RData<-read.csv("AAV9 - RData.csv", header=TRUE,stringsAsFactors = TRUE)

myaov <- aov(Intensity ~ days + Region+days:Region+sex+sex:days+volume.nl., data=RData)

Background

Overview

AAV9-GFP (the adeno-associated viral vector carrying a gene for green fluorescent protein) is widely known for not only being an excellent carrier for gene therapy but also for its wide use in neuronal tract tracing1. However, there are certain difficulties scientists face when using this type of vector. For example, there is no explicit information available explaining how the intensity of such a marker changes over time. This might be a problem when deciding how long to wait, how much to inject, or if the gender or weight of animal matters. The data was taken from a study performed on mice using AAV9-GFP for neuronal tract-tracing of the RVM region of the brain to answer those questions. (click “Experimental Details” tab for more information on the study performed)

Experimental Details

The AVV9-GFP was stereotaxically injected into the RVM region of the brains of 8 adult male and 8 adult female mice (n = 16). Mice were injected with different volumes of the viral vectors (50nl, 100nl, or 150nl randomly) and also had different timelines of the injection and the sacrifice of an animal: 36, 37, 43, 48, 51 days or 5.1, 5.3, 6.1, 6.9, 7.3 weeks respectively.

The brains and the spinal cords of those mice were extracted and analyzed under the same settings using the Olympus FluoView Microscope in LI (Lamina 1), LX (Lamina 10), DLF (Dorso-lateral funiculus) regions of the spinal cord where GFP expression was observed. Average intensity values in each of those regions were recorded. (click “The Data” tab to see the data that was recorded)

The Data

  • ‘fileName’: the name of the file where the data was taken from.

  • ‘mouse’: number of a mouse that was injected.

  • ‘sex’: sex of a mouse.

  • ‘volume.nl.’: the volume of AAV9-GFP that was injected into the RVM region of a mouse.

  • ‘days’: days passed since the injection day.

  • ‘weeks’: weeks passed since the injection day.

  • ‘weight.g.’: the weight of a mouse in grams.

  • ‘Intensity’: the intensity of an image.

  • ‘Region’: region in which the expression was analyzed.

pander(RData, split.table=Inf)
fileName mouse sex volume.nl. days weeks weight.g. Intensity Region
RVM_GFP_50nl_SCcs_m4_x4_Z 4 M 50 37 5.286 32 137.4 DLF
RVM_GFP_100nl_SCcs_m2_x4_Z 2 M 100 43 6.143 32 67.72 DLF
RVM_GFP_50nl_SCcs_m1_x4_Z 1 M 50 43 6.143 33 171.3 DLF
RVM_GFP_100nl_SCcs_m5_x4_Z 5 M 100 37 5.286 31 120.9 DLF
RVM_GFP_50nl_SCcs_m6_x4_Z 6 F 50 43 6.143 28 181.5 DLF
RVM_GFP_100nl_SCcs_m7_x4_Z 7 F 100 43 6.143 32 191.2 DLF
RVM_GFP_150nl_SCcs_m8_x4_Z 8 F 150 36 5.143 33 142.7 DLF
RVM_GFP_50nl_SCcs_m9_x4_Z 9 F 50 36 5.143 25 107.5 DLF
RVM_GFP_150nl_SCcs_m12_x4_Z 12 M 150 37 5.286 29 236 DLF
RVM_GFP_100nl_SCcs_m14_x4_Z 14 F 100 51 7.286 26 829.3 DLF
RVM_GFP_50nl_SCcs_m15_x4_Z 15 F 50 51 7.286 29 278.5 DLF
RVM_GFP_50nl_SCcs_m16_x4_Z 16 M 50 48 6.857 24 51.4 DLF
RVM_GFP_150nl_SCcs_m18_x4_Z 18 M 150 48 6.857 36 211 DLF
RVM_GFP_100nl_SCcs_m19_x4_Z 19 F 100 51 7.286 31 206.3 DLF
RVM_GFP_150nl_SCcs_m20_x4_Z 20 M 150 51 7.286 31 408 DLF
RVM_GFP_150nl_SCcs_m21_x4_Z 21 F 150 51 7.286 31 595.4 DLF
RVM_GFP_50nl_SCcs_m4_x4_Z 4 M 50 37 5.286 32 58.16 LI
RVM_GFP_100nl_SCcs_m2_x4_Z 2 M 100 43 6.143 32 105 LI
RVM_GFP_50nl_SCcs_m1_x4_Z 1 M 50 43 6.143 33 240 LI
RVM_GFP_100nl_SCcs_m5_x4_Z 5 M 100 37 5.286 31 123.4 LI
RVM_GFP_50nl_SCcs_m6_x4_Z 6 F 50 43 6.143 28 134.8 LI
RVM_GFP_100nl_SCcs_m7_x4_Z 7 F 100 43 6.143 32 145.5 LI
RVM_GFP_150nl_SCcs_m8_x4_Z 8 F 150 36 5.143 33 143.3 LI
RVM_GFP_50nl_SCcs_m9_x4_Z 9 F 50 36 5.143 25 113.2 LI
RVM_GFP_150nl_SCcs_m12_x4_Z 12 M 150 37 5.286 29 167.5 LI
RVM_GFP_100nl_SCcs_m14_x4_Z 14 F 100 51 7.286 26 185.2 LI
RVM_GFP_50nl_SCcs_m15_x4_Z 15 F 50 51 7.286 29 165.2 LI
RVM_GFP_50nl_SCcs_m16_x4_Z 16 M 50 48 6.857 24 84.27 LI
RVM_GFP_150nl_SCcs_m18_x4_Z 18 M 150 48 6.857 36 160.3 LI
RVM_GFP_100nl_SCcs_m19_x4_Z 19 F 100 51 7.286 31 116 LI
RVM_GFP_150nl_SCcs_m20_x4_Z 20 M 150 51 7.286 31 92.12 LI
RVM_GFP_150nl_SCcs_m21_x4_Z 21 F 150 51 7.286 31 190.1 LI
RVM_GFP_50nl_SCcs_m4_x4_Z 4 M 50 37 5.286 32 178.6 LX
RVM_GFP_100nl_SCcs_m2_x4_Z 2 M 100 43 6.143 32 67.29 LX
RVM_GFP_50nl_SCcs_m1_x4_Z 1 M 50 43 6.143 33 162 LX
RVM_GFP_100nl_SCcs_m5_x4_Z 5 M 100 37 5.286 31 311.5 LX
RVM_GFP_50nl_SCcs_m6_x4_Z 6 F 50 43 6.143 28 244.5 LX
RVM_GFP_100nl_SCcs_m7_x4_Z 7 F 100 43 6.143 32 242.5 LX
RVM_GFP_150nl_SCcs_m8_x4_Z 8 F 150 36 5.143 33 150.6 LX
RVM_GFP_50nl_SCcs_m9_x4_Z 9 F 50 36 5.143 25 169 LX
RVM_GFP_150nl_SCcs_m12_x4_Z 12 M 150 37 5.286 29 157.5 LX
RVM_GFP_100nl_SCcs_m14_x4_Z 14 F 100 51 7.286 26 699.9 LX
RVM_GFP_50nl_SCcs_m15_x4_Z 15 F 50 51 7.286 29 280.6 LX
RVM_GFP_50nl_SCcs_m16_x4_Z 16 M 50 48 6.857 24 57.32 LX
RVM_GFP_150nl_SCcs_m18_x4_Z 18 M 150 48 6.857 36 373.9 LX
RVM_GFP_100nl_SCcs_m19_x4_Z 19 F 100 51 7.286 31 290.5 LX
RVM_GFP_150nl_SCcs_m20_x4_Z 20 M 150 51 7.286 31 200.9 LX
RVM_GFP_150nl_SCcs_m21_x4_Z 21 F 150 51 7.286 31 587.8 LX

Analysis

Hypotheses

“Note: A factor is defined as a qualitative variable containing at least two categories. The categories of the factor are referred to as the “levels” of the factor." (Garrett Saunders)

Since we are interested in knowing how the intensity (quantitative variable) of the dye changes depending on different factors (qualitative variables), we will need to use a multi-way ANOVA to see which factors are significant and how they affect the intensity. For this analysis, I will use a four-way ANOVA with the factors of days, Region, sex, volume.nl. and days:Region, days:sex interactions. To simplify the model, I did not include any other terms (factors or interactions) that were insignificant here. Thus, we have six sets of hypotheses that need to be stated in order to understand the effect of each on the average value of Intensity.

Applying a four-way ANOVA with the interaction terms to this study, we have the model for the Intensity given by

\[ \underbrace{Y_{ijklm}}_\text{Intensity} = \mu + \alpha_i + \beta_j +\gamma_k+\delta_l+ \alpha\beta_{ij}+\alpha\gamma_{ik} + \epsilon_{ijklm} \]

where \(\mu\) is the grand mean
(The grand mean is the mean of the means of several subsamples, as long as the subsamples have the same number of data points.),

\(\alpha_i\) is the days factor with levels \(1 = 36\), \(2 = 37\), \(3 = 43\), \(4 = 48\), and \(5 = 51\),

\(\beta_j\) is the Region factor with levels \(1 = LX\), \(2 = LI\), and \(3 = DLF\),

\(\gamma_k\) is the sex factor with levels \(1 = F\), \(2 = M\),

\(\delta_l\) is the volume.nl. factor with levels \(1 = 50\), \(2 = 100\), and \(3 = 150\),

\(\alpha\beta_{ij}\) is the interaction of the two days and Region factors which has \(5\times3=15\) levels,

\(\alpha\gamma_{ik}\) is the interaction of the two days and sex factors which has \(5\times2=10\) levels,

\(\epsilon_{ijklm} \sim N(0,\sigma^2)\) is the normally distributed error term.

This model allows us to ask the following questions and hypotheses.

  1. Does the number of days affect the average value of Intensity?

Factor: days with levels \(36\), \(37\), \(43\), \(48\), and \(51\).

\[ H_0: \alpha_{36} = \alpha_{37} = \alpha_{43}= \alpha_{48}= \alpha_{51}= 0 \]

\[ H_a: \alpha_i \neq 0 \ \text{for at least one}\ i\in\{1 = 36, 2 = 37, 3 = 43, 4 = 48, 5 = 51\} \]

  1. Does the Region affect the average value of Intensity?

Factor: Region with levels \(LX\), \(LI\), and \(DLF\). \[ H_0: \beta_{LX} = \beta_{LI} = \beta_{DLF} = 0 \] \[ H_a: \beta_j \neq 0 \ \text{for at least one}\ j\in\{1=LX,2=LI,3=DLF\} \]

  1. Does sex affect the average value of Intensity?

Factor: sex with levels \(F\), and \(M\).

\[ H_0: \gamma_F = \gamma_M = 0 \]

\[ H_a: \gamma_k \neq 0 \ \text{for at least one}\ k\in\{1=F,2=M\} \]

  1. Does volume.nl. affect the average value of Intensity?

Factor: volume.nl. with levels \(50\), \(100\), and \(150\).

\[ H_0: \delta_{50} = \delta_{100} = \delta_{150} = 0 \]

\[ H_a: \delta_l \neq 0 \ \text{for at least one}\ l\in\{1=50, 2=100, 3 = 150\} \]

  1. Does the effect of days change for different Regions in the spinal cord? (Does the effect of days change for different levels of Region?) In other words, is there an interaction between days and Region?

\[ H_0: \alpha\beta_{ij} = 0 \ \text{for all } i,j \] \[ H_a: \alpha\beta_{ij} \neq 0 \ \text{for at least one } i,j \]

  1. Does the effect of days change for different sexes? (Does the effect of days change for different levels of sex?) In other words, is there an interaction between days and sex?

\[ H_0: \alpha\gamma_{ik} = 0 \ \text{for all } i,k \] \[ H_a: \alpha\gamma_{ik} \neq 0 \ \text{for at least one } i,k \]

A significance level of \(\alpha = 0.05\) will be used for this study.

Show the diagnostic plots(click to view)

Permutation Test for four-way ANOVA
  Number of Iterations F value P-value
days 2000 15.68 0
Region 2000 4.943 0.011
sex 2000 5.009 0.027
volume.nl. 2000 4.798 0.032
days:Region 2000 3.249 0.043
days:sex 2000 6.612 0.011

From the table above, we can see that all the p-values are significant (< 0.05), so I reject all the null hypotheses I stated above.

Since all the factors are significant, let’s see in which way the intensity of the expression changes according to each factor and interaction we tested.

Graphical Representation & Summaries

Time Dependence

xyplot(Intensity ~ days, data=RData, type=c("p","a"), main="AAV9-GFP Expression In Adult Mice in the Spinal Cord (LI, LX, DLF)", xlab="Days Passed Since the Day of Injection into RVM region", ylab="Intensities of the  Confocal Images", col = "black",
  scales=list(
  x=list(
      at=seq(35,51,1),
      labels=c("35","","","","","40","","","","","45","","","","","50", "") )))

RData %>%
group_by(days) %>%
  summarise(min = min(Intensity), Q1 = quantile(Intensity, 0.25), med = median(Intensity), Q3 = quantile(Intensity, 0.75), max = max(Intensity), Mean=mean(Intensity), '$sigma$'=sd(Intensity), 'Sample Size'=n()) %>% pander(caption="Summary Statistics of Intensity with Different days")
Summary Statistics of Intensity with Different days
Days min Q1 med Q3 max Mean \(\sigma\) Sample Size
36 107.5 120.5 143 148.8 169 137.7 23.3 6
37 58.16 123.4 157.5 178.6 311.5 165.6 72.97 9
43 67.29 127.3 166.6 203.4 244.5 162.8 62.38 12
48 51.4 64.06 122.3 198.3 373.9 156.4 123.6 6
51 92.12 187.6 278.5 497.9 829.3 341.7 229.2 15

From the graph and table above we can see that the intensity does not change much until greater than 7 weeks (51 days) (mean Intensity of which is 341.7 in comparison to others that stay under 170). This means that the intensity of 36 days (about 5 weeks) injection will have an approximately equivalent expression to the 48 days (less than 7 weeks) one. Since there is no data on days that are below 5 weeks, it is hard to tell if 3 or 4 weeks will have the same result as 5 or 6 weeks.

For comparison, here is a picture of the spinal cord of mouse #8 (36 days, 150 nl, female) to the left and mouse #21 (51 days, 150 nl, female) to the right:



Source of the files: Descending controls of PNs/Vika and Ivan/confocal/AVV9-GFP/SC stacks for expression estimation/SC coronal for presentation png

Region Dependence

xyplot(Intensity ~ Region, data=RData, type=c("p","a"), mmain="AAV9-GFP Expression In Adult Mice in the Spinal Cord (L1, L10, DLF)", xlab="Region of the Spinal Cord", main="AAV9-GFP Expression In Adult Mice in the Spinal Cord (LI, LX, DLF)", ylab="Intensities of the  Confocal Images", col = "black") 

RData %>%
group_by(Region) %>%
  summarise(min = min(Intensity), Q1 = quantile(Intensity, 0.25), med = median(Intensity), Q3 = quantile(Intensity, 0.75), max = max(Intensity), Mean=mean(Intensity), '$sigma$'=sd(Intensity), 'Sample Size'=n()) %>% pander(caption="Summary Statistics of Intensity in Different Regions")
Summary Statistics of Intensity in Different Regions
Region min Q1 med Q3 max Mean \(\sigma\) Sample Size
DLF 51.4 133.3 186.3 246.6 829.3 246 205.3 16
LI 58.16 111.1 139.1 165.8 240 139 45.68 16
LX 57.32 160.8 221.7 295.7 699.9 260.9 172.7 16

From the graph and table above it is obvious that DLF and LX regions have approximately the same mean intensities (246 and 260.9 respectively). However, region LI, on average, has less expression than the other two with a mean of 165.8.

Sex Dependence

xyplot(Intensity ~ sex, data=RData, type=c("p","a"), main="AAV9-GFP Expression In Adult Mice in the Spinal Cord (LI, LX, DLF)", xlab="Sex of a Mouse", ylab="Intensities of the  Confocal Images", col = "black") 

RData %>%
group_by(sex) %>%
  summarise(min = min(Intensity), Q1 = quantile(Intensity, 0.25), med = median(Intensity), Q3 = quantile(Intensity, 0.75), max = max(Intensity), Mean=mean(Intensity), '$sigma$'=sd(Intensity), 'Sample Size'=n()) %>% pander(caption="Summary Statistics of Intensity of Different Sexes")
Summary Statistics of Intensity of Different Sexes
sex min Q1 med Q3 max Mean \(\sigma\) Sample Size
F 107.5 144.9 187.6 279.1 829.3 266.3 199.4 24
M 51.4 90.16 158.9 203.5 408 164.3 96.3 24

On average, females have a better expression than males (mean intensity of 266.3 vs 164.3 respectively).

For comparison, here is the same mouse #21 (51 days, 150 nl, female) to the left and mouse #20 (51 days, 150 nl, male) to the right:



Source of the files: Descending controls of PNs/Vika and Ivan/confocal/AVV9-GFP/SC stacks for expression estimation/SC coronal for presentation png

Volume Dependence

xyplot(Intensity ~ volume.nl., data=RData, type=c("p","a"), main="AAV9-GFP Expression In Adult Mice in the Spinal Cord (LI, LX, DLF)", col = "black", xlab="Volume Injected (nl)", ylab="Intensities of the  Confocal Images",  scales=list(
    x=list(
      at=seq(50, 150, 50))))

RData %>%
group_by(volume.nl.) %>%
  summarise(min = min(Intensity), Q1 = quantile(Intensity, 0.25), med = median(Intensity), Q3 = quantile(Intensity, 0.75), max = max(Intensity), Mean=mean(Intensity), '$sigma$'=sd(Intensity), 'Sample Size'=n()) %>% pander(caption="Summary Statistics of Intensity with Different Volumes")
Summary Statistics of Intensity with Different Volumes
volume.nl. min Q1 med Q3 max Mean \(\sigma\) Sample Size
50 51.4 108.9 163.6 180.7 280.6 156.4 71.74 18
100 67.29 118.4 185.2 266.5 829.3 246.8 223.9 15
150 92.12 154 190.1 304.9 595.4 254.5 160.9 15

100 and 150 nl volumes do not differ much in terms of intensity of the expression (mean of 246.8 and 254.5 respectively), however, 50 nl seems to make the expression significantly lower than 100 and 150 nl (mean of 156.4).

Here is mouse #16 (48 days, 50 nl, male) to the left and the same mouse #18 (48 days, 150 nl, male)to the right:



Source of the files: Descending controls of PNs/Vika and Ivan/confocal/AVV9-GFP/SC stacks for expression estimation/SC coronal for presentation png

Days and Region Interaction

#‘barplot(education, beside=TRUE, main=“College Degrees Awarded by Region”, args.legend=list(x=“topleft”), legend.text = TRUE)’

xyplot(Intensity ~ days, data=RData, groups=Region, type=c("p","a"), main="Interaction Between Days and Region", ylab="Intensities of the  Confocal Images",
  scales=list(
  x=list(
      at=seq(35,51,1),
      labels=c("35","","","","","40","","","","","45","","","","","50", "") )),xlab = "Days Passed Since the Day of Injection into RVM region",  par.settings = list(superpose.symbol = list(col = c("orange","purple", "forestgreen")),
                           superpose.line = list(col = c("orange","purple", "forestgreen"))), auto.key=list(corner=c(1,1),  space = "right"))

  group_by(RData,days, Region) %>%
  summarise(min = min(Intensity), Q1 = quantile(Intensity, 0.25), med = median(Intensity), Q3 = quantile(Intensity, 0.75), max = max(Intensity), Mean=mean(Intensity), 'sisigmas' = sd(Intensity), 'Sample Size'=n()) %>%
pander(caption="Summary Statistics of Interaction Between days and Region", split.table=Inf)
Summary Statistics of Interaction Between days and Region
days Region min Q1 med Q3 max Mean \(\sigma\) Sample Size
36 DLF 107.5 116.3 125.1 133.9 142.7 125.1 24.86 2
36 LI 113.2 120.7 128.3 135.8 143.3 128.3 21.34 2
36 LX 150.6 155.2 159.8 164.4 169 159.8 13.04 2
37 DLF 120.9 129.1 137.4 186.7 236 164.7 62.22 3
37 LI 58.16 90.76 123.4 145.4 167.5 116.4 55.02 3
37 LX 157.5 168 178.6 245 311.5 215.8 83.49 3
43 DLF 67.72 145.4 176.4 183.9 191.2 152.9 57.38 4
43 LI 105 127.3 140.1 169.1 240 156.3 58.35 4
43 LX 67.29 138.3 202.2 243 244.5 179.1 83.86 4
48 DLF 51.4 91.3 131.2 171.1 211 131.2 112.9 2
48 LI 84.27 103.3 122.3 141.3 160.3 122.3 53.74 2
48 LX 57.32 136.5 215.6 294.8 373.9 215.6 223.9 2
51 DLF 206.3 278.5 408 595.4 829.3 463.5 252.3 5
51 LI 92.12 116 165.2 185.2 190.1 149.7 43.54 5
51 LX 200.9 280.6 290.5 587.8 699.9 411.9 218.1 5

Here, regions DLF and LX seem to behave somewhat similarily throughout all the days (almost the same intensity during days 36-48 and then a substantial increase during day 51), but LI seems to have approximately the same intensity throughout all the days.

Days and Sex Interaction

xyplot(Intensity ~ days, data=RData, groups=sex, type=c("p","a"), main="Interaction Between Days and Sex", ylab="Intensities of the  Confocal Images",
  scales=list(
  x=list(
      at=seq(35,51,1),
      labels=c("35","","","","","40","","","","","45","","","","","50", "") )), xlab = "Days Passed Since the Day of Injection into RVM region",  par.settings = list(superpose.symbol = list(col = c("magenta","blue")),
                           superpose.line = list(col = c("magenta","blue"))),
       auto.key=list(corner=c(1,1) ,  space = "right"))

  group_by(RData,days, sex) %>%
  summarise(min = min(Intensity), Q1 = quantile(Intensity, 0.25), med = median(Intensity), Q3 = quantile(Intensity, 0.75), max = max(Intensity), Mean=mean(Intensity), 'sisigmas' = sd(Intensity), 'Sample Size'=n()) %>%
pander(caption="Summary Statistics of Interaction Between days and sex", split.table=Inf)
Summary Statistics of Interaction Between days and sex
days sex min Q1 med Q3 max Mean \(\sigma\) Sample Size
36 F 107.5 120.5 143 148.8 169 137.7 23.3 6
37 M 58.16 123.4 157.5 178.6 311.5 165.6 72.97 9
43 F 134.8 154.5 186.3 229.7 244.5 190 46.56 6
43 M 67.29 77.04 133.5 169 240 135.6 67.94 6
48 M 51.4 64.06 122.3 198.3 373.9 156.4 123.6 6
51 F 116 188.9 279.6 589.7 829.3 368.7 241.3 12
51 M 92.12 146.5 200.9 304.5 408 233.7 160.5 3

The intensities of both sexes on average increase gradually the more days pass. However, males tend to have a significantly lower increase in expression after 37 days than females.

Conclusion

Although some of the samples obtained in this analysis do not have a lot of data points, taking into account the fact that to get a lot of data points for such analysis would be somewhat difficult in the laboratory settings, the data obtained in this study might just be enough to get important insights. The results obtained in this study might potentially decrease the number of sacrificed animals used in such experimentations, money (viruses are expensive), and time (it is time-consuming to analyze and record data under the confocal as well as to make precise injections).

With that, according to the test results, weight does not play a role in determining the intensity of the dye. However, days, sex, volume, and Region in the Spinal cord does matter. The intensity does not change almost at all starting from 5 weeks until hitting the 7-week mark and then increasing drastically. On average, the expression in females is better than males (has greater intensity). The expression of 50nl is significantly lower than both 100 and 150nl. Dorso-lateral funiculus and Lamina 10 on average have the same greater expression than Lamina 1.

It seems like the best expression of the dye appears after the 7-week mark. Because we can see that both males and females increase in intensity with time, but females tend to increase more over the same period, female mice may be better subjects in future studies using GFP expression with this serotype. Due to the lack of significant difference in expression between 100nl and 150nl volumes and that they produce greater intensity than 50nl, it would be best to use 100nl in the future to save on the volume of the viruses used and having better intensity.

In sum, one can decide for themself the best timeline for their particular study taking into account the results of this analysis. The information presented here might also be useful to reflect the timeline of the intensity of the expression for other AAV vectors, as long as the green fluorescent protein serves as a marker as well as the travel distance of the dye is approximately the same as from the RVM region to the Lumbar part of the Spinal Cord.

  1. Chamberlin, N L et al. “Recombinant adeno-associated virus vector: use for transgene expression and anterograde tract tracing in the CNS.” Brain research vol. 793,1-2 (1998): 169-75. doi:10.1016/s0006-8993(98)00169-3↩