# Data processing

Currently, HaDeX is limited to the `cluster` file from DynamX 3.0 or 2.0. Below we explain how the data file is processed.

## Processing data from DynamX

Let’s investigate how the data processing of the `cluster` file from DynamX is conducted on the example file from the package.

### Differences between files

What is the difference between `cluster` files from DynamX 3.0 and 2.0? The datafiles from DynamX 2.0 don’t include `Modification` and `Fragment` columns. The variations of the experiment were limited, while the DynamX 2.0 was the latest version.

### Initial processing of the data

Let’s start with a glimpse of the datafile.

    library(HaDeX)
    dat <- read_hdx(system.file(package = "HaDeX", "HaDeX/data/KD_180110_CD160_HVEM.csv"))
    head(dat, 10)

    ##      Protein Start   End        Sequence Modification Fragment MaxUptake
    ##       <char> <int> <int>          <char>       <lgcl>   <lgcl>     <num>
    ##  1: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##  2: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##  3: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##  4: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##  5: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##  6: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##  7: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##  8: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##  9: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ## 10: db_CD160     1    15 INITSSASQEGTRLN           NA       NA        14
    ##          MHP  State Exposure                    File     z       RT  Inten
    ##        <num> <char>    <num>                  <char> <int>    <num>  <num>
    ##  1: 1590.808  CD160    0.000 KD_160527_CD160_sekw_05     1 3.232479   6592
    ##  2: 1590.808  CD160    0.000 KD_160527_CD160_sekw_05     2 3.238079 394066
    ##  3: 1590.808  CD160    0.000 KD_160527_CD160_sekw_05     3 3.238759 173526
    ##  4: 1590.808  CD160    0.001   KD_160527_CD160_IN_01     2 3.258598 232221
    ##  5: 1590.808  CD160    0.001   KD_160527_CD160_IN_01     3 3.256844 110675
    ##  6: 1590.808  CD160    0.167  KD_160530_CD160_10s_01     2 3.262774  99894
    ##  7: 1590.808  CD160    0.167  KD_160530_CD160_10s_02     2 3.264558 117541
    ##  8: 1590.808  CD160    0.167  KD_160530_CD160_10s_03     2 3.263795  90562
    ##  9: 1590.808  CD160    0.167  KD_160530_CD160_10s_04     2 3.273656  66131
    ## 10: 1590.808  CD160    1.000 KD_160530_CD160_1min_01     2 3.262300 109301
    ##        Center
    ##         <num>
    ##  1: 1591.2584
    ##  2:  796.3552
    ##  3:  531.2633
    ##  4:  796.3634
    ##  5:  531.2849
    ##  6:  800.3610
    ##  7:  800.3852
    ##  8:  800.3682
    ##  9:  800.4242
    ## 10:  800.7878

As you can see, the data file has a very specific structure and is not informative yet. In the file, we have `m/z` values for each `z` value (charge) for each time point for each state of each peptide, repeated as many times as measurement was repeated (each measurement should be repeated at least three times).

Our aim is to have one result with an uncertainty of the measurement per each peptide in each biological state in each measured time point - data in this format allows further calculations, e.q. calculating deuterium uptake values.

For a better understanding of the process of aggregating the data, see the `Data aggregation` article.

Within each replicate of the measurement (we recognize each replicate by the `File` value), the `m/z` values are provided for each possible `z` value. The `m/z` values are in the `Center` column, as it is a geometrical centroid calculated from the isotopic envelope. Firstly, we have to calculate the mass value, measured experimentally:

\[expMass = z \times (Center-protonMass)\tag{1}\]

To aggregate data from different `z` values, we have to calculate the mean mass weighted by intensity. Additional information about this step and how the weighted mean impacts the results can be found in `Mass calculation` article.

\[aggMass = \frac{1}{N}\sum_{k = 1}^{N}Inten_k{\cdot}pepMass_k\tag{2}\].

Where:

- \(aggMass\) - mass of the peptide [Da], average from replicates,
- \(Inten_k\) - intensity of the measurement,
- \(pepMass\) - mass of the peptide, calculated using Equation 1.

As we use the aggregated result from the replicates, we need to calculate an uncertainty associated with the measurement. We use the mean value as the final result, so we need to calculate error as a standard deviation of the mean, according to the Equation 3:

\[u(\vec{x}) = \sqrt{\frac{ \sum_{i=1}^n \left( x_{i} - \overline{x} \right)^2}{n(n-1)}}\tag{3}\].

Where:

- \(x_{i}\) - measured value from a replicate,
- \(\overline{x}\) - mean value from all of the replicates,
- \(n\) - number of replicates.

Now we have the format we want for further calculations.

### Calculation of the deuterium uptake

HaDeX package provides the calculated values in different forms. All of them are provided with associated uncertainty of the measurement. All of the uncertainties are derived from the formula - the Law of propagation of uncertainty:

\[u_{c}(y) = \sqrt{\sum_{k} \left[ \frac{\partial y}{\partial x_{k}} u(x_{k}) \right]^2}\]

#### Deuterium uptake

Deuterium uptake is the increase of the mass of the peptide in time \(t\). The minimal exchange control \(m_{t_0}\) is mass measured directly after adding the buffer (before the start of the exchange), and \(m_t\) is the mass measured in chosen time point \(t\). The value is in Daltons [Da].

\[D = m_{t} - m_{t_0}\] The uncertainty associated with deuterium uptake [Da] (based on equation 3):

\[u_c(D) = \sqrt{u(m_t)^2 + u(m_{t_0})^2}\]

#### Fractional deuterium uptake

Fractional deuterium uptake is the ratio of the increase of the mass in time \(t\) to the maximal exchange control. The maximal exchange control \(m_{t_{100}}\) is measured after a long time (chosen by the experimenter, usually 1440 min = 24 h). It is assumed that after this long time, the exchange is finished. The minimal exchange control \(m_{t_0}\) is mass measured directly after adding the buffer (before the start of the exchange), and \(m_t\) is the mass measured in chosen time point \(t\). This value is a percentage value [%].

\[D_{frac} = \frac{m_{t} - m_{t_0}}{m_{t_{100}} - m_{t_0}}\]

The uncertainty associated with fractional deuterium uptake [%] (based on equation 3):

\[u_{c}(D_{frac}) = \sqrt{ \left[ \frac{1}{m_{t_{100}}-m_{t_0}} u(m_{t}) \right]^2 + \left[ \frac{m_{t} - m_{t_{100}}}{(m_{t_{100}}-m_{t_0})^2} u(m_{t_0}) \right]^2 + \left[ \frac{m_{t_0} - m_{t}}{(m_{t_{100}}-m_{t_0})^2} u (m_{t_{100}}) \right]^2}\]

#### Theoretical deuterium uptake

Theoretical deuterium uptake is the increase of mass in time \(t\) compared with the theoretical value of the peptide mass without any exchange (\(MHP\) - a mass of the singly charged monoisotopic molecular ion), and \(m_t\) is the mass measured in chosen time point \(t\). This value is in daltons [Da]:

\[D_{theo} = m_{t} - MHP\]

The uncertainty associated with theoretical deuterium uptake [Da] (the \(MHP\) value is a constant without measurement uncertainty - based on the equation 3):

\[u(D_{theo}) = u(m_t)\]

#### Theoretical fractional deuterium uptake

Theoretical fractional deuterium uptake is the ratio of the increase of mass in time \(t\) compared with a theoretical value of the mass of the peptide without any exchange to the possible theoretical increase of the mass, based on the maximal potential uptake of the peptide (based on the peptide sequence). This value is a percentage value [%].

\[D_{theo, frac} = \frac{m_{t}-MHP}{MaxUptake \times protonMass}\]

The uncertainty associated with theoretical fractional deuterium uptake [%] (based on the equation 3):

\[u(D_{theo, frac}) = \left|\frac{1}{MaxUptake \times protonMass} u(D_{t}) \right|\]

#### Differential values

Differential value is the way to see how the deuterium uptake differs between two biological states. It allows seeing if the possible difference is statistically important (more information below). This value is calculated as the difference between the previously described (in a chosen form) deuterium uptake of the first and second states.

\[diff = D_{1} - D_{2}\] The uncertainty associated with the difference of deuterium uptake (based on the equation 3):

\[u_{c}(diff) = \sqrt{u(D_{1})^2 + u(D_{2})^2}\]

The convenient way to present results calculated as described is the comparison plot and differential plot (Woods’ plot).

### Additional information

If the file contains modified peptides - the value from column `Modification` is added to the value from column `State` and is treated as a new biological state. The further aspects of the analysis are the same as for non-modified peptides.