Passive Membrane Properties of Dorsal Horn Neurons

Introduction

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There are many diseases or injuries affecting the central nervous system (e.g. Alzheimer’s disease, Parkinson’s disease, traumatic injury) that afflict millions of people throughout the globe. There has been a lot of progress done in the past to better combat these afflictions. Yet, a lot is still unclear. One step forward is classifying and characterizing different neurons in the brain and the spinal cord. A cell’s electrical properties are directly derived from the electrical properties of its membrane. Thus, this project will involve analysis of passive membrane properties (resistance and capacitance) as well as resting potential which will help in the classification of different neuron cells into groups with similar properties.

These parameters will be determined from whole-cell patch-clamp recordings in current-clamp mode with zero input current and in voltage-clamp mode. The analysis could be done on currents induced by a brief voltage step.

All in all, the aim of this project is to test this approach for calculating passive membrane parameters from electrophysiological recordings and use them to characterize dorsal horn neurons from laminae I and II of the spinal cord.

The following document seeks to answer a question if light stimulation of RVM descendaing fibers changes passive membrane properties: membrane resistance(\(R_m\)) and membrane capacitance(\(C_m\)).

Show Data

These results come from 2 adult mice which had 50 nl of ChR2 and YFP-producing viruses injected for 8 weeks. Axon Instruments electrophysiological equipment was used to record lamina I neuron cells’ responses from the Lumbar (L1–6) area of the spinal cord in the whole-cell patch-clamp mode. Optogenetic techniques (with monochromator) were applied for the activation of RVM descending axons. Total of 8 cells were successfully patched and had the data recorded on them.

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

• ‘peak’: the amplitude of the peak of the cell’s current recording when the voltage applied is changed by 10 mV and is measured in \(pA\).

• ‘plato’: mean value of a stabilized current recording after the capacitor is completely recharged and is measured in \(pA\).

• ‘Ra’: Access Resistance and is measured in \(M\Omega\) - resistance between electrodes and the inside environment of the cell, or, in other words, the sum of the pipette resistance and the residual resistance of the ruptured patch.

• ‘Rm+Ra’: the sum of membrane and access resistances and is measured in \(M\Omega\).

• ‘Rm’: membrane resistance and is measured in \(M\Omega\).

• ‘tau’: time constant for the capacitive current to fall to within 1/e of zero and is measured in \(ms\).

• ‘Cm’: membrane capacitance and is measured in \(pF\).

• ‘Ih’: holding current while voltage clamping a cell (the current that is passed into the cell in order to hold it at the command potential) measured in \(pA\).

• ‘Cell’: a cell number from which the measurements were recorded.

• ‘Stimulation_Type’: denotes what type of stimulation was performed for a particular data piece. There were three different types:

  1. “control” - when only the electrical stimulation of the dorsal root was performed.

  2. “monochromator” - when both electrical stimulations of the dorsal root and optogenetic stimulation of RVM descending fibers using 480nm 5Hz 5ms monochromator were performed.

• ‘VC’: current recording when voltage was applied (in a voltage-clamp mode) and is measured in \(mV\).

datatable(results)

Initial Analysis

\(R_m\)

Since we are interested in knowing if there is a difference in the ‘Rm’ values of the spinal cord cells after electrical stimulation of dorsal root with and without simultaneous RVM axons stimulation by light our null and alternative hypotheses for all 3 cells are as follows:

\[ H_0: \mu_{control} = \mu_{monochromator} \]

\[ H_a: \mu_{control} \neq \mu_{monochromator} \]

where,

\(\mu_{control}\) is the mean membrane resistance value \(R_m\) of the patched cell’s response after the axons of RVM were electrically stimulated (in \(MΩ\));

\(\mu_{monochromator}\) is the mean membrane resistance value \(R_m\) of the patched cell’s response after the axons of RVM were simultaneously stimulated electrically and with a monochromator (in \(MΩ\)).

The level of significance is set at \(\alpha\) = 0.05 for this study.

Summary of all Cells together

# library
library(ggplot2)
ylim1 = c(0, 1200)

results$Cell <- as.factor(results$Cell)
results_color <- results %>% 
  mutate(
    Rmpvalue = case_when(
           Cell == 1 ~ "high",
           Cell == 2 ~ "high",
           Cell == 3 ~ "low",
           Cell == 4 ~ "high",
           Cell == 5 ~ "high",
           Cell == 6 ~ "low",
           Cell == 7 ~ "high",
           Cell == 8 ~ "low")
  )


results_color <- results_color %>% 
     mutate(
         colorgroup = case_when(
           Stimulation_Type == "control" & Rmpvalue == "high" ~ "gray58",
           Stimulation_Type == "monochromator" & Rmpvalue == "high" ~ "gray82",
           Stimulation_Type == "control" & Rmpvalue == "low" ~ "skyblue",
           Stimulation_Type == "monochromator" & Rmpvalue == "low" ~ "orange"
          )
        )    

legend_title <- "Stimulation Type"


ggplot(results_color, aes(x=Cell, y=Rm, fill=colorgroup)) +
  geom_boxplot()+ 
  theme_light()+
  coord_cartesian(ylim = ylim1)+
  scale_fill_manual(legend_title,values = c("gray58", "gray82","skyblue","orange"), labels = c("non-signifcant control", "non-significant monochromator", "significant control", "significant monochromator"))+
  ggtitle("Optogenetically Stimulated vs Control\nAdult Mice Dorsal Horn Cells") +
  ylab(expression(R[m]~" (MOhm)")) +
  theme(legend.title=element_text(size=20), plot.title = element_text(size = 30, hjust = 0.5), axis.title=element_text(size=20), legend.text=element_text(size=14), axis.text.x = element_text(size = 14),  axis.text.y = element_text(size = 14))

results %>%
group_by(Cell, Stimulation_Type)%>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm of All Cells control vs Monochromator", split.table=Inf)

summarise() has grouped output by ‘Cell’. You can override using the .groups argument.

Summary Statistics of Rm of All Cells control vs Monochromator

Cell	Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
1	control	166.1	208.7	227.7	250.1	432.4	237.1	52.61	34
1	monochromator	178.4	220.5	229.5	241.5	330.6	232.2	31.01	25
2	control	354.8	832.1	923.7	1017	1446	907.4	162.1	59
2	monochromator	653.1	772.6	846.8	876.3	1072	846.1	110.8	20
3	control	136.5	236.9	248.4	261	337.6	247.6	24.84	70
3	monochromator	225.5	243.5	256.7	278.6	323.5	266.6	29.49	21
4	control	357.3	430.5	470.1	498.8	774.5	473.6	69.66	54
4	monochromator	262.1	430.8	460.2	503	689.8	473.2	93.34	32
5	control	497.9	529.1	554	573.3	589.7	548.7	32.57	10
5	monochromator	503.4	539.3	553.6	570.3	580.8	551.1	22.49	16
6	control	111.5	158.9	188.1	289	425.4	228.9	81.99	105
6	monochromator	126.8	173.4	249.7	285.7	461.1	236.8	67.79	63
7	control	118.2	231.1	318.9	435	3500	413.2	528.5	39
7	monochromator	121.3	309.9	370.7	450.7	2276	512.5	500.1	17
8	control	140	176.5	211	315	451.5	246.2	86.01	39
8	monochromator	105.7	184.2	267.5	289	498.4	249.5	82.15	36

Summary of each Cell individually

Cell 1

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell1results <- filter(results, Cell == 1)

test <- t.test(Rm~Stimulation_Type, data = cell1results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Rm~Stimulation_Type, data = cell1results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell1")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell1results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell1", split.table=Inf)

Summary Statistics of Rm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	166.1	208.7	227.7	250.1	432.4	237.1	52.61	34
monochromator	178.4	220.5	229.5	241.5	330.6	232.2	31.01	25

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell1results$Rm[cell1results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell1results$Rm[cell1results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Rm~Stimulation_Type, data = cell1results), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
0.4461	54.74	0.6573	two.sided	237.1	232.2

Since, our P-value is not significant ( 0.6572771 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

Cell 2

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell2results <- filter(results, Cell == 2)

test <- t.test(Rm~Stimulation_Type, data = cell2results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell2results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell2")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell2results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	354.8	832.1	923.7	1017	1446	907.4	162.1	59
monochromator	653.1	772.6	846.8	876.3	1072	846.1	110.8	20

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell2results$Rm[cell2results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell2results$Rm[cell2results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell2results), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
1.885	48.27	0.06539	two.sided	907.4	846.1

Since, our P-value is not significant (0.0653941 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

Cell 3

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell3results <- filter(results, Cell == 3)

test <- t.test(Rm~Stimulation_Type, data = cell3results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell3results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell3")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell3results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	136.5	236.9	248.4	261	337.6	247.6	24.84	70
monochromator	225.5	243.5	256.7	278.6	323.5	266.6	29.49	21

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell3results$Rm[cell3results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell3results$Rm[cell3results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell3results), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-2.686	29.04	0.01182 *	two.sided	247.6	266.6

Since, our P-value is significant (0.0118229 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

Cell 4

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell4results <- filter(results, Cell == 4)

test <- t.test(Rm~Stimulation_Type, data = cell4results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell4results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell4")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell4results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	357.3	430.5	470.1	498.8	774.5	473.6	69.66	54
monochromator	262.1	430.8	460.2	503	689.8	473.2	93.34	32

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell4results$Rm[cell4results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell4results$Rm[cell4results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell4results), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
0.02405	51.56	0.9809	two.sided	473.6	473.2

Since, our P-value is not significant (0.9809052 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

Cell 5

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell5results <- filter(results, Cell == 5)

test <- t.test(Rm~Stimulation_Type, data = cell5results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell5results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell5")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell5results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	497.9	529.1	554	573.3	589.7	548.7	32.57	10
monochromator	503.4	539.3	553.6	570.3	580.8	551.1	22.49	16

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell5results$Rm[cell5results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell5results$Rm[cell5results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell5results), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-0.2043	14.39	0.841	two.sided	548.7	551.1

Since, our P-value is not significant (0.8409725 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

Cell 6

VC = -10

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell6results_10 <- filter(results, Cell == 6 & VC == -10)

test <- t.test(Rm~Stimulation_Type, data = cell6results_10)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell6results_10,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell6")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell6results_10 %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	111.5	146.3	159.3	173.9	195.7	160.1	18.21	54
monochromator	126.8	145.8	158.4	170.2	209.8	160.5	22.46	19

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell6results_10$Rm[cell6results_10$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell6results_10$Rm[cell6results_10$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell6results_10), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-0.08173	26.8	0.9355	two.sided	160.1	160.5

Since, our P-value is not significant (0.9354678 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

VC = -60

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell6results_60 <- filter(results, Cell == 6 & VC == -60)

test <- t.test(Rm~Stimulation_Type, data = cell6results_60)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell6results_60,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell6")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell6results_60 %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	132.9	275.7	289.8	334.5	425.4	301.8	55.6	51
monochromator	141	247.7	272.3	295.5	461.1	269.7	52.32	44

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell6results_60$Rm[cell6results_60$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell6results_60$Rm[cell6results_60$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell6results_60), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
2.898	92.28	0.004696 * *	two.sided	301.8	269.7

Since, our P-value is significant (0.0046964 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

Cell 7

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell7results <- filter(results, Cell == 7)

test <- t.test(Rm~Stimulation_Type, data = cell7results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell7results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell7")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell7results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	118.2	231.1	318.9	435	3500	413.2	528.5	39
monochromator	121.3	309.9	370.7	450.7	2276	512.5	500.1	17

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell7results$Rm[cell7results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell7results$Rm[cell7results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell7results), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-0.671	32.16	0.507	two.sided	413.2	512.5

Since, our P-value is not significant (0.5070314 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

Cell 8

VC = -10

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell8results_10 <- filter(results, Cell == 8 & VC == -10)

test <- t.test(Rm~Stimulation_Type, data = cell8results_10)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell8results_10,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell8")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell8results_10 %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	140	168.4	190.3	210.5	248.9	192	29.76	26
monochromator	105.7	159	182.3	210.5	498.4	206.5	94.53	18

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell8results_10$Rm[cell8results_10$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell8results_10$Rm[cell8results_10$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell8results_10), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-0.6333	19.35	0.5339	two.sided	192	206.5

Since, our P-value is not significant (0.5339401 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

VC = -60

Below is the boxplot comparison of the \(R_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

cell8results_60 <- filter(results, Cell == 8 & VC == -60)

test <- t.test(Rm~Stimulation_Type, data = cell8results_60)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}

boxplot(Rm~Stimulation_Type, data = cell8results_60,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell8")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

cell8results_60 %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm), Q1 = quantile(Rm, 0.25), med = median(Rm), Q3 = quantile(Rm, 0.75), max = max(Rm), mean=mean(Rm), sd =sd(Rm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm Cell2", split.table=Inf)

Summary Statistics of Rm Cell2

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	285.7	319.6	347	393.1	451.5	354.7	49.63	13
monochromator	255.4	268	282.3	301.5	376	292.4	32.48	18

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell8results_60$Rm[cell8results_60$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm", id=FALSE)
qqPlot(cell8results_60$Rm[cell8results_60$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm", id=FALSE)

Here are the results we get:

pander(t.test(Rm~Stimulation_Type, data = cell8results_60), split.table=Inf)

Welch Two Sample t-test: Rm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
3.953	19.27	0.0008332 * * *	two.sided	354.7	292.4

Since, our P-value is significant (8.3325^{-4} < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

\(C_m\)

Since we are interested in knowing if there is a difference in the ‘Cm’ values of the spinal cord cells after electrical stimulation of dorsal root with and without simultaneous RVM axons stimulation by light our null and alternative hypotheses for all 3 cells are as follows:

\[ H_0: \mu_{control} = \mu_{monochromator} \]

\[ H_a: \mu_{control} \neq \mu_{monochromator} \]

where,

\(\mu_{control}\) is the mean membrane capacitance value \(C_m\) of the patched cell’s response after the axons of RVM were electrically stimulated (in \(pF\));

\(\mu_{monochromator}\) is the mean membrane capacitance value \(C_m\) of the patched cell’s response after the axons of RVM were simultaneously stimulated electrically and with a monochromator (in \(pF\)).

The level of significance is set at \(\alpha\) = 0.05 for this study.

Summary of all Cells together

# library
library(ggplot2)
ylim2 = c(0, 12)

results$Cell <- as.factor(results$Cell)
results_color <- results %>% 
  mutate(
    Cmpvalue = case_when(
           Cell == 1 ~ "low",
           Cell == 2 ~ "low",
           Cell == 3 ~ "high",
           Cell == 4 ~ "high",
           Cell == 5 ~ "low",
           Cell == 6 ~ "low",
           Cell == 7 ~ "high",
           Cell == 8 ~ "low")
  )


results_color <- results_color %>% 
     mutate(
         colorgroup_Cm = case_when(
           Stimulation_Type == "control" & Cmpvalue == "high" ~ "gray58",
           Stimulation_Type == "monochromator" & Cmpvalue == "high" ~ "gray82",
           Stimulation_Type == "control" & Cmpvalue == "low" ~ "skyblue",
           Stimulation_Type == "monochromator" & Cmpvalue == "low" ~ "orange"
          )
        )    

legend_title <- "Stimulation Type"


ggplot(results_color, aes(x=Cell, y=Cm, fill=colorgroup_Cm)) +
  geom_boxplot()+ 
  theme_light()+
  coord_cartesian(ylim = ylim2)+
  scale_fill_manual(legend_title,values = c("gray58", "gray82","skyblue","orange"), labels = c("non-signifcant control", "non-significant monochromator", "significant control", "significant monochromator"))+
  ggtitle("Optogenetically Stimulated vs Control\nAdult Mice Dorsal Horn Cells") +
  ylab(expression(C[m]~" (pF)")) +
  theme(legend.title=element_text(size=20), plot.title = element_text(size = 30, hjust = 0.5), axis.title=element_text(size=20), legend.text=element_text(size=14), axis.text.x = element_text(size = 14),  axis.text.y = element_text(size = 14))

results %>%
group_by(Cell, Stimulation_Type)%>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm of All Cells control vs Monochromator", split.table=Inf)

summarise() has grouped output by ‘Cell’. You can override using the .groups argument.

Summary Statistics of Cm of All Cells control vs Monochromator

Cell	Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
1	control	0.8968	1.374	1.468	1.665	1.784	1.463	0.2258	34
1	monochromator	0.9734	1.467	1.581	1.816	2.103	1.625	0.265	25
2	control	0.2018	0.393	0.5371	0.6598	1.146	0.5272	0.2155	59
2	monochromator	0.5704	0.6623	0.7047	0.775	0.9235	0.7284	0.09291	20
3	control	1.993	3.183	3.595	4.009	8.419	3.602	0.9369	70
3	monochromator	1.536	2.192	5.024	5.739	6.673	4.154	1.847	21
4	control	1.202	1.693	2.721	3.084	3.953	2.532	0.7741	54
4	monochromator	-16.82	1.903	2.43	3.169	5.453	2.029	3.548	32
5	control	0.9523	1.04	1.119	1.168	1.54	1.139	0.1614	10
5	monochromator	0.8441	0.875	0.8963	0.9345	1.032	0.9121	0.05494	16
6	control	2.388	3.946	4.457	5.375	8.391	4.748	1.308	105
6	monochromator	2.463	3.619	4.492	7.097	11	5.361	2.26	63
7	control	0.3176	1.728	2.124	3.294	6.68	2.656	1.513	39
7	monochromator	0.5014	2.379	2.792	3.98	8.797	3.49	2.269	17
8	control	3.462	4.411	5.757	6.73	9.849	5.881	1.766	39
8	monochromator	2.799	5.105	5.834	7.824	18.07	6.743	2.838	36

# library
library(ggplot2)

results$Cell <- as.factor(results$Cell)

legend_title <- "Stimulation Type"


ggplot(results, aes(x=Cell, y=Cm, fill=Stimulation_Type)) +
  geom_boxplot()+ 
  theme_light()+
  coord_cartesian(ylim = ylim1)+
  scale_fill_manual(legend_title,values = c("skyblue","orange"))+
  ggtitle(c(expression(C[m]~"comparison of Control & Monochromator"))) +
  ylab(expression(C[m]~" (MOhm)")) +
  theme(legend.title=element_text(size=20), plot.title = element_text(size = 30), axis.title=element_text(size=20), legend.text=element_text(size=14))

results %>%
group_by(Cell, Stimulation_Type)%>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm of All Cells control vs Monochromator", split.table=Inf)

summarise() has grouped output by ‘Cell’. You can override using the .groups argument.

Summary Statistics of Cm of All Cells control vs Monochromator

Cell	Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
1	control	0.8968	1.374	1.468	1.665	1.784	1.463	0.2258	34
1	monochromator	0.9734	1.467	1.581	1.816	2.103	1.625	0.265	25
2	control	0.2018	0.393	0.5371	0.6598	1.146	0.5272	0.2155	59
2	monochromator	0.5704	0.6623	0.7047	0.775	0.9235	0.7284	0.09291	20
3	control	1.993	3.183	3.595	4.009	8.419	3.602	0.9369	70
3	monochromator	1.536	2.192	5.024	5.739	6.673	4.154	1.847	21
4	control	1.202	1.693	2.721	3.084	3.953	2.532	0.7741	54
4	monochromator	-16.82	1.903	2.43	3.169	5.453	2.029	3.548	32
5	control	0.9523	1.04	1.119	1.168	1.54	1.139	0.1614	10
5	monochromator	0.8441	0.875	0.8963	0.9345	1.032	0.9121	0.05494	16
6	control	2.388	3.946	4.457	5.375	8.391	4.748	1.308	105
6	monochromator	2.463	3.619	4.492	7.097	11	5.361	2.26	63
7	control	0.3176	1.728	2.124	3.294	6.68	2.656	1.513	39
7	monochromator	0.5014	2.379	2.792	3.98	8.797	3.49	2.269	17
8	control	3.462	4.411	5.757	6.73	9.849	5.881	1.766	39
8	monochromator	2.799	5.105	5.834	7.824	18.07	6.743	2.838	36

Summary of each Cell individually

Cell 1

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell1results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell1results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell1")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell1results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0.8968	1.374	1.468	1.665	1.784	1.463	0.2258	34
monochromator	0.9734	1.467	1.581	1.816	2.103	1.625	0.265	25

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell1results$Cm[cell1results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell1results$Cm[cell1results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell1results), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-2.47	46.77	0.01722 *	two.sided	1.463	1.625

Since, our P-value is significant (0.0172217 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Cell 2

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell2results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell2results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell2")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell2results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0.2018	0.393	0.5371	0.6598	1.146	0.5272	0.2155	59
monochromator	0.5704	0.6623	0.7047	0.775	0.9235	0.7284	0.09291	20

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell2results$Cm[cell2results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell2results$Cm[cell2results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell2results), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-5.763	72.51	1.872e-07 * * *	two.sided	0.5272	0.7284

Since, our P-value is significant (1.8716794^{-7} < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Cell 3

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell3results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell3results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell3")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell3results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	1.993	3.183	3.595	4.009	8.419	3.602	0.9369	70
monochromator	1.536	2.192	5.024	5.739	6.673	4.154	1.847	21

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell3results$Cm[cell3results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell3results$Cm[cell3results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell3results), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-1.32	23.17	0.1998	two.sided	3.602	4.154

Since, our P-value is not significant (0.1998297 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Cell 4

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell4results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell4results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell4")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell4results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	1.202	1.693	2.721	3.084	3.953	2.532	0.7741	54
monochromator	-16.82	1.903	2.43	3.169	5.453	2.029	3.548	32

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell4results$Cm[cell4results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell4results$Cm[cell4results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell4results), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
0.7918	32.76	0.4342	two.sided	2.532	2.029

Since, our P-value is not significant (0.4342001 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Cell 5

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell5results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell5results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell5")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell5results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0.9523	1.04	1.119	1.168	1.54	1.139	0.1614	10
monochromator	0.8441	0.875	0.8963	0.9345	1.032	0.9121	0.05494	16

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell5results$Cm[cell5results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell5results$Cm[cell5results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell5results), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
4.286	10.32	0.001486 * *	two.sided	1.139	0.9121

Since, our P-value is significant (0.0014856 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Cell 6

VC = -10

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell6results_10)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell6results_10,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell6")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell6results_10 %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	3.29	4.136	4.407	4.983	5.952	4.535	0.696	54
monochromator	2.79	3.704	3.979	4.379	5.158	3.983	0.5886	19

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell6results_10$Cm[cell6results_10$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell6results_10$Cm[cell6results_10$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell6results_10), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
3.343	37.02	0.001906 * *	two.sided	4.535	3.983

Since, our P-value is significant (0.0019059 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

VC = -60

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell6results_60)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell6results_60,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell6")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell6results_60 %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	2.388	3.6	4.717	6.45	8.391	4.974	1.716	51
monochromator	2.463	3.593	6.353	7.607	11	5.956	2.453	44

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell6results_60$Cm[cell6results_60$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell6results_60$Cm[cell6results_60$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell6results_60), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-2.227	75.4	0.0289 *	two.sided	4.974	5.956

Since, our P-value is significant (0.0289027 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Cell 7

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell7results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell7results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell7")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell7results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0.3176	1.728	2.124	3.294	6.68	2.656	1.513	39
monochromator	0.5014	2.379	2.792	3.98	8.797	3.49	2.269	17

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell7results$Cm[cell7results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell7results$Cm[cell7results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell7results), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-1.388	22.45	0.1787	two.sided	2.656	3.49

Since, our P-value is not significant (0.1787289 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Cell 8

VC = -10

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell8results_10)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell8results_10,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell8")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell8results_10 %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	4.011	5.788	6.529	7.445	9.849	6.702	1.579	26
monochromator	2.799	6.727	7.901	8.791	18.07	8.323	3.298	18

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell8results_10$Cm[cell8results_10$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell8results_10$Cm[cell8results_10$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell8results_10), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-1.937	22.44	0.06546	two.sided	6.702	8.323

Since, our P-value is not significant (0.0654597 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

VC = -60

Below is the boxplot comparison of the \(C_m\) values of the cell that was not stimulated by light (control) and the values when it was stimulated by light (monochromator):

test <- t.test(Cm~Stimulation_Type, data = cell8results_60)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm~Stimulation_Type, data = cell8results_60,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell8")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

cell8results_60 %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm), Q1 = quantile(Cm, 0.25), med = median(Cm), Q3 = quantile(Cm, 0.75), max = max(Cm), mean=mean(Cm), sd =sd(Cm), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm Cell1", split.table=Inf)

Summary Statistics of Cm Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	3.462	3.745	4.306	4.473	5.223	4.238	0.5476	13
monochromator	3.795	4.794	5.194	5.639	6.04	5.163	0.6444	18

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(cell8results_60$Cm[cell8results_60$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Cm", id=FALSE)
qqPlot(cell8results_60$Cm[cell8results_60$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Cm", id=FALSE)

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm~Stimulation_Type, data = cell8results_60), split.table=Inf)

Welch Two Sample t-test: Cm by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-4.306	28.14	0.0001823 * * *	two.sided	4.238	5.163

Since, our P-value is significant (1.8229896^{-4} < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Normalized Data Analysis

Hide Data

norm_results <-read_csv("Normalization_result.csv")
norm_results$X1 <- NULL

\(R_m\)

test <- t.test(Rm_scaled~Stimulation_Type, data = norm_results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Rm_scaled~Stimulation_Type, data = norm_results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell1")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

norm_results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm_scaled), Q1 = quantile(Rm_scaled, 0.25), med = median(Rm_scaled), Q3 = quantile(Rm_scaled, 0.75), max = max(Rm_scaled), mean=mean(Rm_scaled), sd =sd(Rm_scaled), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm_scaled Cell1", split.table=Inf)

Summary Statistics of Rm_scaled Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0	0.1769	0.4079	0.5574	1	0.3854	0.2297	410
monochromator	0	0.2168	0.3994	0.519	1	0.3869	0.2192	230

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(norm_results$Rm_scaled[norm_results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm_scaled", id=FALSE)
qqPlot(norm_results$Rm_scaled[norm_results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm_scaled", id=FALSE)

Because the data is not quiet normal, we will use Permutations Test that allows for non-parametric data and see what results we get:

myTest<-t.test(Rm_scaled~Stimulation_Type, data = norm_results, mu = 0)
observedTestStat <- myTest$statistic

N <- 2000
permutedTestStats <- rep(NA, N)
for (i in 1:N){
  permutedData <- sample(norm_results$Stimulation_Type)
  permutedTest <- t.test(Rm_scaled ~ permutedData, data = norm_results, mu = 0)
  permutedTestStats[i] <- permutedTest$statistic
}

hist(permutedTestStats, col = "skyblue")
abline(v = observedTestStat, col = "red", lwd = 3)

This is the p-value we get:

if (observedTestStat < 0){
 2*sum(permutedTestStats <= observedTestStat)/N 
} else{
  2*sum(permutedTestStats >= observedTestStat)/N
}

## [1] 0.938

Here are the results we get:

pander(t.test(Rm_scaled~Stimulation_Type, data = norm_results), split.table=Inf)

Welch Two Sample t-test: Rm_scaled by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-0.07779	493.3	0.938	two.sided	0.3854	0.3869

Since, our P-value is not significant (0.9380258 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

\(C_m\)

test <- t.test(Cm_scaled~Stimulation_Type, data = norm_results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm_scaled~Stimulation_Type, data = norm_results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell2")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

norm_results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm_scaled), Q1 = quantile(Cm_scaled, 0.25), med = median(Cm_scaled), Q3 = quantile(Cm_scaled, 0.75), max = max(Cm_scaled), mean=mean(Cm_scaled), sd =sd(Cm_scaled), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm_scaled Cell1", split.table=Inf)

Summary Statistics of Cm_scaled Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0	0.2027	0.3058	0.4919	1	0.3801	0.2554	410
monochromator	0	0.168	0.4351	0.6655	1	0.436	0.2977	230

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(norm_results$Rm_scaled[norm_results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm_scaled", id=FALSE)
qqPlot(norm_results$Rm_scaled[norm_results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm_scaled", id=FALSE)

Because the data is not quiet normal, we will use Permutations Test that allows for non-parametric data and see what results we get:

myTest<-t.test(Cm_scaled~Stimulation_Type, data = norm_results, mu = 0)
observedTestStat <- myTest$statistic

N <- 2000
permutedTestStats <- rep(NA, N)
for (i in 1:N){
  permutedData <- sample(norm_results$Stimulation_Type)
  permutedTest <- t.test(Cm_scaled ~ permutedData, data = norm_results, mu = 0)
  permutedTestStats[i] <- permutedTest$statistic
}

hist(permutedTestStats, col = "skyblue")
abline(v = observedTestStat, col = "red", lwd = 3)

This is the p-value we get:

if (observedTestStat < 0){
 2*sum(permutedTestStats <= observedTestStat)/N 
} else{
  2*sum(permutedTestStats >= observedTestStat)/N
}

## [1] 0.025

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm_scaled~Stimulation_Type, data = norm_results), split.table=Inf)

Welch Two Sample t-test: Cm_scaled by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-2.396	417.4	0.017 *	two.sided	0.3801	0.436

Since, our P-value is significant (0.0169986 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Show Data

Here is the link to the google colab where the data was normalized using MinMaxScaler() from sklearn.preprocessing to obtain columns ‘Rm_scaled’ and ‘Cm_scaled’:

https://colab.research.google.com/gist/stassy8/ecbdab4168879c5f1177e650481df3af/min_max_datanormalization.ipynb

datatable(norm_results)

Standardized Data Analysis

Hide Data

standard_results <-read_csv("Standardization_result.csv")
standard_results$X1 <- NULL

\(R_m\)

test <- t.test(Rm_scaled~Stimulation_Type, data = standard_results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Rm_scaled~Stimulation_Type, data = standard_results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell1")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

standard_results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm_scaled), Q1 = quantile(Rm_scaled, 0.25), med = median(Rm_scaled), Q3 = quantile(Rm_scaled, 0.75), max = max(Rm_scaled), mean=mean(Rm_scaled), sd =sd(Rm_scaled), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm_scaled Cell1", split.table=Inf)

Summary Statistics of Rm_scaled Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	-4.293	-0.7052	-0.1357	0.5652	5.96	-0.0276	1.027	410
monochromator	-2.699	-0.5537	-0.05612	0.5529	3.574	0.0492	0.9525	230

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(standard_results$Rm_scaled[standard_results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm_scaled", id=FALSE)
qqPlot(standard_results$Rm_scaled[standard_results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm_scaled", id=FALSE)

Because the data is not quiet normal, we will use Permutations Test that allows for non-parametric data and see what results we get:

myTest<-t.test(Rm_scaled~Stimulation_Type, data = standard_results, mu = 0)
observedTestStat <- myTest$statistic

N <- 2000
permutedTestStats <- rep(NA, N)
for (i in 1:N){
  permutedData <- sample(standard_results$Stimulation_Type)
  permutedTest <- t.test(Rm_scaled ~ permutedData, data = standard_results, mu = 0)
  permutedTestStats[i] <- permutedTest$statistic
}

hist(permutedTestStats, col = "skyblue")
abline(v = observedTestStat, col = "red", lwd = 3)

This is the p-value we get:

if (observedTestStat < 0){
 2*sum(permutedTestStats <= observedTestStat)/N 
} else{
  2*sum(permutedTestStats >= observedTestStat)/N
}

## [1] 0.322

Here are the results we get:

pander(t.test(Rm_scaled~Stimulation_Type, data = standard_results), split.table=Inf)

Welch Two Sample t-test: Rm_scaled by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-0.9514	504.8	0.3419	two.sided	-0.0276	0.0492

Since, our P-value is not significant (0.341876 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

\(C_m\)

test <- t.test(Cm_scaled~Stimulation_Type, data = standard_results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm_scaled~Stimulation_Type, data = standard_results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell2")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

standard_results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm_scaled), Q1 = quantile(Cm_scaled, 0.25), med = median(Cm_scaled), Q3 = quantile(Cm_scaled, 0.75), max = max(Cm_scaled), mean=mean(Cm_scaled), sd =sd(Cm_scaled), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm_scaled Cell1", split.table=Inf)

Summary Statistics of Cm_scaled Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	-2.52	-0.576	-0.1763	0.3139	3.869	-0.1061	0.8099	410
monochromator	-8.6	-0.5839	-0.00626	0.8794	5.011	0.1892	1.252	230

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(standard_results$Rm_scaled[standard_results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm_scaled", id=FALSE)
qqPlot(standard_results$Rm_scaled[standard_results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm_scaled", id=FALSE)

Because the data is not quiet normal, we will use Permutations Test that allows for non-parametric data and see what results we get:

myTest<-t.test(Cm_scaled~Stimulation_Type, data = standard_results, mu = 0)
observedTestStat <- myTest$statistic

N <- 2000
permutedTestStats <- rep(NA, N)
for (i in 1:N){
  permutedData <- sample(standard_results$Stimulation_Type)
  permutedTest <- t.test(Cm_scaled ~ permutedData, data = standard_results, mu = 0)
  permutedTestStats[i] <- permutedTest$statistic
}

hist(permutedTestStats, col = "skyblue")
abline(v = observedTestStat, col = "red", lwd = 3)

This is the p-value we get:

if (observedTestStat < 0){
 2*sum(permutedTestStats <= observedTestStat)/N 
} else{
  2*sum(permutedTestStats >= observedTestStat)/N
}

## [1] 0.001

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm_scaled~Stimulation_Type, data = standard_results), split.table=Inf)

Welch Two Sample t-test: Cm_scaled by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-3.219	338.7	0.00141 * *	two.sided	-0.1061	0.1892

Since, our P-value is significant (0.0014101 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Show Data

Here is the link to the google colab where the data was standardized using StandardScaler() from sklearn.preprocessing to obtain columns ‘Rm_scaled’ and ‘Cm_scaled’:

https://colab.research.google.com/gist/stassy8/6059156381326be744cb015e467d4bae/standard_scalar_datastandardization.ipynb

datatable(standard_results)

Normalized Data Light-Control and Control-Light Analysis

Light-Control

Hide Data

LC_results <-read_csv("Normalization_result_LC.csv")

\(R_m\)

test <- t.test(Rm_scaled~Stimulation_Type, data = LC_results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Rm_scaled~Stimulation_Type, data = LC_results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell1")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

LC_results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm_scaled), Q1 = quantile(Rm_scaled, 0.25), med = median(Rm_scaled), Q3 = quantile(Rm_scaled, 0.75), max = max(Rm_scaled), mean=mean(Rm_scaled), sd =sd(Rm_scaled), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm_scaled Cell1", split.table=Inf)

Summary Statistics of Rm_scaled Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0	0.1496	0.3197	0.5143	1	0.3383	0.2143	265
monochromator	0	0.185	0.3846	0.4817	1	0.3583	0.2088	183

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(LC_results$Rm_scaled[LC_results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm_scaled", id=FALSE)
qqPlot(LC_results$Rm_scaled[LC_results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm_scaled", id=FALSE)

Because the data is not quiet normal, we will use Permutations Test that allows for non-parametric data and see what results we get:

myTest<-t.test(Rm_scaled~Stimulation_Type, data = LC_results, mu = 0)
observedTestStat <- myTest$statistic

N <- 2000
permutedTestStats <- rep(NA, N)
for (i in 1:N){
  permutedData <- sample(LC_results$Stimulation_Type)
  permutedTest <- t.test(Rm_scaled ~ permutedData, data = LC_results, mu = 0)
  permutedTestStats[i] <- permutedTest$statistic
}

hist(permutedTestStats, col = "skyblue")
abline(v = observedTestStat, col = "red", lwd = 3)

This is the p-value we get:

if (observedTestStat < 0){
 2*sum(permutedTestStats <= observedTestStat)/N 
} else{
  2*sum(permutedTestStats >= observedTestStat)/N
}

## [1] 0.312

Here are the results we get:

pander(t.test(Rm_scaled~Stimulation_Type, data = LC_results), split.table=Inf)

Welch Two Sample t-test: Rm_scaled by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-0.9875	397.9	0.324	two.sided	0.3383	0.3583

Since, our P-value is not significant (0.323984 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

\(C_m\)

test <- t.test(Cm_scaled~Stimulation_Type, data = LC_results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm_scaled~Stimulation_Type, data = LC_results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell2")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

LC_results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm_scaled), Q1 = quantile(Cm_scaled, 0.25), med = median(Cm_scaled), Q3 = quantile(Cm_scaled, 0.75), max = max(Cm_scaled), mean=mean(Cm_scaled), sd =sd(Cm_scaled), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm_scaled Cell1", split.table=Inf)

Summary Statistics of Cm_scaled Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0	0.2207	0.3053	0.4559	1	0.375	0.2351	265
monochromator	0	0.1735	0.3667	0.677	1	0.4347	0.3025	183

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(LC_results$Rm_scaled[LC_results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm_scaled", id=FALSE)
qqPlot(LC_results$Rm_scaled[LC_results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm_scaled", id=FALSE)

Because the data is not quiet normal, we will use Permutations Test that allows for non-parametric data and see what results we get:

myTest<-t.test(Cm_scaled~Stimulation_Type, data = LC_results, mu = 0)
observedTestStat <- myTest$statistic

N <- 2000
permutedTestStats <- rep(NA, N)
for (i in 1:N){
  permutedData <- sample(LC_results$Stimulation_Type)
  permutedTest <- t.test(Cm_scaled ~ permutedData, data = LC_results, mu = 0)
  permutedTestStats[i] <- permutedTest$statistic
}

hist(permutedTestStats, col = "skyblue")
abline(v = observedTestStat, col = "red", lwd = 3)

This is the p-value we get:

if (observedTestStat < 0){
 2*sum(permutedTestStats <= observedTestStat)/N 
} else{
  2*sum(permutedTestStats >= observedTestStat)/N
}

## [1] 0.018

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm_scaled~Stimulation_Type, data = LC_results), split.table=Inf)

Welch Two Sample t-test: Cm_scaled by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-2.245	326.3	0.02542 *	two.sided	0.375	0.4347

Since, our P-value is significant (0.0254174 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Show Data

The data was filtered to only contain the sets that had first light recorded and then control.

datatable(LC_results)

Control-Light

Hide Data

CL_results <-read_csv("Normalization_result_CL.csv")

\(R_m\)

test <- t.test(Rm_scaled~Stimulation_Type, data = CL_results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Rm_scaled~Stimulation_Type, data = CL_results,outline=FALSE, col=color, main = c(expression(R[m]~"comparison in Cell1")), xlab ="Stimulation Type", ylab=c(expression(R[m]~" (MOhm)")))

CL_results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Rm_scaled), Q1 = quantile(Rm_scaled, 0.25), med = median(Rm_scaled), Q3 = quantile(Rm_scaled, 0.75), max = max(Rm_scaled), mean=mean(Rm_scaled), sd =sd(Rm_scaled), 'sample size'=n()) %>% pander(caption="Summary Statistics of Rm_scaled Cell1", split.table=Inf)

Summary Statistics of Rm_scaled Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0	0.2977	0.4772	0.5832	1	0.443	0.2145	333
monochromator	0	0.2168	0.3994	0.519	1	0.3869	0.2192	230

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(CL_results$Rm_scaled[CL_results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm_scaled", id=FALSE)
qqPlot(CL_results$Rm_scaled[CL_results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm_scaled", id=FALSE)

Because the data is not quiet normal, we will use Permutations Test that allows for non-parametric data and see what results we get:

myTest<-t.test(Rm_scaled~Stimulation_Type, data = CL_results, mu = 0)
observedTestStat <- myTest$statistic

N <- 2000
permutedTestStats <- rep(NA, N)
for (i in 1:N){
  permutedData <- sample(CL_results$Stimulation_Type)
  permutedTest <- t.test(Rm_scaled ~ permutedData, data = CL_results, mu = 0)
  permutedTestStats[i] <- permutedTest$statistic
}

hist(permutedTestStats, col = "skyblue")
abline(v = observedTestStat, col = "red", lwd = 3)

This is the p-value we get:

if (observedTestStat < 0){
 2*sum(permutedTestStats <= observedTestStat)/N 
} else{
  2*sum(permutedTestStats >= observedTestStat)/N
}

## [1] 0.004

Here are the results we get:

pander(t.test(Rm_scaled~Stimulation_Type, data = CL_results), split.table=Inf)

Welch Two Sample t-test: Rm_scaled by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
3.016	485.7	0.002694 * *	two.sided	0.443	0.3869

Since, our P-value is significant (0.0026936 < \(\alpha\)), we reject the null. This means that there is a significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane resistance of the cell changes significantly from that when there is no light stimulation.

\(C_m\)

test <- t.test(Cm_scaled~Stimulation_Type, data = CL_results)
pvalue <- test[3]
if(pvalue < 0.05){
  pvalueis <- "significant"
  decision <- "we reject the null. This means that there is a significant"
  sign <- "<"
  color <-c("skyblue","orange")
} else {
  pvalueis <- "not significant"
  decision <- "we fail to reject the null. This means that there is no significant"
  sign <- ">"
  color <- c("gray58","gray82")
}


boxplot(Cm_scaled~Stimulation_Type, data = CL_results,outline=FALSE, col=color, main = c(expression(C[m]~"comparison in Cell2")), xlab ="Stimulation Type", ylab=c(expression(C[m]~" (pF)")))

CL_results %>%
group_by(Stimulation_Type) %>%
  summarise(min = min(Cm_scaled), Q1 = quantile(Cm_scaled, 0.25), med = median(Cm_scaled), Q3 = quantile(Cm_scaled, 0.75), max = max(Cm_scaled), mean=mean(Cm_scaled), sd =sd(Cm_scaled), 'sample size'=n()) %>% pander(caption="Summary Statistics of Cm_scaled Cell1", split.table=Inf)

Summary Statistics of Cm_scaled Cell1

Stimulation_Type	min	Q1	med	Q3	max	mean	sd	sample size
control	0	0.2176	0.351	0.5604	1	0.4117	0.2701	333
monochromator	0	0.168	0.4351	0.6655	1	0.436	0.2977	230

Show the diagnostic plots(click to view)

par(mfrow=c(1,2))
qqPlot(CL_results$Rm_scaled[CL_results$Stimulation_Type == "control"], main = "QQ-plot of control", ylab="Rm_scaled", id=FALSE)
qqPlot(CL_results$Rm_scaled[CL_results$Stimulation_Type == "monochromator"], main = "QQ-plot of monochromator", ylab="Rm_scaled", id=FALSE)

Because the data is not quiet normal, we will use Permutations Test that allows for non-parametric data and see what results we get:

myTest<-t.test(Cm_scaled~Stimulation_Type, data = CL_results, mu = 0)
observedTestStat <- myTest$statistic

N <- 2000
permutedTestStats <- rep(NA, N)
for (i in 1:N){
  permutedData <- sample(CL_results$Stimulation_Type)
  permutedTest <- t.test(Cm_scaled ~ permutedData, data = CL_results, mu = 0)
  permutedTestStats[i] <- permutedTest$statistic
}

hist(permutedTestStats, col = "skyblue")
abline(v = observedTestStat, col = "red", lwd = 3)

This is the p-value we get:

if (observedTestStat < 0){
 2*sum(permutedTestStats <= observedTestStat)/N 
} else{
  2*sum(permutedTestStats >= observedTestStat)/N
}

## [1] 0.307

Here are the results of the Independent Samples t Test we get:

pander(t.test(Cm_scaled~Stimulation_Type, data = CL_results), split.table=Inf)

Welch Two Sample t-test: Cm_scaled by Stimulation_Type

Test statistic	df	P value	Alternative hypothesis	mean in group control	mean in group monochromator
-0.9912	460.7	0.3221	two.sided	0.4117	0.436

Since, our P-value is not significant (0.3221177 > \(\alpha\)), we fail to reject the null. This means that there is no significant evidence to conclude that when the axons of RVM are stimulated with monochromator membrane capacitance of the cell changes significantly from that when there is no light stimulation.

Show Data

The data was filtered to only contain the sets that had first control recorded and then light.

datatable(CL_results)