_{0}$
$P_{2}$: probability of two pairs of loci are in a state of interaction;
$P_{1}$: probability of one interacts the other, but the other does not interact;
$P_{0}$: probability of the two not interact.
SLICE Statistical Analysis
$N_{0,0}/N=<t_{0}^{2}>P_{2}+<t_{0}u_{0}>P_{1}+<u_{0}^{2}>P_{0}$
$N_{2,0}/N=N_{0,2}=<t_{1}^{2}>P_{2}+<t_{1}u_{1}>P_{1}+<u_{1}^{2}>P_{0}$
$N_{i,j}$ represent: number i is for A. Number j is for B.(i and j are equal to 0, 1 or 2 loci).

Detection efficiency

As the number of experiments is limited, there should be some detection efficiency. Considering the detection efficiency can expand this SLICE model to accommodate additional complications. It is a statistical method to improve the calculation result. In this part, the GAM data is divided into two types: one is that the locus in the slice is found in the experiments, and the other is that the locus in the slice is not detected in the experiments.

Estimating interaction probabilities of pairs

Based on the estimated detection efficiency and the previous probability of $u_{0},u_{1},u_{2}$,the interaction probability of pairs can be calculated. The loci are detected by next generation sequencing.

Advantages

In comparison with 3C based methods, GAM provides three key advantages.

• The C-method uses a pairwise interaction method, which means that it can only provide pair results. But GAM can detect clustering of multiple gene loci.
• Restriction enzymes play an essential role in C-method. In that case, restriction enzymes sites limit the ligation-based methods. GAM does not have this limitation.
• C-methods require more cells than GAM.