MATH1324 Assignment 4

Statistical Evaluation of Mice Protein Expression Data Set

Executive Summary

The data (‘Mice Protein Expression Data Set’) was collected online (UCI Machine Learning), consisting of 1080 observations over 82 variables. These data consisted of continuous numerical protein expression data, and categorical data including mouse identification and variable exposure. After data exploration, visualization and data preprocessing, two modes of statistical analysis were employed. The first was linear regression analysis. Prior to fitting any regression, a scatter plot assessing the bi variate relationship between the relevant proteins was inspected. In the three relationships considered, the scatter plots demonstrated evidence of a positive linear relationship. A linear regression model was fitted to predict the dependent variable, ITSN1_N, using measurements of DYRK1A_N over all classes of mice. The overall regression model was statistically significant, F(1,1063)=6779.2, p<.001, and explained 86.5% of the variability in ITSN1_N.A linear regression model was fitted to predict the dependent variable, pERK_N, using measurements of DYRK1A_N over all classes of mice. The overall regression model was statistically significant, F(1,1063)=6976.3, p<.001, and explained 86.8% of the variability in pERK_N. A linear regression model was fitted to predict the dependent variable, pERK_N, using measurements of BRAF_N over all classes of mice. The overall regression model was statistically significant, F(1,1063)=4529.1, p<.001, and explained 81.0% of the variability in pERK_N. For all three regression models the 95% CI for the intercept did not pass through 0, which simply indicated the presence of a background, or base, level of protein. For the class c-CS-s, 7 paired t-tests were performed. For ARC_N and BRAF_N (n = 120), the mean difference was found to be -0.256 (SD = 0.101), with t(df=119) = 27.724, p < 0.001, 95% [0.238, 0.274]. There was a statistically significant mean difference. For BRAF_N and DYRK1A_N (n = 120), the mean difference was found to be -0.047 (SD = 0.058), with t(df=119) = 8.871, p < 0.001, 95% [0.037, 0.058]. There was a statistically significant mean difference. For DYRK1A_N and ITSN1_N (n = 120), the mean difference was found to be -0.189 (SD = 0.061), with t(df=119) = 34.216, p < 0.001, 95% [0.178, 0.200]. There was a statistically significant mean difference. For ITSN1_N and pERK_N (n = 120), the mean difference was found to be 0.006 (SD = 0.094), with t(df=119) = -0.696, p > 0.005, 95% [-0.023, 0.011].There was no statistically significant mean difference. For pERK_N and pNUMB_N (n = 120), the mean difference was found to be 0.200 (SD = 0.132), with t(df=119) = -16.569, p < 0.001, 95% [-0.224, -0.176]. There was a statistically significant mean difference. For pNUMB_N and S6_N (n = 120), the mean difference was found to be -0.048 (SD = 0.136), with t(df=119) = 3.892, p < 0.001, 95% [0.024, 0.073]. There was a statistically significant mean difference. For S6_N and SOD1_N (n = 120), the mean difference was found to be 0.125 (SD = 0.131), with t(df=119) = -10.45, p < 0.001, 95% [-0.148, -0.101]. There was a statistically significant mean difference. QQ plots were not used due to all sample and sub sample sizes (n > 30, normality assumed). The granovo.ds() function was used to provide dependent sample assessment plots and summary stats.

Hypothesis Testing

The first statistical analysis will involve linear regression, with the following hypothesis testing:

Linear Regression

• H0:The data do not fit the linear regression model
• HA:The data fit the linear regression model

The Constant, or Intercept Value

• H0:α=0
• HA:α≠0

Slope

• H0:β=0
• HA:β≠0

The second statistical analysis will involve the paired-sample t-test, with the following hypothesis:

Paired-sample t-test

• H0:μΔ=0
• HA:μΔ≠0

Introduction

The chosen data set ‘Mice Protein Expression Data Set’ was generated from experiments by Higuera et al¹ and Ahmed et al². These projects aimed to understand the impacts of Down Syndrome on learning through analysis of protein expression in mice. Down Syndrome (DS) has a prevalence globally of 1 in a 1000 live human births, and is the most common genetically defined cause of intellectual disabilities^1,3. DS in humans is caused by the presence of an additional chromosome 21, referred to as trisomy³. Protein expression is disrupted by human trisomy 21, leading to the physical and intellectual manifestations associated with DS. Due to its prevalence and health implications, a strong imperative exists to further understand and treat the condition.

Davisson et al., successfully manipulated a mouse genome to produce several models of DS in rodents⁴. Known as ‘Ts65Dn’ this mouse is the best-characterized of the DS rodent models⁵. In generating the ‘Mice Protein Expression Data Set’ Higuera et al employed Ts65Dn and normal mice in experimental and control groups, exposing them to a range of variables. The rodents were then euthanized and their cortex protein levels were analysed in a quantitative fashion. From three binary variables, eight classes of mice were used to generate the data set. The eight classes are summarized in Figure 1.

The work of Higuera et al and Ahmed et al aimed to assess the efficacy of pharmacotherapies for treatment of DS - an avenue of treatment that has never been successfully implemented. Ahmed et al statistically evaluated the ‘Mice Protein Expression Data Set’ through the use of the Wilcoxon test, with the subsequent production of ‘self-organizing maps’ to assess proteins critical to learning. Higuera et al also used pair-wise comparisons to evaluate the significance of difference between pairs of the classes, specifically to assess protein dynamics.

In this analysis of the ‘Mice Protein Expression Data Set’ linear relationships between protein expression levels will be statistically evaluated, followed by pair sample t-tests on protein expression for mice in the class ‘c-CS-s’.

Fig 1. Classes of mice. (A) There are eight classes of mice based on genotype (control, c, and trisomy, t), stimulation to learn (Context-Shock, CS, and Shock-Context, SC) and treatment (saline, s, and memantine, m). Learning outcome indicates the response to learning for each class. (B) Number of mice in each class. (C) Format of protein expression data: rows are individual mice, and columns, P 1 … P77, are the measured levels of the 77 proteins⁶.

RStudio Libraries

The libraries rmarkdown, GGally, car, ggplot2, dplyr, gsheet, gridExtra,htmltools, reshape2, granova, psychometric, Hmisc, qwraps & outliers were employed during the analysis.

Data Set

The Excel file ‘Data_Cortex_Nuclear.xls’ was downloaded from UCI’s machine learning repository⁷ into Google Drive (s3644119 at RMIT University) and the imported into the R Studio interactive environment as “ds”.

url <- "https://docs.google.com/spreadsheets/d/158zPd4XCYoaXNzHA2OJPkOmzSWYjwFoEuOiMzV1O-rU/edit?usp=sharing"
ds <- gsheet2tbl(url)

Data Checking

The initial data checking is summarized below (functioning code in Appendix).

Function	Purpose / Outcome
summary(ds)	Confirming the successful importation of the data set. Size was 1080 observations over 82 variables. The 77 protein attributes are continuous numerical data, with NaN values present.
colnames(ds)	Confirming the column names present in the data set. The first column is MouseID (12 - 15 observations per mouse, per protein). The final four columns contain the categorical data about each mouse.
MouseID <- ds$MouseID	Each mouseID is appended with the suffix ’_n’ (where 1 <- n <- 15). For example MouseID ‘309’ is recorded as 309_1, 309_2, … 309_15.

Data Preprocessing - Iteration 1

The native data set will be preprocessed in four iterations for use in our analysis. These data were collected such that they are all on the same scale (approximately 0 - 4) and are intended for direct comparison without any transformation (for example a value of 0.1 for protein A and 1.0 for protein B shows that protein B is expressed 10 times that of protein A). The only transformation performed on these data was column subtraction, for pair t-test analysis (see Data Preprocessing - Iteration 3).

Stripping the measurement count from each mouse

During data collection, per each individual mouse, per each protein, 12 - 15 expression measurements were taken in vitro. As mentioned in the summary above, these were denoted as ’_n’ (where 1 <- n <- 15). For the purpose of this investigation, the _n notation is not required, and will be stripped from the data. The function table(head(ds$MouseID, 150)) samples the first 10 mice in the data set, showing successful removal of _n notation.

MouseID <- gsub("\\_.*", "", ds$MouseID)
ds$MouseID <- MouseID

table(head(ds$MouseID, 150))

 309  311  320  321  322 3415 3499 3507 3520 3521 
  15   15   15   15   15   15   15   15   15   15 

Selecting the target proteins & creating a new dataset

Through the use of self-organizing feature maps, Higuera et al were able to determine the most discriminant proteins in comparison of the control mice classes and the trisomic mice classes¹. For this analysis, these tabulated results were assessed in a semi-quantitative fashion⁸ and the proteins ARC_N, BRAF_N, DYRK1A_N, ITSN1_N, pERK_N, pNUMB_N, S6_N & SOD1_N were selected. A vector of these identifiers was created as target_attributes_proteins. These target proteins, along with the categorical tags Genotype, Treatment, Behavior and class were added to another vector, target_attributes_all. A new data set, ds_filtered was then created, with the native data set observations for the variables of the target_attributes_all vector.

target_attributes_proteins <- c("ARC_N", "BRAF_N", "DYRK1A_N", "ITSN1_N", "pERK_N", 
    "pNUMB_N", "S6_N", "SOD1_N")

target_attributes_all <- c("MouseID", "ARC_N", "BRAF_N", "DYRK1A_N", "ITSN1_N", 
    "pERK_N", "pNUMB_N", "S6_N", "SOD1_N", "Genotype", "Treatment", "Behavior", 
    "class")

ds_filtered <- ds[, target_attributes_all]

Checking the data set ds_filtered

The categorical values in ds_filtered were checked with unique(ds_filtered[,10:13]), not typographical errors were present, as below.

categorical_counts <- ds_filtered[, 10:13]
unique(categorical_counts)

The categorical variable counts are summarized in the below (functions executed in Appendix).

Function	Counts	Total
table(ds_filtered$Genotype)	Control = 570, Ts65Dn = 510	1080
table(ds_filtered$Treatment)	Memantine = 570, Saline = 510	1080
table(ds_filtered$Behavior)	C/S = 525, S/C = 555	1080
table(ds_filtered$class)	c-CS-m = 150, c-CS-s = 135, c-SC-m = 150, c-SC-s = 135, t-CS-m = 135, t-CS-s = 105, t-SC-m = 135, t-SC-s = 135	1080

Data Preprocessing - Iteration 2

Locating NaN Values

The coordinate locations for NaN values are displayed below (the result output was transposed for readability). The expression ds_filtered[c(988, 989, 990),c(1, 10, 11, 12, 13)] was used to identify the mouse/mice and corresponding categories.

t(which(is.na(ds_filtered), arr.ind = TRUE))

    [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18]
row  988  989  990  988  989  990  988  989  990   988   989   990   988   989   990   988   989   990
col    3    3    3    4    4    4    5    5    5     6     6     6     7     7     7     9     9     9

ds_filtered[c(988, 989, 990), c(1, 10, 11, 12, 13)]

Filling the NaN Values

Through use of table(ds_filtered$class) we can see that n = 105 measurements were taken for class ‘t-SC-s’. As outlined in figure 1, ‘t-SC-c’ corresponds to mice with the Ts65Dn genotype (trisomy, t), not stimulated to learn (Shock Context, SC) and saline treatment (saline, s). The mean value for class ‘t-SC-s’ (n = 105), will be used to fill the NaN values.

tSCs_filter <- ds_filtered$class == "t-SC-s"
NaN_column_mask <- c(3, 4, 5, 6, 7, 9)
NaN_3426_tSCs <- ds_filtered[tSCs_filter, NaN_column_mask]
summary_3426_tSCs <- summary(NaN_3426_tSCs)
summary_3426_tSCs

     BRAF_N          DYRK1A_N         ITSN1_N           pERK_N          pNUMB_N           SOD1_N      
 Min.   :0.1940   Min.   :0.1633   Min.   :0.3284   Min.   :0.1492   Min.   :0.2352   Min.   :0.3841  
 1st Qu.:0.2456   1st Qu.:0.2781   1st Qu.:0.4715   1st Qu.:0.2807   1st Qu.:0.2974   1st Qu.:0.5534  
 Median :0.2844   Median :0.3479   Median :0.5519   Median :0.3552   Median :0.3591   Median :0.6467  
 Mean   :0.2867   Mean   :0.3375   Mean   :0.5491   Mean   :0.3577   Mean   :0.3577   Mean   :0.7214  
 3rd Qu.:0.3264   3rd Qu.:0.3916   3rd Qu.:0.6249   3rd Qu.:0.4412   3rd Qu.:0.4072   3rd Qu.:0.8075  
 Max.   :0.4306   Max.   :0.5006   Max.   :0.8362   Max.   :0.5562   Max.   :0.5203   Max.   :1.6105  
 NA's   :3        NA's   :3        NA's   :3        NA's   :3        NA's   :3        NA's   :3       

write.csv(ds_filtered, file = "mouse_data_filtered.csv")
ds_filled_NaN <- gsheet2tbl("https://docs.google.com/spreadsheets/d/1FKFINItxyosgFhwiihpT3MSuMTxR-LaYPNG_XNctwlU/edit?usp=sharing")

The filtered mouse data was exported using write.csv and added to Google Sheets. The NaN values were filled as follows BRAF_N = 0.2867, DYRK1A_N = 0.3375, ITSN1_N = 0.5491, pERK_N = 0.3577, pNUMB_N = 0.3577 and SOD1_N = 0.7214. The data set was then imported as ds_Filled_NaN. These data were checked for NaN as follows.

NaN_check <- ds_filled_NaN[tSCs_filter, NaN_column_mask]
summary_NaN_check <- summary(NaN_check)
summary_NaN_check

     BRAF_N          DYRK1A_N         ITSN1_N           pERK_N          pNUMB_N           SOD1_N      
 Min.   :0.1940   Min.   :0.1633   Min.   :0.3284   Min.   :0.1492   Min.   :0.2352   Min.   :0.3841  
 1st Qu.:0.2467   1st Qu.:0.2785   1st Qu.:0.4755   1st Qu.:0.2823   1st Qu.:0.2996   1st Qu.:0.5536  
 Median :0.2867   Median :0.3466   Median :0.5491   Median :0.3560   Median :0.3577   Median :0.6571  
 Mean   :0.2867   Mean   :0.3375   Mean   :0.5491   Mean   :0.3577   Mean   :0.3577   Mean   :0.7214  
 3rd Qu.:0.3252   3rd Qu.:0.3900   3rd Qu.:0.6243   3rd Qu.:0.4404   3rd Qu.:0.4070   3rd Qu.:0.8067  
 Max.   :0.4306   Max.   :0.5006   Max.   :0.8362   Max.   :0.5562   Max.   :0.5203   Max.   :1.6105  

Mean Fill Summary	BRAF_N	DYRK1A_N	ITSN1_N	pERK_N	pNUMB_N	SOD1_N
Native Data Mean	0.2867	0.3375	0.5491	0.3577	0.3577	0.7214
Preprocessed Data Mean	0.2867	0.3375	0.5491	0.3577	0.3577	0.7214
Delta Mean	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

• All mean values remained the same to four decimal places.

Data Exploration through Visualization

Scatter Plot Matrix

The preprocessed data will first be visualized with a scatter plot matrix using the ggpairs function. The upper section of the plot will be an xy contour, the lower an xy scatter and the diagonal density plots. A scatter plot matrix is a suitable at this stage as it gives a quantitative overview of these data and provides direction for further analysis.

• Note scatter plot matrix code will be displayed only once.

scatter_matrix <- ggpairs(data = ds_filled_NaN, columns = target_attributes_proteins, 
    mapping = aes(colour = class), diag = list(continuous = wrap("densityDiag", 
        alpha = I(0.1)), mapping = ggplot2::aes(fill = class)), upper = list(continuous = wrap("density", 
        alpha = I(0.5)), combo = "box"), lower = list(continuous = wrap("points", 
        alpha = I(0.4), size = 0.1)))
scatter_matrix_adjusted <- scatter_matrix + theme(panel.spacing = grid::unit(0, 
    "lines"), axis.text = element_text(size = rel(0.5)), strip.text = element_text(face = "bold", 
    size = 7), strip.text.x = element_text(margin = margin(0.1, 0, 0.1, 0, "cm")), 
    strip.text.y = element_text(margin = margin(0, 0.1, 0, 0.1, "cm")))
scatter_matrix_adjusted + theme(panel.border = element_rect(fill = NA, colour = "grey30", 
    size = 0.2))

The resultant plot, shows six of the proteins to be correlated (qualitatively) in a linear fashion;

• DYRK1A_N vs BRAF_N
• ITSN1_N vs BRAF_N
• pERK_N vs BRAF_N
• ITSN1_N vs DYRK1A_N
• pERK_N vs DYRK1A_N
• pERK_N vs ITSN1_N

This will provide direction for subsequent statistical analysis.

Other trends noticeable include inversely proportional relationships (e.g., SOD1_N vs BRAF_N), weak correlation (e.g., pNUMB_N vs BRAF_N) and no correlation (e.g., pNUMB_N vs ARC_N). Also of note, in the columns ARC_N, BRAF_N, DYRK1A_N, ITSN1_N and pERK_N, a series of points (amber colour) are seen to lay outside the main clusters in every individual scatter plot. Bar charts for two target proteins exhibiting these outliers were plotted.

Bar Chart for pERK & BRAF

The resultant plots show clusters of outliers for the class, ‘c-CS-s’.

• Note box plot code will be displayed only once.

BRAF_N_Hist <- ggplot(data = ds_filled_NaN, aes(x = ds_filled_NaN$class, y = BRAF_N, 
    fill = ds_filled_NaN$class)) + geom_boxplot() + theme(legend.title = element_blank(), 
    axis.title = element_text(size = 8)) + labs(title = NULL, x = "BRAF_N Expression", 
    y = NULL) + guides(fill = FALSE) + coord_flip()

pERK_N_Hist <- ggplot(data = ds_filled_NaN, aes(x = ds_filled_NaN$class, y = pERK_N, 
    fill = ds_filled_NaN$class)) + geom_boxplot() + theme(legend.title = element_blank(), 
    axis.title = element_text(size = 8)) + labs(title = NULL, x = "pERK_N Expression", 
    y = NULL) + guides(fill = FALSE) + coord_flip()

grid.arrange(BRAF_N_Hist, pERK_N_Hist, nrow = 2)

The most extreme outlier for each protein was determined using the outlier() function, in conjunction with filtering.

ds_filled_NaN[ds_filled_NaN$ARC_N == outlier(ds_filled_NaN$ARC_N), c(1, 2, 10, 
    11, 12, 13)]

ds_filled_NaN[ds_filled_NaN$BRAF_N == outlier(ds_filled_NaN$BRAF_N), c(1, 3, 
    10, 11, 12, 13)]

ds_filled_NaN[ds_filled_NaN$DYRK1A_N == outlier(ds_filled_NaN$DYRK1A_N), c(1, 
    4, 10, 11, 12, 13)]

ds_filled_NaN[ds_filled_NaN$ITSN1_N == outlier(ds_filled_NaN$ITSN1_N), c(1, 
    5, 10, 11, 12, 13)]

ds_filled_NaN[ds_filled_NaN$pERK_N == outlier(ds_filled_NaN$pERK_N), c(1, 6, 
    10, 11, 12, 13)]

ds_filled_NaN[ds_filled_NaN$pNUMB_N == outlier(ds_filled_NaN$pNUMB_N), c(1, 
    7, 10, 11, 12, 13)]

ds_filled_NaN[ds_filled_NaN$S6_N == outlier(ds_filled_NaN$S6_N), c(1, 8, 10, 
    11, 12, 13)]

ds_filled_NaN[ds_filled_NaN$SOD1_N == outlier(ds_filled_NaN$SOD1_N), c(1, 9, 
    10, 11, 12, 13)]

Max. Outlier Summary	ARC_N	BRAF_N	DYRK1A_N	ITSN1_N	pERK_N	pNUMB_N	S6_N	SOD1_N
Value	0.0673	2.1334	2.5164	2.6027	3.5667	0.6311	0.8226	1.8729
MouseID	3415	3484	3484	3484	3484	3497	3483	3411
Genotype	Control	Control	Control	Control	Control	Control	Ts65Dn	Ts65Dn
Treatment	Memantine	Saline	Saline	Saline	Saline	Saline	Saline	Memantine
Behaviour	C/S	C/S	C/S	C/S	C/S	C/S	C/S	S/C
Class	c-CS-m	c-CS-m	c-CS-m	c-CS-s	c-CS-s	c-CS-s	t-CS-s	t-SC-m

• Mouse ID 3484 contributed 50% of the maximum outliers, and was dropped from the data set.

Data Preprocessing - Iteration 3

Dropping MouseID 3484

ds_filled_NaN <- ds_filled_NaN[!(ds_filled_NaN$MouseID == 3484),]

• This gives a resultant data set of size [13 variables by 1065 observations].

Data Exploration through Visualization

Scatter Plot Matrix - MouseID 3484 dropped

Box Plots for each Protein

The bar plots were an excellent source of qualitative information. As demonstrated for ITSN1_N and SOD1_N, below.

Protein	Qualitative Observation
ITSN1_N	The distributions and corresponding mean values occur in a series of pairs. It appears that first two components of each class (genotype and learning stimuli) are deterministic in the expression of ITSN1_N.
SOD1_N	Expression of SOD1_N is determined predominantly by the learning stimuli applied. In the four classes of CS, the expression levels have tight distributions and similar means. In the four classes of SC, the expression levels have wide distributions, with varied means.

Statistical Analysis Part 1 - Linear Regression and Correlation

Of the 6 previously mentioned pairs of qualitative linear relationships, three will be used for statistical analysis.

• ITSN1_N vs DYRK1A_N
• pERK_N vs DYRK1A_N
• pERK_N vs BRAF_N

For each pair of target proteins, all classes will be analyzed together. If linear relationships are statistically significant, this will indicate the dependent relationships are maintained over the changes in genotype, treatment and behaviour.

target_attributes_linear <- c("BRAF_N", "DYRK1A_N", "ITSN1_N", "pERK_N")

ITSN1_N vs DYRK1A_N

Fitting the Data to a Linear Regression Model

• H0: Accross all eight classes of mice, the expression of ITSN1_N was not linearly dependent to the expression of DYRK1A_N
• HA: Accross all eight classes of mice, the expression of ITSN1_N was linearly dependent to the expression of DYRK1A_N

ITSN1_N_VS_DYRK1A_N <- lm(ITSN1_N ~ DYRK1A_N, data = ds_filled_NaN)
ITSN1_N_VS_DYRK1A_N %>% summary()

Call:
lm(formula = ITSN1_N ~ DYRK1A_N, data = ds_filled_NaN)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.54552 -0.04070 -0.00268  0.03774  0.24657 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.178032   0.005445   32.70   <2e-16 ***
DYRK1A_N    1.037442   0.012600   82.34   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.0643 on 1063 degrees of freedom
Multiple R-squared:  0.8645,    Adjusted R-squared:  0.8643 
F-statistic:  6779 on 1 and 1063 DF,  p-value: < 2.2e-16

ITSN1_N_VS_DYRK1A_N %>% anova()

Analysis of Variance Table

Response: ITSN1_N
            Df  Sum Sq Mean Sq F value    Pr(>F)    
DYRK1A_N     1 28.0244 28.0244  6779.2 < 2.2e-16 ***
Residuals 1063  4.3943  0.0041                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

• The p-value of the observed F statistic was found to be 2.2e-16. As p is less than the 0.05 level of significance, we reject H0.

The Constant, or Intercept Value

• H0:α=0
• HA:α≠0

ITSN1_N_VS_DYRK1A_N %>% summary() %>% coef()

             Estimate  Std. Error  t value      Pr(>|t|)
(Intercept) 0.1780317 0.005445164 32.69538 7.787868e-163
DYRK1A_N    1.0374418 0.012600150 82.33567  0.000000e+00

• t = 32.696, p < 0.001
  The constant is statistically significant at the 0.05 level. This means that there is statistically significant evidence that the constant is not 0. Their would always be some amount of the target proteins being expressed.

ITSN1_N_VS_DYRK1A_N %>% confint()

                2.5 %    97.5 %
(Intercept) 0.1673472 0.1887162
DYRK1A_N    1.0127178 1.0621658

• 95% CI for the Intercept is found to be [0.167, 0.189]
  H0:α=0 is not captured by this interval, so was rejected.

The Slope

• H0:β=0
• HA:β≠0

2 * pt(q = 82.33567, df = 1063, lower.tail = FALSE)

[1] 0

As p < .05, we reject H0. The 95% CI for b was found to [1.013, 1.062]. This 95% CI does not capture H0, therefore it was rejected.

There was a statistically significant positive relationship between the expression of DYRK1A_N and ITSN1_N.

ITSN1_N_VS_DYRK1A_N_XY <- ggplot(data = ds_filled_NaN, aes(x = DYRK1A_N, y = ITSN1_N, 
    colour = class))
ITSN1_N_VS_DYRK1A_N_XY + geom_point(alpha = I(0.9), size = 0.8) + stat_smooth(method = "lm", 
    col = "black", size = 0.5) + labs(title = "ITSN1_N versus DYRK1A_N Protein Expression Scatter Plot", 
    y = "ITSN1_N", x = "DYRK1A_N") + theme(legend.title = element_blank(), axis.title = element_text(size = 8), 
    title = element_text(size = 9)) + annotate("text", x = 0.6, y = 1.25, label = "R Squared") + 
    annotate("text", x = 0.6, y = 1.15, label = format(summary(lm(ITSN1_N ~ 
        DYRK1A_N, data = ds_filled_NaN))$r.squared, digits = 3))

pERK_N vs DYRK1A_N

Fitting the Data to a Linear Regression Model

• H0: Accross all eight classes of mice, the expression of pERK_N was not linearly dependent to the expression of DYRK1A_N
• HA: Accross all eight classes of mice, the expression of pERK_N was linearly dependent to the expression of DYRK1A_N

pERK_N_VS_DYRK1A_N <- lm(pERK_N ~ DYRK1A_N, data = ds_filled_NaN)
pERK_N_VS_DYRK1A_N %>% summary()

Call:
lm(formula = pERK_N ~ DYRK1A_N, data = ds_filled_NaN)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.94073 -0.05411 -0.00875  0.05405  0.31963 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.048086   0.007251  -6.631 5.28e-11 ***
DYRK1A_N     1.401485   0.016779  83.524  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.08562 on 1063 degrees of freedom
Multiple R-squared:  0.8678,    Adjusted R-squared:  0.8677 
F-statistic:  6976 on 1 and 1063 DF,  p-value: < 2.2e-16

pERK_N_VS_DYRK1A_N %>% anova()

Analysis of Variance Table

Response: pERK_N
            Df Sum Sq Mean Sq F value    Pr(>F)    
DYRK1A_N     1 51.143  51.143  6976.3 < 2.2e-16 ***
Residuals 1063  7.793   0.007                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

• The p-value of the observed F statistic was found to be 2.2e-16. As p is less than the 0.05 level of significance, we reject H0.

The Constant, or Intercept Value

• H0:α=0
• HA:α≠0

pERK_N_VS_DYRK1A_N %>% summary() %>% coef()

             Estimate  Std. Error   t value     Pr(>|t|)
(Intercept) -0.048086 0.007251214 -6.631441 5.280216e-11
DYRK1A_N     1.401485 0.016779364 83.524345 0.000000e+00

• t = -6.631, p < 0.001
  The constant is statistically significant at the 0.05 level. This means that there is statistically significant evidence that the constant is not 0. Their would always be some amount of the target proteins being expressed.

pERK_N_VS_DYRK1A_N %>% confint()

                  2.5 %      97.5 %
(Intercept) -0.06231432 -0.03385768
DYRK1A_N     1.36856094  1.43440981

• 95% CI for the Intercept is found to be [-0.062, -0.034]
  H0:α=0 is not captured by this interval, so was rejected.

The Slope

• H0:β=0
• HA:β≠0

2 * pt(q = 83.524345, df = 1063, lower.tail = FALSE)

[1] 0

As p < .05, we reject H0. The 95% CI for b was found to [1.369, 1.434]. This 95% CI does not capture H0, therefore it was rejected.

There was a statistically significant positive relationship between the expression of pERK_N and DYRK1A_N.

pERK_N_VS_DYRK1A_N_XY <- ggplot(data = ds_filled_NaN, aes(x = DYRK1A_N, y = pERK_N, 
    colour = class))
pERK_N_VS_DYRK1A_N_XY + geom_point(alpha = I(0.9), size = 0.8) + stat_smooth(method = "lm", 
    col = "black", size = 0.5) + labs(title = "pERK_N versus DYRK1A_N Protein Expression Scatter Plot", 
    y = "pERK_N", x = "DYRK1A_N") + theme(legend.title = element_blank(), axis.title = element_text(size = 8), 
    title = element_text(size = 9)) + annotate("text", x = 0.6, y = 1.3, label = "R Squared") + 
    annotate("text", x = 0.6, y = 1.2, label = format(summary(lm(pERK_N ~ DYRK1A_N, 
        data = ds_filled_NaN))$r.squared, digits = 3))

pERK_N vs BRAF_N

Fitting the Data to a Linear Regression Model

• H0: Accross all eight classes of mice, the expression of pERK_N was not linearly dependent to the expression of BRAF_N
• HA: Accross all eight classes of mice, the expression of pERK_N was linearly dependent to the expression of BRAF_N

pERK_N_VS_BRAF_N <- lm(pERK_N ~ BRAF_N, data = ds_filled_NaN)
pERK_N_VS_BRAF_N %>% summary()

Call:
lm(formula = pERK_N ~ BRAF_N, data = ds_filled_NaN)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.30232 -0.06317 -0.00958  0.04958  0.42462 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.066629   0.009219  -7.228 9.37e-13 ***
BRAF_N       1.629637   0.024215  67.299  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1027 on 1063 degrees of freedom
Multiple R-squared:  0.8099,    Adjusted R-squared:  0.8097 
F-statistic:  4529 on 1 and 1063 DF,  p-value: < 2.2e-16

pERK_N_VS_BRAF_N %>% anova()

Analysis of Variance Table

Response: pERK_N
            Df Sum Sq Mean Sq F value    Pr(>F)    
BRAF_N       1 47.733  47.733  4529.1 < 2.2e-16 ***
Residuals 1063 11.203   0.011                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

• The p-value of the observed F statistic was found to be 2.2e-16. As p is less than the 0.05 level of significance, we reject H0.

The Constant, or Intercept Value

• H0:α=0
• HA:α≠0

pERK_N_VS_BRAF_N %>% summary() %>% coef()

               Estimate  Std. Error  t value     Pr(>|t|)
(Intercept) -0.06662867 0.009218592 -7.22764 9.369867e-13
BRAF_N       1.62963697 0.024214953 67.29879 0.000000e+00

• t = -7.228, p < 0.001
  The constant is statistically significant at the 0.05 level. This means that there is statistically significant evidence that the constant is not 0. Their would always be some amount of the target proteins being expressed.

pERK_N_VS_BRAF_N %>% confint()

                  2.5 %      97.5 %
(Intercept) -0.08471737 -0.04853996
BRAF_N       1.58212243  1.67715150

• 95% CI for the Intercept is found to be [-0.085, -0.049]
  H0:α=0 is not captured by this interval, so was rejected.

The Slope

• H0:β=0
• HA:β≠0

2 * pt(q = 67.29879, df = 1063, lower.tail = FALSE)

[1] 0

As p < .05, we reject H0. The 95% CI for b was found to [1.582, 1.677]. This 95% CI does not capture H0, therefore it was rejected.

There was a statistically significant positive relationship between the expression of pERK_N and BRAF_N.

Data Preprocessing - Iteration 4

Creating Columns for Paired t-test Analysis

The following columns were created using the mutate() function. All classes were then dropped except ‘c-CS-s’ (this corresponds to the control group with normal genotype, saline treatment and CS learning).

ds_filled_NaN <- ds_filled_NaN %>% mutate(d_ARC_BRAF = BRAF_N - ARC_N)
ds_filled_NaN <- ds_filled_NaN %>% mutate(d_BRAF_DYRK1A = DYRK1A_N - BRAF_N)
ds_filled_NaN <- ds_filled_NaN %>% mutate(d_DYRK1A_ITSN1 = ITSN1_N - DYRK1A_N)
ds_filled_NaN <- ds_filled_NaN %>% mutate(d_ITSN1_pERK = pERK_N - ITSN1_N)
ds_filled_NaN <- ds_filled_NaN %>% mutate(d_pERK_pNUMB = pNUMB_N - pERK_N)
ds_filled_NaN <- ds_filled_NaN %>% mutate(d_pNUMB_S6 = S6_N - pNUMB_N)
ds_filled_NaN <- ds_filled_NaN %>% mutate(d_S6_SOD1 = SOD1_N - S6_N)

ds_cCSs <- ds_filled_NaN[(ds_filled_NaN$class == "c-CS-s"), ]

Statistical Analysis Part 2 - Paired two-sample t-tests

Analysis was conducted for 7 pairs of protein expression levels in all mice from the class ‘c-CS-s’. These were considered dependent (paired) samples as the mice from each individual class were all exposed to the same set of variables.

Critical Value - All Paris

qt(p = 0.025, df = 119)

[1] -1.9801

ARC_N & BRAF_N for c-CS-s

t.test(ds_cCSs$d_ARC_BRAF, mu = 0, alternative = "two.sided")

    One Sample t-test

data:  ds_cCSs$d_ARC_BRAF
t = 27.724, df = 119, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 0.2377760 0.2743528
sample estimates:
mean of x 
0.2560644 

granova.ds(data.frame(ds_cCSs$ARC_N, ds_cCSs$BRAF_N), xlab = "ARC_N", ylab = "BRAF_N")

            Summary Stats
n                 120.000
mean(x)             0.114
mean(y)             0.370
mean(D=x-y)        -0.256
SD(D)               0.101
ES(D)              -2.531
r(x,y)             -0.096
r(x+y,d)           -0.983
LL 95%CI           -0.274
UL 95%CI           -0.238
t(D-bar)          -27.724
df.t              119.000
pval.t              0.000

The t* values are ± 1.98. As t = 27.72 is more extreme than + 1.98, H0 should be rejected (additionally the 95% CI of the mean difference is found to be [0.24 0.27], which does not contain capture H0). There was a statistically significant mean difference between the expression of ARC_N and BRAF_N for the c-CS-s (n = 120).

BRAF_N & DYRK1A_N for c-CS-s

t.test(ds_cCSs$d_BRAF_DYRK1A, mu = 0, alternative = "two.sided")

    One Sample t-test

data:  ds_cCSs$d_BRAF_DYRK1A
t = 8.8709, df = 119, p-value = 8.741e-15
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 0.03654614 0.05754950
sample estimates:
 mean of x 
0.04704782 

granova.ds(data.frame(ds_cCSs$BRAF_N, ds_cCSs$DYRK1A_N), xlab = "BRAF_N", ylab = "DYRK1A_N")

            Summary Stats
n                 120.000
mean(x)             0.370
mean(y)             0.417
mean(D=x-y)        -0.047
SD(D)               0.058
ES(D)              -0.810
r(x,y)              0.828
r(x+y,d)            0.028
LL 95%CI           -0.058
UL 95%CI           -0.037
t(D-bar)           -8.871
df.t              119.000
pval.t              0.000

The t* values are ± 1.98. As t = 8.87 is more extreme than + 1.98, H0 should be rejected (additionally the 95% CI of the mean difference is found to be [0.04 0.06], which does not contain capture H0). There was a statistically significant mean difference between the expression of BRAF_N and DYRK1A_N for the c-CS-s (n = 120).

DYRK1A_N & ITSN1_N for c-CS-s

t.test(ds_cCSs$d_DYRK1A_ITSN1, mu = 0, alternative = "two.sided")

    One Sample t-test

data:  ds_cCSs$d_DYRK1A_ITSN1
t = 34.216, df = 119, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 0.1784135 0.2003316
sample estimates:
mean of x 
0.1893725 

granova.ds(data.frame(ds_cCSs$DYRK1A_N, ds_cCSs$ITSN1_N), xlab = "DYRK1A_N", 
    ylab = "ITSN1_N")

            Summary Stats
n                 120.000
mean(x)             0.417
mean(y)             0.606
mean(D=x-y)        -0.189
SD(D)               0.061
ES(D)              -3.123
r(x,y)              0.887
r(x+y,d)           -0.493
LL 95%CI           -0.200
UL 95%CI           -0.178
t(D-bar)          -34.216
df.t              119.000
pval.t              0.000

The t* values are ± 1.98. As t = 34.22 is more extreme than + 1.98, H0 should be rejected (additionally the 95% CI of the mean difference is found to be [0.18 0.20], which does not contain capture H0). There was a statistically significant mean difference between the expression of DYRK1A_N and ITSN1_N for the c-CS-s (n = 120).

ITSN1_N & pERK_N for c-CS-s

t.test(ds_cCSs$d_ITSN1_pERK, mu = 0, alternative = "two.sided")

    One Sample t-test

data:  ds_cCSs$d_ITSN1_pERK
t = -0.69643, df = 119, p-value = 0.4875
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.02289979  0.01098278
sample estimates:
   mean of x 
-0.005958507 

granova.ds(data.frame(ds_cCSs$ITSN1_N, ds_cCSs$pERK_N), xlab = "ITSN1_N", ylab = "pERK_N")

            Summary Stats
n                 120.000
mean(x)             0.606
mean(y)             0.600
mean(D=x-y)         0.006
SD(D)               0.094
ES(D)               0.064
r(x,y)              0.835
r(x+y,d)           -0.458
LL 95%CI           -0.011
UL 95%CI            0.023
t(D-bar)            0.696
df.t              119.000
pval.t              0.488

The t* values are ± 1.98. As t = -0.70, t is less extreme than than -1.98, H0 cannot be rejected on critical value. The 95% CI of the mean difference is found to be [-0.02 0.01], H0 cannot be rejected on 95% CI. As p > 0.05, we fail to reject H0. There was not a statistically significant mean difference between the expression of ITSN1_N and pERK_N for the c-CS-s (n = 120).

pERK_N & pNUMB_N for c-CS-s

t.test(ds_cCSs$d_pERK_pNUMB, mu = 0, alternative = "two.sided")

    One Sample t-test

data:  ds_cCSs$d_pERK_pNUMB
t = -16.569, df = 119, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.2236380 -0.1758912
sample estimates:
 mean of x 
-0.1997646 

granova.ds(data.frame(ds_cCSs$pERK_N, ds_cCSs$pNUMB_N), xlab = "pERK_N", ylab = "pNUMB_N")

            Summary Stats
n                 120.000
mean(x)             0.600
mean(y)             0.400
mean(D=x-y)         0.200
SD(D)               0.132
ES(D)               1.513
r(x,y)              0.667
r(x+y,d)            0.793
LL 95%CI            0.176
UL 95%CI            0.224
t(D-bar)           16.569
df.t              119.000
pval.t              0.000

The t* values are ± 1.98. As t = -16.57 is more extreme than - 1.98, H0 should be rejected (additionally the 95% CI of the mean difference is found to be [-0.22 -0.18], which does not contain capture H0). There was a statistically significant mean difference between the expression of pERK_N and pNUMB_N for the c-CS-s (n = 120).

pNUMB_N & S6_N for c-CS-s

t.test(ds_cCSs$d_pNUMB_S6, mu = 0, alternative = "two.sided")

    One Sample t-test

data:  ds_cCSs$d_pNUMB_S6
t = 3.892, df = 119, p-value = 0.0001644
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 0.02379530 0.07308288
sample estimates:
 mean of x 
0.04843909 

granova.ds(data.frame(ds_cCSs$pNUMB_N, ds_cCSs$S6_N), xlab = "pNUMB_N", ylab = "S6_N")

            Summary Stats
n                 120.000
mean(x)             0.400
mean(y)             0.449
mean(D=x-y)        -0.048
SD(D)               0.136
ES(D)              -0.355
r(x,y)              0.123
r(x+y,d)           -0.513
LL 95%CI           -0.073
UL 95%CI           -0.024
t(D-bar)           -3.892
df.t              119.000
pval.t              0.000

The t* values are ± 1.98. As t = 3.89 is more extreme than + 1.98, H0 should be rejected (additionally the 95% CI of the mean difference is found to be [0.02 0.07], which does not contain capture H0). There was a statistically significant mean difference between the expression of pNUMB_N and S6_N for the c-CS-s (n = 120).

S6_N & SOD1_N for c-CS-s

t.test(ds_cCSs$d_S6_SOD1, mu = 0, alternative = "two.sided")

    One Sample t-test

data:  ds_cCSs$d_S6_SOD1
t = -10.45, df = 119, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.1482443 -0.1010126
sample estimates:
 mean of x 
-0.1246285 

granova.ds(data.frame(ds_cCSs$S6_N, ds_cCSs$SOD1_N), xlab = "S6_N", ylab = "SOD1_N")

            Summary Stats
n                 120.000
mean(x)             0.449
mean(y)             0.324
mean(D=x-y)         0.125
SD(D)               0.131
ES(D)               0.954
r(x,y)              0.101
r(x+y,d)            0.709
LL 95%CI            0.101
UL 95%CI            0.148
t(D-bar)           10.450
df.t              119.000
pval.t              0.000

The t* values are ± 1.98. As t = -10.45 is more extreme than - 1.98, H0 should be rejected (additionally the 95% CI of the mean difference is found to be [-0.15 -0.10], which does not contain capture H0). There was a statistically significant mean difference between the expression of S6_N and SOD1_N for the c-CS-s (n = 120).

Discussion

The following was determined over the duration of the investigation,

• ITSN1_N vs DYRK1A_N (over all classes of mice) had a statistically significant linearly dependent positive relationship.
• pERK_N vs DYRK1A_N (over all classes of mice) had a statistically significant linearly dependent positive relationship.
• pERK_N vs BRAF_N (over all classes of mice) had a statistically significant linearly dependent positive relationship.

This is signficant as it shows the relationship between these expression of proteins is nto affected by the variables of the experiment.

• There was a statistically significant mean difference between the expression of ARC_N and BRAF_N for the c-CS-s.
• There was a statistically significant mean difference between the expression of BRAF_N and DYRK1A_N for the c-CS-s.
• There was a statistically significant mean difference between the expression of DYRK1A_N and ITSN1_N for the c-CS-s.
• There was not a statistically significant mean difference between the expression of ITSN1_N and pERK_N for the c-CS-s.
• There was a statistically significant mean difference between the expression of pERK_N and pNUMB_N for the c-CS-s.
• There was a statistically significant mean difference between the expression of pNUMB_N and S6_N for the c-CS-s.
• There was a statistically significant mean difference between the expression of S6_N and SOD1_N for the c-CS-s.

The strengths of the investigation included high sample size (overall and in sub-categories), use of various visualizations for data exploration and interprettation, different statistical analysis methods. Limitations included the complex nature of the data set. For example only 7 paired t-tests could reasonably be performed. For the class c-CS-s, this doesn’t represent every possible combination. Comparisons between classes inside individual target proteins would have also been a rich source of data.

Conclusion

The ‘Mice Protein Expression Data Set’, [82 attributes by 1080 observations] was imported into the RStudio interactive environment, explored, cleaned and analysed. Analysis was performed using paired t-tests and linear regression techniques. A series of visualizations, including scatter plot matrices, box plots and dependent sample assessment plots were used. It was determined that several of the proteins had statistically significant linear relationships. Only one pair of classes tested had no statistically significant mean difference, indicating a high degree of expression variablitity for over the class c-CS-s.

References (see last page)

---

Appendix - Not considered for grading

summary(ds)

   MouseID             DYRK1A_N         ITSN1_N           BDNF_N           NR1_N           NR2A_N     
 Length:1080        Min.   :0.1453   Min.   :0.2454   Min.   :0.1152   Min.   :1.331   Min.   :1.738  
 Class :character   1st Qu.:0.2881   1st Qu.:0.4734   1st Qu.:0.2874   1st Qu.:2.057   1st Qu.:3.156  
 Mode  :character   Median :0.3664   Median :0.5658   Median :0.3166   Median :2.297   Median :3.761  
                    Mean   :0.4258   Mean   :0.6171   Mean   :0.3191   Mean   :2.297   Mean   :3.844  
                    3rd Qu.:0.4877   3rd Qu.:0.6980   3rd Qu.:0.3482   3rd Qu.:2.528   3rd Qu.:4.440  
                    Max.   :2.5164   Max.   :2.6027   Max.   :0.4972   Max.   :3.758   Max.   :8.483  
                    NA's   :3        NA's   :3        NA's   :3        NA's   :3       NA's   :3      
     pAKT_N           pBRAF_N          pCAMKII_N        pCREB_N           pELK_N          pERK_N      
 Min.   :0.06324   Min.   :0.06404   Min.   :1.344   Min.   :0.1128   Min.   :0.429   Min.   :0.1492  
 1st Qu.:0.20575   1st Qu.:0.16459   1st Qu.:2.480   1st Qu.:0.1908   1st Qu.:1.204   1st Qu.:0.3374  
 Median :0.23118   Median :0.18230   Median :3.327   Median :0.2106   Median :1.356   Median :0.4436  
 Mean   :0.23317   Mean   :0.18185   Mean   :3.537   Mean   :0.2126   Mean   :1.429   Mean   :0.5459  
 3rd Qu.:0.25726   3rd Qu.:0.19742   3rd Qu.:4.482   3rd Qu.:0.2346   3rd Qu.:1.561   3rd Qu.:0.6633  
 Max.   :0.53905   Max.   :0.31707   Max.   :7.464   Max.   :0.3062   Max.   :6.113   Max.   :3.5667  
 NA's   :3         NA's   :3         NA's   :3       NA's   :3        NA's   :3       NA's   :3       
     pJNK_N            PKCA_N           pMEK_N            pNR1_N          pNR2A_N          pNR2B_N      
 Min.   :0.05211   Min.   :0.1914   Min.   :0.05682   Min.   :0.5002   Min.   :0.2813   Min.   :0.3016  
 1st Qu.:0.28124   1st Qu.:0.2818   1st Qu.:0.24429   1st Qu.:0.7435   1st Qu.:0.5903   1st Qu.:1.3813  
 Median :0.32133   Median :0.3130   Median :0.27739   Median :0.8211   Median :0.7196   Median :1.5637  
 Mean   :0.31351   Mean   :0.3179   Mean   :0.27503   Mean   :0.8258   Mean   :0.7269   Mean   :1.5620  
 3rd Qu.:0.34871   3rd Qu.:0.3523   3rd Qu.:0.30345   3rd Qu.:0.8985   3rd Qu.:0.8486   3rd Qu.:1.7485  
 Max.   :0.49343   Max.   :0.4740   Max.   :0.45800   Max.   :1.4082   Max.   :1.4128   Max.   :2.7240  
 NA's   :3         NA's   :3        NA's   :3         NA's   :3        NA's   :3        NA's   :3       
    pPKCAB_N          pRSK_N            AKT_N             BRAF_N          CAMKII_N          CREB_N      
 Min.   :0.5678   Min.   :0.09594   Min.   :0.06442   Min.   :0.1439   Min.   :0.2130   Min.   :0.1136  
 1st Qu.:1.1683   1st Qu.:0.40414   1st Qu.:0.59682   1st Qu.:0.2643   1st Qu.:0.3309   1st Qu.:0.1618  
 Median :1.3657   Median :0.44060   Median :0.68247   Median :0.3267   Median :0.3603   Median :0.1796  
 Mean   :1.5253   Mean   :0.44285   Mean   :0.68224   Mean   :0.3785   Mean   :0.3634   Mean   :0.1805  
 3rd Qu.:1.8859   3rd Qu.:0.48210   3rd Qu.:0.75969   3rd Qu.:0.4136   3rd Qu.:0.3939   3rd Qu.:0.1957  
 Max.   :3.0614   Max.   :0.65096   Max.   :1.18217   Max.   :2.1334   Max.   :0.5862   Max.   :0.3196  
 NA's   :3        NA's   :3         NA's   :3         NA's   :3        NA's   :3        NA's   :3       
     ELK_N            ERK_N          GSK3B_N           JNK_N            MEK_N            TRKA_N      
 Min.   :0.4977   Min.   :1.132   Min.   :0.1511   Min.   :0.0463   Min.   :0.1472   Min.   :0.1987  
 1st Qu.:0.9444   1st Qu.:1.992   1st Qu.:1.0231   1st Qu.:0.2204   1st Qu.:0.2471   1st Qu.:0.6171  
 Median :1.0962   Median :2.401   Median :1.1598   Median :0.2449   Median :0.2734   Median :0.7050  
 Mean   :1.1734   Mean   :2.474   Mean   :1.1726   Mean   :0.2416   Mean   :0.2728   Mean   :0.6932  
 3rd Qu.:1.3236   3rd Qu.:2.873   3rd Qu.:1.3097   3rd Qu.:0.2633   3rd Qu.:0.3008   3rd Qu.:0.7742  
 Max.   :2.8029   Max.   :5.198   Max.   :2.4758   Max.   :0.3872   Max.   :0.4154   Max.   :1.0016  
 NA's   :18       NA's   :3       NA's   :3        NA's   :3        NA's   :7        NA's   :3       
     RSK_N            APP_N          Bcatenin_N        SOD1_N           MTOR_N           P38_N       
 Min.   :0.1074   Min.   :0.2356   Min.   :1.135   Min.   :0.2171   Min.   :0.2011   Min.   :0.2279  
 1st Qu.:0.1496   1st Qu.:0.3663   1st Qu.:1.827   1st Qu.:0.3196   1st Qu.:0.4104   1st Qu.:0.3520  
 Median :0.1667   Median :0.4020   Median :2.115   Median :0.4441   Median :0.4525   Median :0.4078  
 Mean   :0.1684   Mean   :0.4048   Mean   :2.147   Mean   :0.5426   Mean   :0.4525   Mean   :0.4153  
 3rd Qu.:0.1845   3rd Qu.:0.4419   3rd Qu.:2.424   3rd Qu.:0.6958   3rd Qu.:0.4880   3rd Qu.:0.4663  
 Max.   :0.3051   Max.   :0.6327   Max.   :3.681   Max.   :1.8729   Max.   :0.6767   Max.   :0.9333  
 NA's   :3        NA's   :3        NA's   :18      NA's   :3        NA's   :3        NA's   :3       
    pMTOR_N          DSCR1_N          AMPKA_N           NR2B_N          pNUMB_N          RAPTOR_N     
 Min.   :0.1666   Min.   :0.1553   Min.   :0.2264   Min.   :0.1848   Min.   :0.1856   Min.   :0.1948  
 1st Qu.:0.6835   1st Qu.:0.5309   1st Qu.:0.3266   1st Qu.:0.5149   1st Qu.:0.3128   1st Qu.:0.2761  
 Median :0.7608   Median :0.5767   Median :0.3585   Median :0.5635   Median :0.3474   Median :0.3049  
 Mean   :0.7590   Mean   :0.5852   Mean   :0.3684   Mean   :0.5653   Mean   :0.3571   Mean   :0.3158  
 3rd Qu.:0.8415   3rd Qu.:0.6344   3rd Qu.:0.4008   3rd Qu.:0.6145   3rd Qu.:0.3927   3rd Qu.:0.3473  
 Max.   :1.1249   Max.   :0.9164   Max.   :0.7008   Max.   :0.9720   Max.   :0.6311   Max.   :0.5267  
 NA's   :3        NA's   :3        NA's   :3        NA's   :3        NA's   :3        NA's   :3       
    TIAM1_N          pP70S6_N          NUMB_N          P70S6_N          pGSK3B_N          pPKCG_N      
 Min.   :0.2378   Min.   :0.1311   Min.   :0.1180   Min.   :0.3441   Min.   :0.09998   Min.   :0.5988  
 1st Qu.:0.3720   1st Qu.:0.2811   1st Qu.:0.1593   1st Qu.:0.8267   1st Qu.:0.14925   1st Qu.:1.2968  
 Median :0.4072   Median :0.3777   Median :0.1782   Median :0.9313   Median :0.16021   Median :1.6646  
 Mean   :0.4186   Mean   :0.3945   Mean   :0.1811   Mean   :0.9431   Mean   :0.16121   Mean   :1.7066  
 3rd Qu.:0.4560   3rd Qu.:0.4811   3rd Qu.:0.1972   3rd Qu.:1.0451   3rd Qu.:0.17174   3rd Qu.:2.1130  
 Max.   :0.7221   Max.   :1.1292   Max.   :0.3166   Max.   :1.6800   Max.   :0.25321   Max.   :3.3820  
 NA's   :3        NA's   :3                                                                            
     CDK5_N            S6_N           ADARB1_N       AcetylH3K9_N         RRP1_N             BAX_N        
 Min.   :0.1812   Min.   :0.1302   Min.   :0.5291   Min.   :0.05253   Min.   :-0.06201   Min.   :0.07233  
 1st Qu.:0.2726   1st Qu.:0.3167   1st Qu.:0.9305   1st Qu.:0.10357   1st Qu.: 0.14902   1st Qu.:0.16817  
 Median :0.2938   Median :0.4010   Median :1.1283   Median :0.15042   Median : 0.16210   Median :0.18074  
 Mean   :0.2924   Mean   :0.4292   Mean   :1.1974   Mean   :0.21648   Mean   : 0.16663   Mean   :0.17931  
 3rd Qu.:0.3125   3rd Qu.:0.5349   3rd Qu.:1.3802   3rd Qu.:0.26965   3rd Qu.: 0.17741   3rd Qu.:0.19158  
 Max.   :0.8174   Max.   :0.8226   Max.   :2.5399   Max.   :1.45939   Max.   : 0.61238   Max.   :0.24114  
                                                                                                          
     ARC_N            ERBB4_N           nNOS_N            Tau_N             GFAP_N           GluR3_N      
 Min.   :0.06725   Min.   :0.1002   Min.   :0.09973   Min.   :0.09623   Min.   :0.08611   Min.   :0.1114  
 1st Qu.:0.11084   1st Qu.:0.1470   1st Qu.:0.16645   1st Qu.:0.16799   1st Qu.:0.11277   1st Qu.:0.1957  
 Median :0.12163   Median :0.1564   Median :0.18267   Median :0.18863   Median :0.12046   Median :0.2169  
 Mean   :0.12152   Mean   :0.1565   Mean   :0.18130   Mean   :0.21049   Mean   :0.12089   Mean   :0.2219  
 3rd Qu.:0.13196   3rd Qu.:0.1654   3rd Qu.:0.19857   3rd Qu.:0.23394   3rd Qu.:0.12772   3rd Qu.:0.2460  
 Max.   :0.15875   Max.   :0.2087   Max.   :0.26074   Max.   :0.60277   Max.   :0.21362   Max.   :0.3310  
                                                                                                          
    GluR4_N            IL1B_N          P3525_N          pCASP9_N         PSD95_N          SNCA_N      
 Min.   :0.07258   Min.   :0.2840   Min.   :0.2074   Min.   :0.8532   Min.   :1.206   Min.   :0.1012  
 1st Qu.:0.10889   1st Qu.:0.4756   1st Qu.:0.2701   1st Qu.:1.3756   1st Qu.:2.079   1st Qu.:0.1428  
 Median :0.12355   Median :0.5267   Median :0.2906   Median :1.5227   Median :2.242   Median :0.1575  
 Mean   :0.12656   Mean   :0.5273   Mean   :0.2913   Mean   :1.5483   Mean   :2.235   Mean   :0.1598  
 3rd Qu.:0.14195   3rd Qu.:0.5770   3rd Qu.:0.3116   3rd Qu.:1.7131   3rd Qu.:2.420   3rd Qu.:0.1733  
 Max.   :0.53700   Max.   :0.8897   Max.   :0.4437   Max.   :2.5862   Max.   :2.878   Max.   :0.2576  
                                                                                                      
  Ubiquitin_N     pGSK3B_Tyr216_N      SHH_N            BAD_N            BCL2_N            pS6_N        
 Min.   :0.7507   Min.   :0.5774   Min.   :0.1559   Min.   :0.0883   Min.   :0.08066   Min.   :0.06725  
 1st Qu.:1.1163   1st Qu.:0.7937   1st Qu.:0.2064   1st Qu.:0.1364   1st Qu.:0.11555   1st Qu.:0.11084  
 Median :1.2366   Median :0.8499   Median :0.2240   Median :0.1523   Median :0.12947   Median :0.12163  
 Mean   :1.2393   Mean   :0.8488   Mean   :0.2267   Mean   :0.1579   Mean   :0.13476   Mean   :0.12152  
 3rd Qu.:1.3631   3rd Qu.:0.9162   3rd Qu.:0.2417   3rd Qu.:0.1740   3rd Qu.:0.14823   3rd Qu.:0.13196  
 Max.   :1.8972   Max.   :1.2046   Max.   :0.3583   Max.   :0.2820   Max.   :0.26151   Max.   :0.15875  
                                                    NA's   :213      NA's   :285                        
    pCFOS_N            SYP_N          H3AcK18_N           EGR1_N          H3MeK4_N          CaNA_N      
 Min.   :0.08542   Min.   :0.2586   Min.   :0.07969   Min.   :0.1055   Min.   :0.1018   Min.   :0.5865  
 1st Qu.:0.11351   1st Qu.:0.3981   1st Qu.:0.12585   1st Qu.:0.1551   1st Qu.:0.1651   1st Qu.:1.0814  
 Median :0.12652   Median :0.4485   Median :0.15824   Median :0.1749   Median :0.1940   Median :1.3174  
 Mean   :0.13105   Mean   :0.4461   Mean   :0.16961   Mean   :0.1831   Mean   :0.2054   Mean   :1.3378  
 3rd Qu.:0.14365   3rd Qu.:0.4908   3rd Qu.:0.19788   3rd Qu.:0.2045   3rd Qu.:0.2352   3rd Qu.:1.5858  
 Max.   :0.25653   Max.   :0.7596   Max.   :0.47976   Max.   :0.3607   Max.   :0.4139   Max.   :2.1298  
 NA's   :75                         NA's   :180       NA's   :210      NA's   :270                      
   Genotype          Treatment           Behavior            class          
 Length:1080        Length:1080        Length:1080        Length:1080       
 Class :character   Class :character   Class :character   Class :character  
 Mode  :character   Mode  :character   Mode  :character   Mode  :character  
                                                                            
                                                                            
                                                                            
                                                                            

colnames(ds)

 [1] "MouseID"         "DYRK1A_N"        "ITSN1_N"         "BDNF_N"          "NR1_N"          
 [6] "NR2A_N"          "pAKT_N"          "pBRAF_N"         "pCAMKII_N"       "pCREB_N"        
[11] "pELK_N"          "pERK_N"          "pJNK_N"          "PKCA_N"          "pMEK_N"         
[16] "pNR1_N"          "pNR2A_N"         "pNR2B_N"         "pPKCAB_N"        "pRSK_N"         
[21] "AKT_N"           "BRAF_N"          "CAMKII_N"        "CREB_N"          "ELK_N"          
[26] "ERK_N"           "GSK3B_N"         "JNK_N"           "MEK_N"           "TRKA_N"         
[31] "RSK_N"           "APP_N"           "Bcatenin_N"      "SOD1_N"          "MTOR_N"         
[36] "P38_N"           "pMTOR_N"         "DSCR1_N"         "AMPKA_N"         "NR2B_N"         
[41] "pNUMB_N"         "RAPTOR_N"        "TIAM1_N"         "pP70S6_N"        "NUMB_N"         
[46] "P70S6_N"         "pGSK3B_N"        "pPKCG_N"         "CDK5_N"          "S6_N"           
[51] "ADARB1_N"        "AcetylH3K9_N"    "RRP1_N"          "BAX_N"           "ARC_N"          
[56] "ERBB4_N"         "nNOS_N"          "Tau_N"           "GFAP_N"          "GluR3_N"        
[61] "GluR4_N"         "IL1B_N"          "P3525_N"         "pCASP9_N"        "PSD95_N"        
[66] "SNCA_N"          "Ubiquitin_N"     "pGSK3B_Tyr216_N" "SHH_N"           "BAD_N"          
[71] "BCL2_N"          "pS6_N"           "pCFOS_N"         "SYP_N"           "H3AcK18_N"      
[76] "EGR1_N"          "H3MeK4_N"        "CaNA_N"          "Genotype"        "Treatment"      
[81] "Behavior"        "class"          

MouseID

   [1] "309_1"     "309_2"     "309_3"     "309_4"     "309_5"     "309_6"     "309_7"     "309_8"    
   [9] "309_9"     "309_10"    "309_11"    "309_12"    "309_13"    "309_14"    "309_15"    "311_1"    
  [17] "311_2"     "311_3"     "311_4"     "311_5"     "311_6"     "311_7"     "311_8"     "311_9"    
  [25] "311_10"    "311_11"    "311_12"    "311_13"    "311_14"    "311_15"    "320_1"     "320_2"    
  [33] "320_3"     "320_4"     "320_5"     "320_6"     "320_7"     "320_8"     "320_9"     "320_10"   
  [41] "320_11"    "320_12"    "320_13"    "320_14"    "320_15"    "321_1"     "321_2"     "321_3"    
  [49] "321_4"     "321_5"     "321_6"     "321_7"     "321_8"     "321_9"     "321_10"    "321_11"   
  [57] "321_12"    "321_13"    "321_14"    "321_15"    "322_1"     "322_2"     "322_3"     "322_4"    
  [65] "322_5"     "322_6"     "322_7"     "322_8"     "322_9"     "322_10"    "322_11"    "322_12"   
  [73] "322_13"    "322_14"    "322_15"    "3415_1"    "3415_2"    "3415_3"    "3415_4"    "3415_5"   
  [81] "3415_6"    "3415_7"    "3415_8"    "3415_9"    "3415_10"   "3415_11"   "3415_12"   "3415_13"  
  [89] "3415_14"   "3415_15"   "3499_1"    "3499_2"    "3499_3"    "3499_4"    "3499_5"    "3499_6"   
  [97] "3499_7"    "3499_8"    "3499_9"    "3499_10"   "3499_11"   "3499_12"   "3499_13"   "3499_14"  
 [105] "3499_15"   "3507_1"    "3507_2"    "3507_3"    "3507_4"    "3507_5"    "3507_6"    "3507_7"   
 [113] "3507_8"    "3507_9"    "3507_10"   "3507_11"   "3507_12"   "3507_13"   "3507_14"   "3507_15"  
 [121] "3520_1"    "3520_2"    "3520_3"    "3520_4"    "3520_5"    "3520_6"    "3520_7"    "3520_8"   
 [129] "3520_9"    "3520_10"   "3520_11"   "3520_12"   "3520_13"   "3520_14"   "3520_15"   "3521_1"   
 [137] "3521_2"    "3521_3"    "3521_4"    "3521_5"    "3521_6"    "3521_7"    "3521_8"    "3521_9"   
 [145] "3521_10"   "3521_11"   "3521_12"   "3521_13"   "3521_14"   "3521_15"   "294_1"     "294_2"    
 [153] "294_3"     "294_4"     "294_5"     "294_6"     "294_7"     "294_8"     "294_9"     "294_10"   
 [161] "294_11"    "294_12"    "294_13"    "294_14"    "294_15"    "3412_1"    "3412_2"    "3412_3"   
 [169] "3412_4"    "3412_5"    "3412_6"    "3412_7"    "3412_8"    "3412_9"    "3412_10"   "3412_11"  
 [177] "3412_12"   "3412_13"   "3412_14"   "3412_15"   "3413_1"    "3413_2"    "3413_3"    "3413_4"   
 [185] "3413_5"    "3413_6"    "3413_7"    "3413_8"    "3413_9"    "3413_10"   "3413_11"   "3413_12"  
 [193] "3413_13"   "3413_14"   "3413_15"   "3419_1"    "3419_2"    "3419_3"    "3419_4"    "3419_5"   
 [201] "3419_6"    "3419_7"    "3419_8"    "3419_9"    "3419_10"   "3419_11"   "3419_12"   "3419_13"  
 [209] "3419_14"   "3419_15"   "3420_1"    "3420_2"    "3420_3"    "3420_4"    "3420_5"    "3420_6"   
 [217] "3420_7"    "3420_8"    "3420_9"    "3420_10"   "3420_11"   "3420_12"   "3420_13"   "3420_14"  
 [225] "3420_15"   "3500_1"    "3500_2"    "3500_3"    "3500_4"    "3500_5"    "3500_6"    "3500_7"   
 [233] "3500_8"    "3500_9"    "3500_10"   "3500_11"   "3500_12"   "3500_13"   "3500_14"   "3500_15"  
 [241] "3503_1"    "3503_2"    "3503_3"    "3503_4"    "3503_5"    "3503_6"    "3503_7"    "3503_8"   
 [249] "3503_9"    "3503_10"   "3503_11"   "3503_12"   "3503_13"   "3503_14"   "3503_15"   "362_1"    
 [257] "362_2"     "362_3"     "362_4"     "362_5"     "362_6"     "362_7"     "362_8"     "362_9"    
 [265] "362_10"    "362_11"    "362_12"    "362_13"    "362_14"    "362_15"    "364_1"     "364_2"    
 [273] "364_3"     "364_4"     "364_5"     "364_6"     "364_7"     "364_8"     "364_9"     "364_10"   
 [281] "364_11"    "364_12"    "364_13"    "364_14"    "364_15"    "365_1"     "365_2"     "365_3"    
 [289] "365_4"     "365_5"     "365_6"     "365_7"     "365_8"     "365_9"     "365_10"    "365_11"   
 [297] "365_12"    "365_13"    "365_14"    "365_15"    "3477_1"    "3477_2"    "3477_3"    "3477_4"   
 [305] "3477_5"    "3477_6"    "3477_7"    "3477_8"    "3477_9"    "3477_10"   "3477_11"   "3477_12"  
 [313] "3477_13"   "3477_14"   "3477_15"   "3478_1"    "3478_2"    "3478_3"    "3478_4"    "3478_5"   
 [321] "3478_6"    "3478_7"    "3478_8"    "3478_9"    "3478_10"   "3478_11"   "3478_12"   "3478_13"  
 [329] "3478_14"   "3478_15"   "3479_1"    "3479_2"    "3479_3"    "3479_4"    "3479_5"    "3479_6"   
 [337] "3479_7"    "3479_8"    "3479_9"    "3479_10"   "3479_11"   "3479_12"   "3479_13"   "3479_14"  
 [345] "3479_15"   "3480_1"    "3480_2"    "3480_3"    "3480_4"    "3480_5"    "3480_6"    "3480_7"   
 [353] "3480_8"    "3480_9"    "3480_10"   "3480_11"   "3480_12"   "3480_13"   "3480_14"   "3480_15"  
 [361] "3484_1"    "3484_2"    "3484_3"    "3484_4"    "3484_5"    "3484_6"    "3484_7"    "3484_8"   
 [369] "3484_9"    "3484_10"   "3484_11"   "3484_12"   "3484_13"   "3484_14"   "3484_15"   "3497_1"   
 [377] "3497_2"    "3497_3"    "3497_4"    "3497_5"    "3497_6"    "3497_7"    "3497_8"    "3497_9"   
 [385] "3497_10"   "3497_11"   "3497_12"   "3497_13"   "3497_14"   "3497_15"   "50810A_1"  "50810A_2" 
 [393] "50810A_3"  "50810A_4"  "50810A_5"  "50810A_6"  "50810A_7"  "50810A_8"  "50810A_9"  "50810A_10"
 [401] "50810A_11" "50810A_12" "50810A_13" "50810A_14" "50810A_15" "50810D_1"  "50810D_2"  "50810D_3" 
 [409] "50810D_4"  "50810D_5"  "50810D_6"  "50810D_7"  "50810D_8"  "50810D_9"  "50810D_10" "50810D_11"
 [417] "50810D_12" "50810D_13" "50810D_14" "50810D_15" "50810F_1"  "50810F_2"  "50810F_3"  "50810F_4" 
 [425] "50810F_5"  "50810F_6"  "50810F_7"  "50810F_8"  "50810F_9"  "50810F_10" "50810F_11" "50810F_12"
 [433] "50810F_13" "50810F_14" "50810F_15" "3422_1"    "3422_2"    "3422_3"    "3422_4"    "3422_5"   
 [441] "3422_6"    "3422_7"    "3422_8"    "3422_9"    "3422_10"   "3422_11"   "3422_12"   "3422_13"  
 [449] "3422_14"   "3422_15"   "3423_1"    "3423_2"    "3423_3"    "3423_4"    "3423_5"    "3423_6"   
 [457] "3423_7"    "3423_8"    "3423_9"    "3423_10"   "3423_11"   "3423_12"   "3423_13"   "3423_14"  
 [465] "3423_15"   "3424_1"    "3424_2"    "3424_3"    "3424_4"    "3424_5"    "3424_6"    "3424_7"   
 [473] "3424_8"    "3424_9"    "3424_10"   "3424_11"   "3424_12"   "3424_13"   "3424_14"   "3424_15"  
 [481] "3481_1"    "3481_2"    "3481_3"    "3481_4"    "3481_5"    "3481_6"    "3481_7"    "3481_8"   
 [489] "3481_9"    "3481_10"   "3481_11"   "3481_12"   "3481_13"   "3481_14"   "3481_15"   "3488_1"   
 [497] "3488_2"    "3488_3"    "3488_4"    "3488_5"    "3488_6"    "3488_7"    "3488_8"    "3488_9"   
 [505] "3488_10"   "3488_11"   "3488_12"   "3488_13"   "3488_14"   "3488_15"   "3489_1"    "3489_2"   
 [513] "3489_3"    "3489_4"    "3489_5"    "3489_6"    "3489_7"    "3489_8"    "3489_9"    "3489_10"  
 [521] "3489_11"   "3489_12"   "3489_13"   "3489_14"   "3489_15"   "3490_1"    "3490_2"    "3490_3"   
 [529] "3490_4"    "3490_5"    "3490_6"    "3490_7"    "3490_8"    "3490_9"    "3490_10"   "3490_11"  
 [537] "3490_12"   "3490_13"   "3490_14"   "3490_15"   "3516_1"    "3516_2"    "3516_3"    "3516_4"   
 [545] "3516_5"    "3516_6"    "3516_7"    "3516_8"    "3516_9"    "3516_10"   "3516_11"   "3516_12"  
 [553] "3516_13"   "3516_14"   "3516_15"   "J2292_1"   "J2292_2"   "J2292_3"   "J2292_4"   "J2292_5"  
 [561] "J2292_6"   "J2292_7"   "J2292_8"   "J2292_9"   "J2292_10"  "J2292_11"  "J2292_12"  "J2292_13" 
 [569] "J2292_14"  "J2292_15"  "3414_1"    "3414_2"    "3414_3"    "3414_4"    "3414_5"    "3414_6"   
 [577] "3414_7"    "3414_8"    "3414_9"    "3414_10"   "3414_11"   "3414_12"   "3414_13"   "3414_14"  
 [585] "3414_15"   "3416_1"    "3416_2"    "3416_3"    "3416_4"    "3416_5"    "3416_6"    "3416_7"   
 [593] "3416_8"    "3416_9"    "3416_10"   "3416_11"   "3416_12"   "3416_13"   "3416_14"   "3416_15"  
 [601] "3417_1"    "3417_2"    "3417_3"    "3417_4"    "3417_5"    "3417_6"    "3417_7"    "3417_8"   
 [609] "3417_9"    "3417_10"   "3417_11"   "3417_12"   "3417_13"   "3417_14"   "3417_15"   "3429_1"   
 [617] "3429_2"    "3429_3"    "3429_4"    "3429_5"    "3429_6"    "3429_7"    "3429_8"    "3429_9"   
 [625] "3429_10"   "3429_11"   "3429_12"   "3429_13"   "3429_14"   "3429_15"   "3504_1"    "3504_2"   
 [633] "3504_3"    "3504_4"    "3504_5"    "3504_6"    "3504_7"    "3504_8"    "3504_9"    "3504_10"  
 [641] "3504_11"   "3504_12"   "3504_13"   "3504_14"   "3504_15"   "3505_1"    "3505_2"    "3505_3"   
 [649] "3505_4"    "3505_5"    "3505_6"    "3505_7"    "3505_8"    "3505_9"    "3505_10"   "3505_11"  
 [657] "3505_12"   "3505_13"   "3505_14"   "3505_15"   "3522_1"    "3522_2"    "3522_3"    "3522_4"   
 [665] "3522_5"    "3522_6"    "3522_7"    "3522_8"    "3522_9"    "3522_10"   "3522_11"   "3522_12"  
 [673] "3522_13"   "3522_14"   "3522_15"   "361_1"     "361_2"     "361_3"     "361_4"     "361_5"    
 [681] "361_6"     "361_7"     "361_8"     "361_9"     "361_10"    "361_11"    "361_12"    "361_13"   
 [689] "361_14"    "361_15"    "363_1"     "363_2"     "363_3"     "363_4"     "363_5"     "363_6"    
 [697] "363_7"     "363_8"     "363_9"     "363_10"    "363_11"    "363_12"    "363_13"    "363_14"   
 [705] "363_15"    "293_1"     "293_2"     "293_3"     "293_4"     "293_5"     "293_6"     "293_7"    
 [713] "293_8"     "293_9"     "293_10"    "293_11"    "293_12"    "293_13"    "293_14"    "293_15"   
 [721] "3411_1"    "3411_2"    "3411_3"    "3411_4"    "3411_5"    "3411_6"    "3411_7"    "3411_8"   
 [729] "3411_9"    "3411_10"   "3411_11"   "3411_12"   "3411_13"   "3411_14"   "3411_15"   "3418_1"   
 [737] "3418_2"    "3418_3"    "3418_4"    "3418_5"    "3418_6"    "3418_7"    "3418_8"    "3418_9"   
 [745] "3418_10"   "3418_11"   "3418_12"   "3418_13"   "3418_14"   "3418_15"   "3501_1"    "3501_2"   
 [753] "3501_3"    "3501_4"    "3501_5"    "3501_6"    "3501_7"    "3501_8"    "3501_9"    "3501_10"  
 [761] "3501_11"   "3501_12"   "3501_13"   "3501_14"   "3501_15"   "3502_1"    "3502_2"    "3502_3"   
 [769] "3502_4"    "3502_5"    "3502_6"    "3502_7"    "3502_8"    "3502_9"    "3502_10"   "3502_11"  
 [777] "3502_12"   "3502_13"   "3502_14"   "3502_15"   "3530_1"    "3530_2"    "3530_3"    "3530_4"   
 [785] "3530_5"    "3530_6"    "3530_7"    "3530_8"    "3530_9"    "3530_10"   "3530_11"   "3530_12"  
 [793] "3530_13"   "3530_14"   "3530_15"   "3534_1"    "3534_2"    "3534_3"    "3534_4"    "3534_5"   
 [801] "3534_6"    "3534_7"    "3534_8"    "3534_9"    "3534_10"   "3534_11"   "3534_12"   "3534_13"  
 [809] "3534_14"   "3534_15"   "3605_1"    "3605_2"    "3605_3"    "3605_4"    "3605_5"    "3605_6"   
 [817] "3605_7"    "3605_8"    "3605_9"    "3605_10"   "3605_11"   "3605_12"   "3605_13"   "3605_14"  
 [825] "3605_15"   "3606_1"    "3606_2"    "3606_3"    "3606_4"    "3606_5"    "3606_6"    "3606_7"   
 [833] "3606_8"    "3606_9"    "3606_10"   "3606_11"   "3606_12"   "3606_13"   "3606_14"   "3606_15"  
 [841] "18899_1"   "18899_2"   "18899_3"   "18899_4"   "18899_5"   "18899_6"   "18899_7"   "18899_8"  
 [849] "18899_9"   "18899_10"  "18899_11"  "18899_12"  "18899_13"  "18899_14"  "18899_15"  "3476_1"   
 [857] "3476_2"    "3476_3"    "3476_4"    "3476_5"    "3476_6"    "3476_7"    "3476_8"    "3476_9"   
 [865] "3476_10"   "3476_11"   "3476_12"   "3476_13"   "3476_14"   "3476_15"   "3483_1"    "3483_2"   
 [873] "3483_3"    "3483_4"    "3483_5"    "3483_6"    "3483_7"    "3483_8"    "3483_9"    "3483_10"  
 [881] "3483_11"   "3483_12"   "3483_13"   "3483_14"   "3483_15"   "3498_1"    "3498_2"    "3498_3"   
 [889] "3498_4"    "3498_5"    "3498_6"    "3498_7"    "3498_8"    "3498_9"    "3498_10"   "3498_11"  
 [897] "3498_12"   "3498_13"   "3498_14"   "3498_15"   "50810B_1"  "50810B_2"  "50810B_3"  "50810B_4" 
 [905] "50810B_5"  "50810B_6"  "50810B_7"  "50810B_8"  "50810B_9"  "50810B_10" "50810B_11" "50810B_12"
 [913] "50810B_13" "50810B_14" "50810B_15" "50810C_1"  "50810C_2"  "50810C_3"  "50810C_4"  "50810C_5" 
 [921] "50810C_6"  "50810C_7"  "50810C_8"  "50810C_9"  "50810C_10" "50810C_11" "50810C_12" "50810C_13"
 [929] "50810C_14" "50810C_15" "50810E_1"  "50810E_2"  "50810E_3"  "50810E_4"  "50810E_5"  "50810E_6" 
 [937] "50810E_7"  "50810E_8"  "50810E_9"  "50810E_10" "50810E_11" "50810E_12" "50810E_13" "50810E_14"
 [945] "50810E_15" "3421_1"    "3421_2"    "3421_3"    "3421_4"    "3421_5"    "3421_6"    "3421_7"   
 [953] "3421_8"    "3421_9"    "3421_10"   "3421_11"   "3421_12"   "3421_13"   "3421_14"   "3421_15"  
 [961] "3425_1"    "3425_2"    "3425_3"    "3425_4"    "3425_5"    "3425_6"    "3425_7"    "3425_8"   
 [969] "3425_9"    "3425_10"   "3425_11"   "3425_12"   "3425_13"   "3425_14"   "3425_15"   "3426_1"   
 [977] "3426_2"    "3426_3"    "3426_4"    "3426_5"    "3426_6"    "3426_7"    "3426_8"    "3426_9"   
 [985] "3426_10"   "3426_11"   "3426_12"   "3426_13"   "3426_14"   "3426_15"   "3491_1"    "3491_2"   
 [993] "3491_3"    "3491_4"    "3491_5"    "3491_6"    "3491_7"    "3491_8"    "3491_9"    "3491_10"  
 [ reached getOption("max.print") -- omitted 80 entries ]

table(ds_filtered$Genotype)

Control  Ts65Dn 
    570     510 

table(ds_filtered$Treatment)

Memantine    Saline 
      570       510 

table(ds_filtered$Behavior)

C/S S/C 
525 555 

table(ds_filtered$class)

c-CS-m c-CS-s c-SC-m c-SC-s t-CS-m t-CS-s t-SC-m t-SC-s 
   150    135    150    135    135    105    135    135 

---

1. Higuera, C., Gardiner, K. J., & Cios, K. J. (2015). Self-Organizing Feature Maps Identyfy Proteins Critical to Learning in a Mouse Model of Down Syndrome. PLoS ONE, 10(6).↩

2. Ahmed, M. M., Dhanasekaran, A. R., Block, A., Tong, S., Costa, A. C. S., Stasko, M., & Gardiner, K. J. (2014). Protein Dynamics Associated with Failed and Rescues Learning in the TS65Dn Mouse Model of Down Syndrome. PLoS ONE, 10(3).↩

3. Costa, A., Scott-McKean, J., & Stasko, M. (2008). Acute injections of the NMDA receptor antagonist memantine rescue performance deficits of the Ts65Dn mouse model of Down syndrome on a fear conditioning test. Neuropsychopharmacology, 33(7), 1624-1632.↩

4. Davisson, M., Schmidt, C., Reeves, R., Irving, N., Akeson, E., Harris, B., & Bronson, R. (1993). Segmental trisomy as a mouse model for Down syndrome. Prog Clin Biol Res, 384, 117-133.↩

5. Mitra, A., Blank, M., & Madison, D. (2012). Developmentally altered inhibition in Ts65Dn, a mouse model of Down syndrome. Brain Research, 1440, 1-8.↩

6. http://journals.plos.org/plosone/article/figure/image?size=medium&id=10.1371/journal.pone.0129126.g001↩

7. http://archive.ics.uci.edu/ml/↩

8. https://docs.google.com/spreadsheets/d/1scXPvhOh3kmANCAhf1X_CLwJQckOJA-WMP_f9lHVri4/edit?usp=sharing, CONTROL MICE PROTEINS http://www.plosone.org/article/fetchSingleRepresentation.action?uri=info:doi/10.1371/journal.pone.0129126.s003, TRISOMIC MICE PROTEINS, http://www.plosone.org/article/fetchSingleRepresentation.action?uri=info:doi/10.1371/journal.pone.0129126.s004↩