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User:Egm4313.s12.team8.colocar/R4.3

Problem
Consider the L2-ODE-CC below with $$ \displaystyle log(1+x)$$ as excitation:

$$ \displaystyle y''-3y'+2y = r(x)$$ $$ \displaystyle r(x) = log(1+x)$$

and the initial conditions $$ \displaystyle y(-\frac3{4})=1, y'(-\frac3{4})=0 $$

1. Develop $$ \displaystyle log(1+x)$$ in Taylor series about $$ \displaystyle \widehat{x}=0$$ to reproduce the figure below

2. Let $$ \displaystyle r_n(x)$$ be truncated Taylor series, with n terms--which is also the highest degree of the Taylor (power) series--of $$ \displaystyle log(1+x)$$. Find $$ \displaystyle y_n(x),$$ for n = 4, 7, 11, such that: $$ \displaystyle y_{n}''+ay_{n}'+by_{n}=r_n(x)$$ with the same initial conditions mentioned earlier. Plot $$ \displaystyle y_{n}(x)$$ for n = 4, 7, 11 for $$ \displaystyle x$$ in $$ \displaystyle [-\frac3{4},3].$$

3. Use the matlab command ode45 to integrate numerically the given equation to obtain the numerical solution for $$ \displaystyle y(x).$$ Plot $$ \displaystyle y(x)$$ in the same figure with $$ \displaystyle y_n(x).$$

Solution
1. The Taylor series about a point $$ \displaystyle \hat{x} $$ is defined as $$ \displaystyle  f(x) = \sum_{n=0}^\infty \frac{f^{n} (\hat x)}{n!} (x - \hat x)^n $$

For $$ \displaystyle \hat{x}=0, $$ we can expand the series as $$ \displaystyle f(x) = \sum_{n=0}^\infty \frac{f^{n}(0)}{n!} x^n = \frac{f^{0}(0)}{0!} x^0 + \frac{f^{1}(0)}{1!} x^1 + \frac{f^{2}(0)}{2!} x^2 + \frac{f^{3}(0)}{3!} x^3 + \cdots + \frac{f^{n}(0)}{n!} x^n $$

Deriving $$ \displaystyle ln(1+x) $$ yields $$ \displaystyle \frac{1}{x+1} $$

Plugging the derivative into the expanded series yields $$ \displaystyle log(1+x) = \sum_{n=0}^\infty \frac{f^{0}(0)}{n!}x^0 = \frac{1}{0!}ln(1)x^0 + \frac{1}{1!}\frac{1}{0+1}x^1 - \frac{1}{2!}\frac{1}{(0+1)^2}x^2 + \frac{1}{3!}\frac{2}{(0+1)^3}x^3 \cdots + \frac{1}{n!}\frac{f^n(0)}{(1)^n}x^n $$

Simplified gives us $$ \displaystyle ln(1+x) = \sum_{n=0}^\infty \frac{f^{0}(0)}{n!}x^0 = 0+ \frac{x^1}{1} - \frac{x^2}{2} + \frac{x^3}{3} + \cdots + \frac{x^n}{n} $$

Or from the Mercator series, $$\log(1+x)=\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} x^n = x - \frac{x^2}{2} + \frac{x^3}{3} - \cdots \quad$$ so, T4 (n = 4) $$ \displaystyle ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4}$$

T7 (n = 7) $$ \displaystyle ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \frac{x^5}{5} - \frac{x^6}{6} + \frac{x^7}{7}$$

T11 (n = 11) $$ \displaystyle ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \frac{x^5}{5} - \frac{x^6}{6} + \frac{x^7}{7} - \frac{x^8}{8} + \frac{x^9}{9} - \frac{x^{10}}{10} + \frac{x^{11}}{11}$$

T16 (n = 16) $$ \displaystyle ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \frac{x^5}{5} - \frac{x^6}{6} + \frac{x^7}{7} - \frac{x^8}{8} + \frac{x^9}{9} - \frac{x^{10}}{10} + \frac{x^{11}}{11} - \frac{x^{12}}{12} + \frac{x^{13}}{13} - \frac{x^{14}}{14} + \frac{x^{15}}{15} - \frac{x^{16}}{16}$$

Creating a function in MATLAB, we can code and plot

2. To find $$ \displaystyle y_n(x), $$ we must first determine the homogeneous and particular solutions. We know the characteristic equation to be $$ \displaystyle \lambda^2 -3\lambda + 2 = 0, $$ so $$ \displaystyle (\lambda - 2)(\lambda - 1) = 0, $$

Knowing $$ \displaystyle \lambda = 1,2, $$ the homogeneous solution is defined as $$ \displaystyle y_h = c_1e^x + c_2e^{2x}$$

n = 4 The particular solution for n = 4 can be obtained from the following: $$ \displaystyle y_p = K_4x^4 + K_3x^3 + K_2x^2 + K_1x^1 + K_0. $$ Also, $$ \displaystyle y_p' = 4K_4x^3 + 3K_3x^2 + 2K_2x + K_1 $$ and $$ \displaystyle y_p'' = 12K_4x^2 + 6K_3x + 2K_2. $$

Plugging back into the given ODE, and equating to the excitation gives us $$ \displaystyle (12K_4x^2 + 6K_3x + 2K_2) - 3(4K_4x^3 + 3K_3x^2 + 2K_2x + K_1) + 2(K_4x^4 + K_3x^3 + K_2x^2 + K_1x^1 + K_0) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} $$

Simplified, $$ \displaystyle (12K_4x^2 + 6K_3x + 2K_2) - (12K_4x^3 + 9K_3x^2 + 6K_2x + 3K_1) + (2K_4x^4 + 2K_3x^3 + 2K_2x^2 + 2K_1x^1 + 2K_0) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} $$

Creating a matrix for Matlab to solve for the unknown values of K $$ \begin{bmatrix} 2 & -3 & 2 & 0 & 0 \\ 0 & 2 & -6 & 6 & 0 \\ 0 & 0 & 2 & -9 & 12 \\ 0 & 0 & 0 & 2 & -12 \\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}

\begin{bmatrix} K_0 \\ K_1 \\ K_2 \\ K_3 \\ K_4 \end{bmatrix} =

\begin{bmatrix} 0 \\ 1 \\ -\frac{1}{2} \\ \frac{1}{3} \\ -\frac{1}{4} \end{bmatrix}$$

Now, we have $$ \displaystyle y_p = 0.0543x^4 + 0.3981x^3 + 1.5743x^2 + 3.7458x^1 + 4.0444 $$ and our final solution is $$ \displaystyle y_n(x) = c_1e^x + c_2e^{2x} + 0.0543x^4 + 0.3981x^3 + 1.5743x^2 + 3.7458x^1 + 4.0444 $$

Evaluating at our initial conditions gives $$ \displaystyle y_n(-\frac3{4}) = c_1e^{-\frac3{4}} + c_2e^{2(-\frac3{4})} + 0.0543(-\frac3{4})^4 + 0.3981(-\frac3{4})^3 + 1.5743(-\frac3{4})^2 + 3.7458(-\frac3{4})^1 + 4.0444 = 1 $$ and

$$ \displaystyle y'_n(-\frac3{4}) = c_1e^{-\frac3{4}} + 2c_2e^{2(-\frac3{4})} + 4(0.0543)(-\frac3{4})^3 + 3(0.3981)(-\frac3{4})^2 + 2(1.5743)(-\frac3{4}) + 3.7458 = 0 $$

Solving for the constants gives us $$ \displaystyle c_1 = -4.4579 $$ $$ \displaystyle c_2 = 0.0526 $$

Therefore, $$ \displaystyle y_n(x) = -4.4579e^x + 0.0526e^{2x} + 0.0543x^4 + 0.3981x^3 + 1.5743x^2 + 3.7458x^1 + 4.0444 $$ and

n = 7 The particular solution for n = 7 can be obtained from the following: $$ \displaystyle y_p = K_7x^7 + K_6x^6 + K_5x^5 + K_4x^4 + K_3x^3 + K_2x^2 + K_1x^1 + K_0. $$ Also, $$ \displaystyle y_p' = 7K_7x^6 + 6K_6x^5 + 5K_5x^4 + 4K_4x^3 + 3K_3x^2 + 2K_2x + K_1 $$ and $$ \displaystyle y_p'' = 42K_7x^5 + 30K_6x^4 + 20K_5x^3 + 12K_4x^2 + 6K_3x + 2K_2. $$

Plugging back into the given ODE, and equating to the excitation gives us $$ \displaystyle (42K_7x^5 + 30K_6x^4 + 20K_5x^3 + 12K_4x^2 + 6K_3x + 2K_2) - 3(7K_7x^6 + 6K_6x^5 + 5K_5x^4 + 4K_4x^3 + 3K_3x^2 + 2K_2x + K_1) + \cdots $$ $$ \displaystyle 2(K_7x^7 + K_6x^6 + K_5x^5 + K_4x^4 + K_3x^3 + K_2x^2 + K_1x^1 + K_0) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \frac{x^5}{5} - \frac{x^6}{6} + \frac{x^7}{7} $$

Simplified, $$ \displaystyle (42K_7x^5 + 30K_6x^4 + 20K_5x^3 + 12K_4x^2 + 6K_3x + 2K_2) - (21K_7x^6 + 18K_6x^5 + 15K_5x^4 + 12K_4x^3 + 9K_3x^2 + 6K_2x + 3K_1) + \cdots $$ $$ \displaystyle (2K_7x^7 + 2K_6x^6 + 2K_5x^5 + 2K_4x^4 + 2K_3x^3 + 2K_2x^2 + 2K_1x^1 + 2K_0) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \frac{x^5}{5} - \frac{x^6}{6} + \frac{x^7}{7} $$

Creating a matrix for Matlab to solve for the unknown values of K $$ \begin{bmatrix} 2 & -3 &  2 &   0 &   0 &  0 &  0 &  0 \\ 0 &   2  & -6 &  6 &   0 &  0 &  0 &  0 \\ 0 &   0  &   2 & -9 &  12 &  0 &  0 &  0 \\ 0 &   0  &   0 &   2 & -12 & 20 &  0 &  0 \\ 0 &   0  &   0 &   0 &   2 & -15 &  30 &  0 \\ 0 &   0  &   0 &   0 &   0 &  2 & -18 &  42 \\ 0 &   0  &   0 &   0 &   0 &  0 &  2 & -21 \\ 0 &   0  &   0 &   0 &   0 &  0 &  0 &  2 \end{bmatrix}

\begin{bmatrix} K_0 \\ K_1 \\ K_2 \\ K_3 \\ K_4 \\ K_5 \\ K_6 \\ K_7 \end{bmatrix} =

\begin{bmatrix} 0 \\ 1 \\ -\frac{1}{2} \\ \frac{1}{3} \\ -\frac{1}{4} \\ \frac{1}{5} \\ -\frac{1}{6} \\ \frac{1}{7} \end{bmatrix}$$

Now, we have $$ \displaystyle y_p = 0.0310x^7 + 0.3619x^6 + 2.6492x^5 + 14.4946x^4 + 60.5479x^3 + 185.6066x^2 + 375.3933x + 377.4833 $$

and our final solution is $$ \displaystyle y_n(x) = c_1e^x + c_2e^{2x} + 0.0310x^7 + 0.3619x^6 + 2.6492x^5 + 14.4946x^4 + 60.5479x^3 + 185.6066x^2 + 375.3933x + 377.4833 $$

Evaluating at our initial conditions gives $$ \displaystyle y_n(-\frac3{4}) = c_1e^{-\frac3{4}} + c_2e^{2(-\frac3{4})} + 0.0310(-\frac3{4})^7 + 0.3619(-\frac3{4})^6 + 2.6492(-\frac3{4})^5 + \cdots $$ $$ \displaystyle 14.4946(-\frac3{4})^4 + 60.5479(-\frac3{4})^3 + 185.6066(-\frac3{4})^2 + 375.3933(-\frac3{4}) + 377.4833 = 1$$  and

$$ \displaystyle y'_n(-\frac3{4}) = c_1e^{-\frac3{4}} + 2c_2e^{2(-\frac3{4})} + 7(0.0310)(-\frac3{4})^6 + 6(0.3619)(-\frac3{4})^5 + \cdots $$ $$ \displaystyle 5(2.6492)(-\frac3{4})^4 + 4(14.4946)(-\frac3{4})^3 + 3(60.5479)(-\frac3{4})^2 + 2(185.6066)(-\frac3{4}) + 375.3933 = 0 $$

Solving for the constants gives us $$ \displaystyle c_1 = -2.6757 $$ $$ \displaystyle c_2 = -375.1733 $$

Therefore, $$ \displaystyle y_n(x) = -2.6757e^x - 375.1733e^{2x} + 0.0310x^7 + 0.3619x^6 + 2.6492x^5 + 14.4946x^4 + 60.5479x^3 + 185.6066x^2 + 375.3933x + 377.4833 $$ and

n = 11 The particular solution for n = 11 can be obtained from the following: $$ \displaystyle y_p = K_11x^11 + K_10x^10 + K_9x^9 + K_8x^8 + K_7x^7 + K_6x^6 + K_5x^5 + K_4x^4 + K_3x^3 + K_2x^2 + K_1x^1 + K_0. $$ Also, $$ \displaystyle y_p' = 11K_11x^10 + 10K_10x^9 + 9K_9x^8 + 8K_8x^7 + 7K_7x^6 + 6K_6x^5 + 5K_5x^4 + 4K_4x^3 + 3K_3x^2 + 2K_2x + K_1 $$ and $$ \displaystyle y_p'' = 110K_11x^9 + 90K_10x^8 + 72K_9x^7 + 56K_8x^6 + 42K_7x^5 + 30K_6x^4 + 20K_5x^3 + 12K_4x^2 + 6K_3x + 2K_2. $$

Plugging back into the given ODE, and equating to the excitation gives us $$ \displaystyle (110K_11x^9 + 90K_10x^8 + 72K_9x^7 + 56K_8x^6 + 42K_7x^5 + 30K_6x^4 + 20K_5x^3 + 12K_4x^2 + 6K_3x + 2K_2) - 3(11K_11x^10 + \cdots $$ $$ \displaystyle 10K_10x^9 + 9K_9x^8 + 8K_8x^7 + 7K_7x^6 + 6K_6x^5 + 5K_5x^4 + 4K_4x^3 + 3K_3x^2 + 2K_2x + K_1) + 2(K_11x^11 + K_10x^10 + K_9x^9 + K_8x^8 + K_7x^7 + K_6x^6 + K_5x^5 + \cdots $$ $$ \displaystyle K_4x^4 + K_3x^3 + K_2x^2 + K_1x^1 + K_0) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \frac{x^5}{5} - \frac{x^6}{6} + \frac{x^7}{7} - \frac{x^7}{8} + \frac{x^7}{9} - \frac{x^7}{10} + \frac{x^7}{11} $$

Simplified, $$ \displaystyle (110K_11x^9 + 90K_10x^8 + 72K_9x^7 + 56K_8x^6 + 42K_7x^5 + 30K_6x^4 + 20K_5x^3 + 12K_4x^2 + 6K_3x + 2K_2) - \cdots $$ $$ \displaystyle (33K_11x^10 + 30K_10x^9 + 27K_9x^8 + 24K_8x^7 + 21K_7x^6 + 18K_6x^5 + 15K_5x^4 + 12K_4x^3 + 9K_3x^2 + 6K_2x + 3K_1) + \cdots $$ $$ \displaystyle (2K_11x^11 + 2K_10x^10 + 2K_9x^9 + 2K_8x^8 + 2K_7x^7 + 2K_6x^6 + 2K_5x^5 + 2K_4x^4 + 2K_3x^3 + 2K_2x^2 + 2K_1x^1 + 2K_0) = \cdots $$ $$ \displaystyle x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \frac{x^5}{5} - \frac{x^6}{6} + \frac{x^7}{7} - \frac{x^7}{8} + \frac{x^7}{9} - \frac{x^7}{10} + \frac{x^7}{11}$$

Creating a matrix for Matlab to solve for the unknown values of K

Now, we have $$ \displaystyle y_p = 0.0197x^11 + 0.3474x^10 + 4.1499x^9 + 40.4165x^8 + \cdots $$ $$ \displaystyle 335.6321x^7 + 2392.5102x^6 + 20348.2561x^5 + 140399.9629x^4 + 638917.2891x^3 + 2032728.1323x^2 + 4181432.7467x + 4239420.9877 $$

and our final solution is $$ \displaystyle y_n(x) = c_1e^x + c_2e^{2x} + 0.0197x^11 + 0.3474x^10 + 4.1499x^9 + \cdots $$ $$ \displaystyle 40.4165x^8 + 335.6321x^7 + 2392.5102x^6 + 20348.2561x^5 + 140399.9629x^4 + 638917.2891x^3 + 2032728.1323x^2 + 4181432.7467x + 4239420.9877 $$

Evaluating at our initial conditions gives $$ \displaystyle y_n(-\frac3{4}) = c_1e^{-\frac3{4}} + c_2e^{2(-\frac3{4})} + 0.0197(-\frac3{4})^11 + 0.3474(-\frac3{4})^10 + 4.1499(-\frac3{4})^9 + 40.4165(-\frac3{4})^8 + \cdots $$ $$ \displaystyle 335.6321(-\frac3{4})^7 + 2392.5102(-\frac3{4})^6 + 20348.2561(-\frac3{4})^5 + 140399.9629(-\frac3{4})^4 + 638917.2891(-\frac3{4})^3 +  \cdots $$ $$ \displaystyle 2032728.1323(-\frac3{4})^2 + 4181432.7467(-\frac3{4}) + 4239420.9877 = 1 $$   and

$$ \displaystyle y'_n(-\frac3{4}) = c_1e^{-\frac3{4}} + 2c_2e^{2(-\frac3{4})} + 11(0.0197)(-\frac3{4})^10 + 10(0.3474)(-\frac3{4})^9 + \cdots $$ $$ \displaystyle 9(4.1499)(-\frac3{4})^8 + 8(40.4165)(-\frac3{4})^7 + 7(335.6321)(-\frac3{4})^6 + 6(2392.5102)(-\frac3{4})^5 + 5(20348.2561)(-\frac3{4})^4 + \cdots $$ $$ \displaystyle 4(140399.9629)(-\frac3{4})^3 + 3(638917.2891)(-\frac3{4})^2 + 2(2032728.1323)(-\frac3{4}) + 4181432.7467 = 0 $$

Solving for the constants gives us $$ \displaystyle c_1 = -484 $$ $$ \displaystyle c_2 = -1753750 $$

Therefore, $$ \displaystyle y_n(x) = -484e^x - 1753750e^{2x} + 0.0197x^11 + 0.3474x^10 + 4.1499x^9 + 40.4165x^8 + \cdots $$ $$ \displaystyle 335.6321x^7 + 2392.5102x^6 + 20348.2561x^5 + 140399.9629x^4 + 638917.2891x^3 + 2032728.1323x^2 + \cdots $$ $$ \displaystyle 4181432.7467x + 4239420.9877 $$ and 3. The Following Matlab function uses ode45 to calculate and graph alongside the functions previously obtained.

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User:Egm4313.s12.team11.Suh

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Bayesian Hypothesis Testing Guide

This page will serve as a guide for those that want to do Bayesian hypothesis testing. It's a collaborative effort to try and gather as many procedures(and code) possible that currently exists in Bayesian statistics. The goal is to create an easy to read, easy to apply guide for each method depending on your data and your design. Most of these methods can be applied in scientific disciplines such as Social sciences, Psychology, HCI and others. The philosophy behind this guide is to always keep things simple. Just as we don't ask for my visitors on any website to understand HTTP requests, the same should apply for someone that wants to perform Bayesian statistics. You only need to know what your input is and how to interpret the output. Therefore, the emphasis here is taken away from the mathematical aspects of Bayesian statistics in favor of the actual application.

Note: Some of the terms used in this guide may have been altered in order to match those from the traditional NHST procedures. This was made so that people that already use NHST techniques can easily find the Bayesian equivalents. In addition, terms from traditional hypothesis testing and survey designs won't be explained here. Bayesian definitions will be explained here when appropriate but you can also get a basic introduction here as well as here.

Experimental Designs

 * Bayesian t-test hypothesis testing for two independent groups(For interval values that are normally distributed)

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Fruit flies

This is a brief course of how to grow fruit flies with limited resources. The methods presented are only one example. In other words, this it not a source for a university research but instead aims for a level of natural-science in high school. The course haven’t either included what sorts of experiments are interesting to do, instead, puts focus on how to grow, manage and take care of them.

Fruit Fly – Drosophila Melanogaster
A fruit fly lives for approximately 14 days. During this period it goes from egg, larvae, cocoon till a fly. It takes around ten days for the fly to develop from the day when the egg is laid. Notable, females are ready for courting around 10 hours after they have hatched.

Different flies

 * The female fly is larger than the male and have a greyish rear part.
 * The male fly is smaller than the female and their rear part is black. As well, the male have a constellation of spiky hair around the genitalia used to attached the female during the mating process.
 * You can perceive a female virgin by its whiter rear part.

Short basics of cultivation

 * Try to have around 20 flies in a vial.
 * Always mark a new vial with a unique number and the date of transfer.
 * Transfer flies every 2-3 day.
 * Food never has to be replaced, if a old vial runs out of food, replace the whole vial.
 * Keep track on how you transfer your flies from old vials to new vials. Best way to do it is to continuously update a schedule.
 * Keep in mind that you will have to spend more time than intended in the beginning, and over all, growing fruit flies may be time-consuming.

Environment
It’s important to keep the environment stable. The easiest way is to grow the flies in a normally tempered room. Larger rooms will give a more sustainable environment. Keep in mind that temperature and humidity can vary largely in environments you don't expect it to (night time, day time, sunny or cloudy), therefore, investigate the room before starting to grow the flies. It could be a good idea to place a glass of wine close to the cultivation, since some flies will escape. The flies like the smell of the wine and drown when they land in the liquid.

 * The optimal temperature to grow flies in is 25°C - 28°C. Flies may live at 20°C or under, but the flies reproduce faster if it is warmer. On the other hand, temperatures above 29° - 30° will make the male flies sterile
 * Humidity should be around 50% - 60% outside the vials, if air easily can pass through the seal. There shouldn’t be any liquid water on the wall of the vial, because of the risk of “drowning” the flies. If the water from the food (see below) is not enough to sustain the humidity level, small bottles of water can be placed close by the vials (doesn't work if growing the flies in a room).

Case, vials and seals
Depending on your intentions on experiments, or if there is no well tempered room to place the flies, you may have choose to place the flies in a bigger case. The more volume the easier it is to keep the humidity and the temperature at a desired level.

 * The case shouldn't be much smaller than 30*20*20 centimeters. Moreover, the case preferably should be transparent and allow some air exchange with the outside.
 * The best and easiest vials to use are the one that can be bought.
 * To the standard vial you can by foam rubber seals which are the easiest to use. Otherwise, pressing together a piece of cotton is a good solution.

Sterilize materials
Depending on the level of research, you should sterilize the materials and most importantly the vials.

 * 1) Prepare a container filled with distilled water, something to heat the water with (a burner and a tripod from the chemistry lab), vials and tools (e.g. a suitable pairs of forceps). Hand wash the container, vials and the tools before use.
 * 2) Heat the water to a boiling temperature.
 * 3) Clean the tools. A recommendation is to have two containers, one smaller for cleaning the tools and enough, in order to save the time it take to get the water boiling.
 * 4) Heat new distilled water for the vials.
 * 5) When boiling, put in as many vials as there is room for 5 seconds.
 * 6) Place to dry.
 * 7) Put away the vials in a closed container. They can be stored for a longer time.

Seals should not be sterilized, since they doesn't endure the heat of boiling water.

Food
The food is vital for the flies and influences the environment and the relative time of reproduction. The food is the most important medium which is to keep the humidity at a desirable level. Therefore, the amount of liquid in the food and its consistency are important to have in mind. Do evaluate how the food is working for your usage and try to optimize. There are many different recipes that are to be found on the internet, below is an example of a bought medium mixed with water.

 * 1) Prepare vials, a big container, the food medium, jest, viscous syrup, some small spoons and something to stir with.
 * 2) Work by a water tap and hand wash the tools.
 * 3) Fill the container with your choice of food medium and a spoon of jest per five decilitre food medium. Mix.
 * 4) Pour in the right amount of water, but replace one tenth of the water with syrup to get a firmer consistence. Stir.
 * 5) The consistence of the food should be solid, but if you gently press on it with a finger you should be going down/in to the medium, and get wet.
 * 6) Portion the food into the vials, about 1.5 centimeters of the vials height from the bottom should consist of food. Press the down the food into one solid mass.

Things to keep in mind
 * You save time if you make much food at the same time, but if you do not use the food filled vials directly, they should be stored in a refrigerator.
 * If the food tends to fall down during transfer (see below), you could add more syrup to make it stickier. Though, don't replace the water entirely, since the food in that case will become too dry.

Transfer of flies from vials to vials
Transfer flies to a new vial every 2-3 day. Mark the new vial and prepare it with food before transfer. Have a new seal ready. This process is easier done in pairs.

 * 1) Bump the vial with the flies on to the table gently, enough to keep the flies in the bottom of the vial. Try to tilt the vial and bump the edge of the bottom on to the table, so the flies do not fall directly into the food, where they may get stuck.
 * 2) Remove the seal so the opening is all clear.
 * 3) Quickly put the new vial on top of the old one, leaving no gap for escape.
 * 4) Turn the two vials upside down, meanwhile keeping the two vials together.
 * 5) Bump the vials to the table so the flies fall down in to the new vial.
 * 6) Part the vials and (together with your friend) quickly seal the vials. Be aware of flies that still may be in the old vial.

Things to keep in mind
 * Food may fall down during transfer when bumping the vial, a devastating catastrophe. Therefore, try do make the process/bumping as quick and gently as possible.
 * If using cotton seal: If some of the cotton from the seal sticks to the vial’s wall, creating a “net/beard”, remove it quickly before turning the vial upside down, meanwhile bumping the vial into the table in order to keep the flies in place.
 * When sealing, be aware of not crushing the flies with seal
 * If you are doing any experiments where it is important to keep track of where the flies are transferred, you should organize a schedule before starting to grow the flies.

Exterminate flies and reuse the vials
The food in older vials may after a while look really nasty (grey and very wet). Preferable is to kill the flies and reuse the vials. There is numerous ways to kill flies. It is important to try to keep the population under a decided amount, otherwise the flies tend to grow into uncontrollable numbers. The best way to kill the flies, and be sure there is no living larvae left in the vial, is to simply but the vial into the freezer. Afterwards, clean and sterilise the vials thoroughly.

Put flies to sleep (with CO2)
When you need to count the flies accurately, transfer them in a certain number or divide by any attribute (e.g. male or female). WHOP The procedure following is designed by a shortage of founds, there are much better methods to use. You definitely have to be more than two for this to work.

 * 1) Prepare the CO2 tank, plates with high edges (preferable transparent material), soft brushes to move around the flies and if needed new vials with seal.
 * 2) Gently push the slang from the CO2 tube into the seal to pour the gas into the vial. Be careful so the seal doesn’t slide in and crush the flies.
 * 3) When flies are sound asleep, transfer them to the plate.
 * 4) The flies will eventually wake up, therefore pour in CO2 onto the plate when needed. Since the CO2 is heavier than air it will stay in the plate for a while.
 * 5) Do what you have to do with your pencils, but work fast.

Things to keep in mind
 * Flies sometimes wake up faster then predicted, always be ready with the CO2.
 * Try to give the flies small but many doses of CO2, since too much at a time will suffocate them.
 * Some flies will inevitable escape, therefore, be in another room than the cultivation.
 * Do not try to enclose the flies into any plate or container, since, they eventually will wake up and it will be very difficult to put them back to sleep or in a veil.

Literature and sources
A schoolteacher presenting his methods and choice of project/experiment. A database of the Drosophila genes and genomes. An over-all article. Course material and setups.
 * http://biology.arizona.edu/sciconn/lessons2/Geiger/intro2.htm#disease
 * http://flybase.org/
 * http://en.wikipedia.org/wiki/Drosophila_melanogaster
 * http://www.is.wayne.edu/mnissani/PAGEPUB/FLIES.HTM

Source of images

 * Figure I: Kevin Edwards, 2012-03-11, http://bio.illinoisstate.edu/kaedwar/other/Sexing_Drosophila.shtml
 * Figures II – V: illustrated by Henrik Almquist

Acknowledge
This document is based on information acquired through experience and sources found under the title Literature and sources. Additionally, there has been a contact with a section at Stockholm University's which work with fruit flies. This is the product produced after a project work at the high school of Rudbeck in Sweden during the autumn 2011 and spring 2012. The team consisted of three members: Gustav Nordqvist, Jonathan Nilson and Henrik Almquist.

Do not hesitate to contact us if there are any questions or remarks. Email: me@gmail.com

title: Fruit flies


text: File:Cordic tb.vhdl.20120314.pdf

title: File:Cordic tb.vhdl.20120314.pdf


text:
Talk:Fruit flies

--LemonJaune (talk) 09:43, 14 March 2012 (UTC) Hi, just added this article, but i'm wondering about the last part, Acknowledge. Should it be removed?

title: Talk:Fruit flies


text:
Bayesian t-test hypothesis testing for two independent groups

This method is based on the book "Bayesian Cognitive Modeling: A Practical Course" by Michael Lee and Eric-Jan Wagenmakers. Additionally, a published scientific article can be found here. Some of the code may have been changed in order to make the application of the method easier. If you want to learn more about the model and the code you can read the book.

Both groups should have their data normally distributed.

The procedure is being done using R and OpenBugs.

Input
Set the first three lines according to your setup and data. You also need to set the file that contains the OpenBUGS model which you can find at the end of this page. If you wish to change the priors you can, just remember that you need to adjust the prior for hypothesis 2 and hypothesis 3 in order apply only for positive or negative numbers. Also you can change the itterations and the burnin if you want to improve your results.

Output
The hypotheses for this test are as follows:

 * H0 - δ = 0 means that there is no difference between the two groups
 * H1 - δ <>0 means that there is a difference between the two groups
 * H2 - δ < 0 means that group 2 has larger values than group 1
 * H3 - δ > 0 means that group 1 has larger values than group 2

The output produces a set of results in text such as these along with the probability distribution plots for each one of them. Both are useful for making a decision about your hypothesis. As an example, you can use the graph and determine if at the point δ=0 your posterior(your results after the data) are higher or lower than the prior(your initial belief). If the posterior is higher than the prior at δ=0 then it reinforces the fact that the null hypothesis(H0) is probably true. If the posterior is lower than the prior then the data weakens your belief that the null hypothesis is true.

You determined which hypothesis is more likely based on the Bayes Factor. The way to interpret a general Bayes Factor is the following. If a Bayes factor is denoted as BFxy then you say that the data are n times more likely under Hx than Hy. An example based on the BF10 would be that the data would be 0.53 times more likely under H1 than H0. If we use the BF01 then we would say that the data are 1.87 times more likely under H0 than H1(which is more meaningful). Basically, one version of Bayes factor(e.g. BF01) is the inverted version of the other(e.g BF10).

You determine how strong is your evidence based on the Bayes factor by looking at the table here.

In the first two cases the evidence is "Barely worth mentioning" for H0. But, the third result (7.67) is considered "Substantial" evidence in favor of H0, indicating that when we consider if group 1 has a bigger effect than group 2, there is substantial evidence to say that is unlikely(providing proof for H0).

When publishing you are going to have to report also the process you obtained your results and the numbers of itterations for the MCMC test along with the burnin value and the chains(in this case 3).

The model specifications are:


text:
Progress and Prospects in Parkinson's Research/Causes/Inheritance

< Back to Causes

Background
Diagnosed PD cases can be divided into Sporadic and Familial categories. The second of these categories refers to instances where an onset Mendelianpattern is established or a link to a known PD related mutation has occurred.

The first genetic link to PD was published by Nussbaum et al (1997) and this precipitated an avalanche of similar findings. Currently familial causes are widely quoted as accounting for 5% of diagnosed cases, yet genetic studies account for over 50% of PD research. The reason for this imbalance is:-

 * Research is producing more and more genetic links with the disease and 5% is probably a considerable underestimate.
 * There are indications that many patients must first have a genetic predilection towards the disease which is then triggered by some external factor.
 * If a precursor genetic pattern(s) could be established this might provide a biomarker for the disease.
 * Familial cases provide a useful starting point for elucidating the subsequent course of the disease.
 * Genetic mutations can be inducted into laboratory animals. Breeding transgenic strains of mice, rats, zebra fish, nematode worms and yeast have been produced successfully to enable aspects of the disease to be studied and the effects of new therapies to be tested.

Gene association studies
Gene association studies is a technique in widespread use by genetic researchers, who take a cohort of patients with a diagnosed disease and compare their genes with a matching (control) cohort of people without the disease. The control cohort is generally matched for age, gender and ethnicity.

Statistical analysis of the results can identify individual genes, which are deemed to influence the onset of the disease. Further analysis can then isolate the specific SNP and Genotype responsible for the mutation. The results are published in a peer-reviewed journal and can form the basis for further research.

The results of such studies of PD are sometimes questionable because:-
 * They are not always borne out by repeat studies.
 * The cohorts chosen are small or ill-matched.
 * The control cohort may include undiagnosed PD cases such as those that are in the Prodromeprodromal or presymptomatic stage of the disease.
 * The PD cohort may contain misdiagnosed cases.
 * A single mutation could produce a metabolic chain of events and compromise otherwise healthy genes.

Nevertheless the metaanalysis of repeat studies may identify significant genes.

Other complicating factors are:-
 * Many results identify intergenic SNPs as the source of the mutation and the regulatory role of intergenic material in gene expression is still being elucidated.
 * Many results show negative results i.e. the mutation reduces the risk of PD.
 * Many results show contradictory markers for ethnicity i.e. a SNP may lower the risk for one ethnic group and raise it for another.

A number of public domain web sites are available which summarise the results of PD genetic research to date.

PD-Gene
PD-Gene is a database for Parkinson’s Disease gene association studies maintained by the Max Planck Institute in Berlin in conjunction with the Michael J. Fox Foundation and the Alzheimer Research Forum.

As of October 2012 it is the distillation of 876 studies and identifies 914 PD-related genes and 3443 SNPs. Search arguments are gene, protein, polymorphism, study and keyword, or one can drill down through the sequence chromosome/ gene/ SNP. Chromosome diagrams show the locus of each identified gene.

Parkinson Disease Mutation Database
This database, which is curated by Karen Nuytemans, PhD. of the Neurogenerative Brain Diseases Group, Flanders Institute for Biotechnology and the University of Antwerp, aims “to collect all known mutations and non-pathogenic coding variations in the genes related to Parkinson disease”.

The contents summarised at October 2012 are:-

Parkinson’s Disease Mutations Database
This is curated by the Parkinson's Institute of the Leiden University Medical Centre, Germany. In order to use the service it is necessary to download the LOVD which stands for Leiden Open (source) Variation Database.

The gene variations currently (October 2012) available are for the '''LRRK2. PARK11, PARK2, PARK7, PINK1 and SNCA''' genes.

Mutation Database for Parkinson’s Disease
This is curated by the Institute for Infocomm Research in Singapore. In August 2011 it contained 2,391 entries for 202 genes extracted from 576 publications. The contents of the web site are:-

Where is genetic research going?
Genetic research in relation to the disease is still in its infancy and currently raises more questions than answers. It is a reasonable assumption that gene association studies will throw up many more PD-related SNPs and each one brings with it the questions - what activates the SNP and what happens consequentially inside the affected cell to invoke PD? The observed variable effects of ethnicity and recent work on Alzheimer’s Disease indicate that single SNPs may not work in isolation and that different SNP permutations may have different outcomes. There are also indications that intergenic SNPs may influence the workings of otherwise healthy genes. This accords with observation that Parkinson’s Disease is a very personalised complaint. No two patients exhibit the same mix of symptoms or react to medication in the same way. Patterns of symptoms associated with patterns of SNPs may emerge and, as gene sequencing becomes economical and commonplace, genetic profiling can be expected to become a useful tool for diagnosis and prescription.

The following table summarises the current state of kmowledge of the PARKxx series of mutations.


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Template:PD Causes Pages

Parent Page:
 * Progress and Prospects in Parkinson's Research

Sub Pages:
 * Inheritance - Trauma - Deficiencies - Infection - Toxins

title: Template:PD Causes Pages


text:
Template:PD Inheritance Pages

Causes > Inheritance

Sub Pages:
 * SNCA  -   LRRK2  -  MAPT  -  GBA  -  HLA

title: Template:PD Inheritance Pages


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Progress and Prospects in Parkinson's Research/Causes/Inheritance/SNCA

"The SNCA_gene has been implicated in the onset of some types of familial Parkinson’s Disease."

Background
Its official Full Name is “Synuclein, alpha (Non A4 Component of Amyloid precursor)”.

Like many other genes, SNCA is known by more than one name. Alternative names are: In the human genome SNCA is to be found on the long arm of chromosome 4.
 * PD1 = Parkinson’s Disease 1
 * NACP = Non-Amyloid Component of senile plaques Precursor protein)
 * PARK1
 * PARK4

The cytogenetic location is 4q21.

The molecular base pairs are from 90,645,249 to 90,759,446.

The PD Gene database (2011) lists 49 Polymorphisms for this gene, of which 39 are termed ‘Significant’. It also cites 103 Caucasian gene association studies, 18 Asian gene association studies and 4 Family-based studies.

What does SNCA do?
In a healthy brain SNCA provides instructions for the production of a protein called Alpha Synuclein. This protein is abundant in the brain, where it is found in the neocortex, hippocampus, substantia nigra, thalamus, and cerebellum. Smaller quantities are also found in muscles and in the heart.

In the brain, alpha synuclein is found mainly at the tips of nerve cells in structures called presynaptic terminals. Here it interacts with fats and other related proteins. The role of the presynaptic terminals is to release neurotransmitters from compartments known as synaptic vesicles. Much has still to be learned about the precise function(s) of alpha-synuclein. There are indications that it has a role in maintaining a supply of synaptic vesicles for the presynaptic terminals. It may also help regulate the release of dopamine in dopaminergic neurons.

It has also been found in neuronal mitochondria by Zhang et al (2008) and Liu et al (2009)   Alpha-synuclein is highly expressed in the mitochondria in the olfactory bulb, hippocampus, striatum, and thalamus. It is suggested that alpha-synuclein in mitochondria is differentially expressed in different brain regions and the background levels of mitochondrial alpha-synuclein may be a potential factor affecting mitochondrial function and predisposing some neurons to degeneration.

Alpha-synuclein is specifically upregulated in a discrete population of presynaptic terminals of the brain during a period of acquisition-related synaptic rearrangement. It has been shown by Alim et al (2002) that alpha synuclein significantly interacts with tubulin, and by Alim et al (2004) that alpha-synuclein may have an activity as a potential microtubule-associated protein like tau

What is the effect of mutations?
At the moment the effects of SNCA mutations have been classified into two types.

One type of alteration changes one of the protein building blocks (amino acids) used to make alpha synuclein. In some cases, the amino acid alanine is replaced with the amino acid threonine at protein position 53 (written as Ala53Thr) or with the amino acid proline at position 30 (written as Ala30Pro). In a few cases, the amino acid glutamic acid is replaced with the amino acid lysine at position 46 (written as Glu46Lys). These mutations cause the alpha synuclein protein to misfold, or take on an incorrect 3-dimensional shape, which renders it ineffective.

In the other type of alteration, one of the two SNCA genes in each cell is inappropriately duplicated or triplicated. Instead of the normal two copies of the SNCA gene, each cell has three or four copies, which leads to an excess amount of alpha synuclein.

Mutated or excess alpha synuclein proteins may cluster together to form oligomers and impair neuronal functions in specific regions of the brain. For example, aggregated alpha synuclein may disrupt the regulation of dopamine, which allows dopamine to accumulate to toxic levels and eventually kill the nerve cell. Researchers also suspect that the resultant misfolded or excess alpha-synuclein shuts down the cell machinery that removes unwanted proteins. Unwanted proteins may then clog the cell and impair neuron functions.

Misfolded alpha-synuclein is also a major component of Lewy bodies. These are abnormal deposits that appear in certain nerve cells in the brain. Lewy bodies in a region of the brain called the substantia nigra, which provide the neurotransmitters that control balance and movement, are a characteristic feature of Parkinson's disease.

Is it associated with other diseases?
Two mutations cause a particular disorder known as Dementia with Lewy bodies. The symptoms typically include dementia, visual hallucinations, fluctuations in attention, and changes characteristic of Parkinson’s disease such as trembling or rigidity of limbs, slow movement, and impaired balance and coordination.

One of the SNCA mutations responsible for dementia with Lewy bodies replaces the amino acid glutamic acid with the amino acid lysine at position 46 in the alpha-synuclein protein (written as Glu46Lys). The other mutation, which replaces the amino acid alanine with the amino acid threonine at position 53 (written as Ala53Thr), is associated with the features of both Parkinson's disease and dementia with Lewy bodies.

Research
The SNCA gene continues to generate a considerable amount of research interest because:
 * It was the first gene to demonstrate a genetic link to PD;
 * There is a considerable body of gene association data to draw on;
 * It codes for the alpha-synuclein protein, which has been shown to be significantly involved in the pathogenesis of the disease.

Two pieces of ongoing research are of note.

Rogers, Jack T (2009) of Massachusetts General Hospital is currently engaged in the search for a novel therapy involving SNCA. Ongoing clinical trials are taking place in conjunction with the treatment of Alzheimer’s Disease of a drug called Posiphen. This acts upon the SNCA gene and serves to block the production of alpha synuclein. The researchers plan to extend this trial to test the drug’s efficacy as a treatment for SNCA-related Parkinson’s Disease.

SNCA has also been implicated in the onset of a Parkinson plus condition called Multiple System Atrophy. Currently there is no easy was of distinguishing between the two conditions. Scholz, Sonia W. and Mhyre, Timothy R. (2010)   of Georgetown University are conducting a detailed comparison of the pathology of the two conditions with a view to defining the associated therapeutic targets.

Related Pages
<Back to


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Progress and Prospects in Parkinson's Research/Causes/Inheritance/GBA

The GBA gene has been implicated in the onset of some types of familial Parkinson’s Disease.

General Data
Its official Full Name is “Glucosidase Beta Acid”.

Like many other genes GBA is known by more than one name.

Alternative names are:-
 * GCB
 * GBA1
 * GLUC

In the human genome it is to be found on the long arm of chromosome 1.

The cytogenetic location is 1q22

The molecular base pairs are from 155,204,238 to 155,214,632

The PD Gene database (2011) lists 2 Polymorphisms for this gene both of which are termed ‘Significant’. It also cites 27 Caucasian gene association studies, 5 Asian studies, 9 Other/Mixed studies and 1 Caucasian Family-based study.

What does GBA do?
In a healthy brain GBA codes for production of a lysosomal enzyme that breaks down glucocerebrosidase, a potentially harmful fatty substance normally found in the body, into a sugar (glucose) and a simple fat molecule (ceramide). The expressed protein is 515 amino acids long.

What is the effect of mutations?
Mutations of the GBA gene are inextricably associated with Gaucher's Disease. Reference to GBA in the On-line Mendelian Inheritance in Man database produces considerable data on Gaucher’s with incidental references to Parkinsonism. There are three types of Gaucher’s and Type 3 is the one which is more commonly associated with neurological dysfunction.

This variant of Parkinson’s Disease could therefore be viewed as a subset of Type 3 Gaucher’s and differs from other forms of Parkinson’s Disease in a number of ways:-

•	The onset is earlier. GBA-PD manifests itself at an average age of 41.

•	It is recessive. Both parents have to have the same polymorphism before the mutation can express itself. Carriers of a single version of the defect are unaffected and the disease can skip generations.

•	Patients do not accumulate clumps of the protein alpha synuclein (Lewy bodies) in their dopaminergic neurons and instead have an excess of glucocerebrosidase.

•	It is particularly prevalent among people whose pedigree is descended from Ashkenazi Jews.

The faulty gene thus allows accumulation of glucocerebrosidase, which can harm the spleen, liver, lungs, bone marrow and the brain. Over 300 potentially harmful polymorphisms of the GBA gene have been identified. Two which have been linked to Parkinson’s Disease are GBA_N370S and rs2230288.

Research
Sidransky et al (2009)  described a  link between PD and GBA. Its publication produced the following observations from Adam S. Bristol 29.11.2009.:-

"“I'm somewhat surprised that this paper has not received more attention than it has ... the study was indeed a tour de force in that it coordinated a risk analysis of GBA mutations in over 10,000 subjects across 16 research centers worldwide. A major challenge in a study of this type is coordinating and standardizing the data collection.  This issue is particularly relevant here as nearly 300 GBA mutations of different types (e.g. missense, point mutations, etc.) have been identified to date; ideally, one would like measure the combined frequency of all GBA mutations and the risk of PD. Of course, how PD is diagnosed can vary too, so the analysis is not trivial."

The take-home messages for me were as follows:-

"•	While the data sets were 'incomplete' in the sense that not all subjects had full GBA exon sequencing to identify all mutations nor did they get a full work-up for a complete clinical data set, the inclusion of so many patients across multiple ethnicities and geographies lends a robustness to the findings that previous studies of GBA lacked."

"•	GBA mutations were associated with earlier onset of PD, family history of PD, and higher incidence of non-motor symptoms, but lower incidence of bradykinesia and resting tremor."

"•	These relationships are probably underestimated because of the incomplete genetic and phenotypic data available. That is, if samples from all patients had been fully sequenced, other rarer mutations would likely have been found."

"•	Intriguingly, the odds ratio, or the strength of the associations, varied quite significantly across patient cohorts. What other co-factors might account for this?"

"This study has clear implications for genetic counselling, but my mind leaps immediately to therapeutics. Might this finding lead to a new treatment approach?  Sidransky et al. argue that GBA is a susceptibility factor and not a cause of PD, but even so, might targeting GBA in PD patients with identified GBA mutations be included in the overall treatment regime?  It's too early to tell, but here is some food for thought."

''As readers may know, glucocerebrosidase (GBA) is a lysosome enzyme which, when deficient due to mutations, results in Gaucher's disease. The N370S and L444P mutations included in the Sidransky et al. study are involved in Gaucher's disease, a lysosomal storage disease that presents with neurological signs among others. Indeed, parkinsonian symptoms have been observed in Gaucher's patients and the relatives of Gaucher's disease patients have been observed to have a higher incidence of PD. Gaucher's disease patients are typically treated (quite successfully) with an intravenous enzyme replacement therapy. Given the current understanding of GBA and PD, this treatment is not practical or advisable for PD patients. An orally-delivered small molecule that targets GBA might be a possibility if the safety profile is sufficient and it doesn't adversely affect current standard of care. Amicus Therapeutics is developing a compound that hits and "re-activates" the N370S mutated GBA.”''

Horowitz et al (2011) identified a further PD-related mutation at E326K.

Where do we go from here?
Bianco and Bjorklund (2009) have developed a mouse model of a GBA-PD mutation and are testing this against a series of environmental ‘triggers’ to see which are likely to invoke the disease.

Bonkowsy (2010) is developing a zebra fish model of a GBA-PD mutation and using it to test how GBA might combine with other genes to invoke the disease.

Theoretically GBA cases of PD could be eliminated in future by identifying carriers of single copies of the mutant genes and counselling them not to mate with other like carriers!


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Progress and Prospects in Parkinson's Research/Causes/Inheritance/LRRK2

"The LRRK2 gene has been implicated in the onset of some types of familial Parkinson’s Disease."

General data
The full official name of LRRK2 is Leucine-Rich Repeat Kinase 2.

Like many other genes, LRRK2 is known by more than one name. Alternative names are:-
 * PARK8
 * ROCO2

In the human genome LRRK2 is to be found on the long arm of chromosome 12.

The cytogenetic location is 12q12.

The molecular base pairs are from 40,618,812 to 40,763,086.

The PD Gene database (2011) lists 50 Polymorphisms for this gene, of which 38 are termed ‘Significant’. It also cites 102 Caucasian gene association studies, 21 Asian gene association studies and 4 Caucasian Family-based studies.

What does LRRK2 do?
The LRRK2 gene provides instructions for making a protein called dardarin. It is active in the brain and other tissues throughout the body, but overall little is known about this gene or the dardarin protein. One common mutation occurs in the Basque region of Spain and the name is derived from 'dardara' the Basque word for tremor.

Studies of the gene's instructions have revealed some clues about its function. Part of the LRRK2 gene provides instructions for making a protein segment (LRR domain, see the image, below) that is rich in a protein building block (an amino acid) called leucine.

Proteins with leucine-rich regions appear to play a role in activities that require protein to protein interactions, such as transmitting signals or helping to assemble the cell's structural framework (cytoskeleton). Other parts of the LRRK2 gene provide instructions for protein regions called the ROC-COR domain and the WD40 domain. These domains also suggest that dardarin is capable of multiple protein to protein interactions.

Additional research findings indicate that dardarin has an enzyme activity known as a kinase. Proteins with kinase activity assist in the transfer of a phosphate group (a cluster of oxygen and phosphorus atoms) from the energy molecule ATP to amino acids in certain proteins. This phosphate transfer is called phosphorylation, and it is an essential step in turning on and off many cell activities. Dardarin has a second enzyme activity referred to as a GTPase activity. This activity is associated with a region of the protein called the ROC domain. The ROC domain may act as a molecular switch that controls the overall shape of the dardarin protein. In one model the Y1699C pathogenic mutation in the COR domain is proposed to enhance interaction between the GTPase and COR domains and cause both a reduction in LRRK2 GTPase activity and alter the shape of the LRRK2 protein in such a way as to disrupt LRRK2 dimerization.

 Purified LRRK2 forms homodimers.

The effect of mutation
Toft et al 2005 linked a heterozygous mutation in the LRRK2 gene with PD. It is Gly2019Ser.

They observed that related incidence of the disease was age–dependant, increasing from 21% at the age of 50 years to 81% at 70 years. The late onset of disease observed for G2019S LRRK2 mutation is similar to that seen in most cases of Parkinsonism (idiopathic) and differs from the earlier disease onset seen for other forms of inherited Parkinsonism. G2019S LRRK2 mutation is associated with Lewy body formation which is also characteristic of most cases of Parkinson disease

The Basque mutation referred to above replaces the amino acid Arginine with the amino acid Glycine at protein position 1396 (written as Arg1396Gly or R1396G).

Studies in Chinese and Japanese populations have identified another LRRK2 mutation that replaces the amino acid Glycine with the amino acid Arginine at protein position 2385 (written as Gly2385Arg or G2385R).

Research
Justus Daeschel of Mayo University,Jacksonville is working on a project to generate LRRK2-specific antibodies in models devoid of the murine homologue of LRRK2. Their project description states:-

"The lack of endogenous LRRK2 protein renders the models much more susceptible to the antigen response caused by human LRRK2 fragments and stimulates the immune system to produce highly specific and sensitive antibodies. Our first experiment has been designed to test (i) five LRRK2 peptides, (ii) the recombinant LRRK2 C-terminus and (iii) cDNA encoding the LRRK2 C-terminus, to examine their respective ability to induce the generation of LRRK2 specific antibodies. After this pre-screening the best antigen will then be selected for the generation of monoclonal antibodies."

Goldberg, Matthew and Albanesi, Joseph P. of the University of Texas are addressing major unanswered questions including ‘what causes LRRK2 protein to associate with cellular membranes’ and ‘can preventing LRRK2 membrane association mitigate the effects of LRRK2 mutations that cause Parkinson’s disease? Their project description states:- "We hypothesize that LRRK2 cycles between cytosolic and membrane-bound states according to various post-translational modifications. We will use an array of biochemical and cell biological methods to identify the cellular mechanisms that regulate LRRK2 membrane association. We will also determine if these mechanisms are affected by disease-linked LRRK2 mutations. We will attempt to generate variants of LRRK2 with reduced ability to associate with cellular membranes. These LRRK2 variants may be useful research tools to discover novel therapies for Parkinson’s disease based on inhibiting LRRK2-mediated neurotoxicity."

Yulan, Xiong and Dawson, Ted M. of the John Hopkins University School of Medicine have developed mutated LRRK2 forms of yeast. Their related project description states:- "A budding yeast model of LRRK2-induced toxicity has been established recently and revealed a key role of GTPase activity in pathobiology of LRRK2. We have performed a genome-wide genetic screen and identified the modifiers of LRRK2-induced toxicity based on this LRRK2-yeast model. The human homologs of the modifiers of LRRK2-induced toxicity identified from yeast model will be characterized and validated in cell culture and primary neuronal cultures in vitro. To validate the modifiers of LRRK2-induced toxicity in vivo, the human homologues of the yeast modifiers will be tested in preventing or exacerbating dopaminergic neurodegeneration and motor dysfunction in the LRRK2 Drosophila mode."

LRRK2 is a complex gene and Rudenko, Iakov N, Ruth Chia, and Mark R Cookson discuss what might be effective therapeutic strategies targeting this gene.


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Progress and Prospects in Parkinson's Research/Causes/Inheritance/MAPT

"The MAPT gene has been implicated in the onset of some types of familial Parkinson’s Disease."

General data
Its full official name is Microtubule-Associated Protein Tau.

Like many other genes MAPT is known by more than one name. Alternative names are:-

 * TAU
 * MTBT2
 * FTDP-17
 * FLJ31424
 * MSTD
 * PPND
 * DDPAC
 * MAPTL
 * MTBT1
 * STU/MAPT

In the human genome MAPT is to be found on the long arm of chromosome 17.

The cytogenetic location is 17q21.31.

The molecular base pairs are from 43,971,747 to 44,105,699.

The PD Gene database (2011)   lists 36 Polymorphisms for this gene, of which 29 are termed ‘Significant’. It also cites 87 Caucasian gene association studies, 1 African descent gene association study,9 Asian gene association studies, 3 Other/Mixed gene association studies and 6 Caucasian Family-based studies.

What does MAPT do?
This gene encodes the microtubule-associated protein tau (MAPT) whose transcript undergoes complex, regulated alternative splicing, giving rise to several mRNA species. MAPT transcripts are differentially expressed in the nervous system, depending on stage of neuronal maturation and neuron type.

The effect of Mutations
2005

Tobin et al evaluated the association of the MAPT region with PD in a large cohort of familial PD cases. They found that SNP rs1800547 was significantly associated with PD affection and the H1 haplotype was associated with a significantly increased risk for PD.

2010

Edwards et al carried out a genome-wide association study for PD with a cohort of 1752 cases and 1745 controls. SNPs in SNCA (rs2736990}, and the MAPT region (rs11012} were found to have an increased risk for PD.

Wray & Lewis have specified the role of this gene thus:-

"In the adult human CNS, tau exists as six protein isoforms which differ by the presence of either 0, 1, or 2 N-terminal inserts and either three (3R) or four (4R) microtubule binding repeats located at the C terminus of the protein. Tau binds to and stabilizes microtubules via its C-terminal repeats in a process regulated by phosphorylation, where the phosphorylation of tau at specific residues favors its detachment from the microtubules."

and later:-

"In PD, variation at the SNCA locus has been shown to act synergistically with variation at MAPT to increase disease risk, i.e., the increase in risk when carrying both risk variants is greater than the additive risk of carrying each variant in isolation. In vitro work has shown that α-synuclein and tau are able to influence each other's polymerization, and diffuse tau pathology is observed in transgenic mice expressing the α-synuclein A53T mutation."

MAPT gene mutations have been associated with several neurodegenerative disorders such as Alzheimer's disease, Pick's disease, frontotemporal dementia, cortico-basal degeneration and progressive supranuclear palsy

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text:
Progress and Prospects in Parkinson's Research/Causes/Inheritance/HLA

This is a stub. Please help to develop it. The HLA region has been implicated in the onset of some types of familial Parkinson’s Disease.

General Data
The human leukocyte antigen (HLA) system is the name of a super locus contains a large number of genes related to immune system functions. Different classes have different functions: Its purpose came to light when the reasons for the rejections of organ transplants were evaluated.

It is found on chromosome 6.

Research
In 2010 Hamza et al published the results of a new human Genome-Wide Wide Association Study (GWAS). The genes of a cohort of 2,000 PD patients of Caucasian ethnicity were compared with a matched cohort of 1,986 people without the disease and significant differences were recorded. The study confirmed previous findings of a link between the incidence of PD and variations in the SNCA, MAPT and GAK genes. It also noted a previously unrecorded PD risk for variations in the HLA genetic region, which was significant, both because it involved the human immune system, and also pointed to genetic influences in the late onset of sporadic cases of the disease.

The weight to be attached to GWAS results depends upon a number of factors:- •The size, degree of matching and composition of the cohorts;

•Whether the findings are corroborated by repeat studies;

•The significance of the related genes.

Significant genetic variations can form a target for future therapeutic intervention but to define ”significance” it is first necessary to disentangle the process of tagging, whereby one expressed gene tags another for subsequent expression. Tagging can be multi-level and have a cascade effect within a cell, whereby one risk gene may be the progenitor of several others. Variations are also often found in intergenic (so-called ‘junk’) DNA, which regulate or mediate the expression of coding genes.

A follow-up study by Hill-Burns et al has sought to evaluate the 107 variants located to date in the HLA region. The researchers employed a process called “step-wise conditional analysis”, which eliminated subordinate SNPs. This reduced the number of risk SNPs from 107 to 4 standalone examples, which could be the subject of further research. The implication that PD might be the result of an immunity deficiency has yet to be evaluated fully.


text:
Progress and Prospects in Parkinson's Research/Causes/Trauma

< Back to Causes

General
“Trauma" is the Greek word for "a wound" (and for "damage or defeat").  In medical parlance it refers to a serious or critical bodily injury, wound or shock, which can be inflicted physically or emotionally.  For editing purposes here we shall regard 'trauma' as any physical abnormality linked to the onset  of PD.

Trauma can be classified according to its severity under the headings:- : 1 Minor, 2 Moderate, 3 Serious, 4 Severe, 5 Critical, 6 Maximal. It is a major cause of mortality with some 10% of deaths worldwide being attributed to this cause.

Research
1991

Factor & Weiner reviewed 97 PD patients with 64 spouses acting as controls. Twenty PD patients and five controls reported head injury associated with alteration or loss of consciousness (p less than 0.05). Injury occurred at a mean of 37.7 years before onset of PD and 37.2 years before survey completion in the two groups, respectively.

1997

Lees (1997) stated that:-

"Post-traumatic Parkinson's syndrome may occur following cumulative head trauma in contact sports and exceptionally rarely after single severe closed head injury. It remains uncertain, however, whether physical injury should be considered one aetiological factor in the pathogenesis of Parkinson's disease."

1999

Taylor et al recruited 140 PD patients and analysed the risk factors that may have led to their condition. They concluded that:-

"Head trauma was a significant risk factor in the onset of the disease and A mean latency of 36. 5 (SE=2.81) years passed between the age of first reported head injury and PD onset."

2002

Tsai et al studied the causes of Parkinson’s Disease among people under 40 years old and concluded that:-

"“Keeping all other variables constant, head injury was a risk factor and exercise appeared to be a protective factor.”"

1991

Contradictory evidence came from Goetz and Stebbing who monitored 10 PD patients with head trauma for one year and concluded:-

"” Based on these data, we conclude that trauma or stress caused by motor vehicle accidents can transiently exacerbate parkinsonian dysfunction without causing persistent increased disability or an alteration in disease course."

2012

Lee, Pei-Chen et al enrolled 357 incident idiopathic PD cases and 754 population controls from 2001 to 2011 in central California. Participants were asked to report all head injuries with loss of consciousness for >5 minutes. Paraquat exposure was assessed via a validated geographic information system (GIS) based on records of pesticide applications to agricultural crops in California since 1974 and ambient pesticide exposure within 500 m of residences and workplaces were recorded.

They observed a 2-fold increase in risk of PD for subjects who reported a Traumatic Brain Injury (TBI),  and a weaker association for paraquat exposures. However, the risk of developing PD was 3-fold higher in study participants with a TBI and exposure to paraquat than those exposed to neither risk factor.

Dementia pugilistica
(Also known as chronic traumatic encephalopathy (CTE)).

This form of Parkinsonism is specifically associated with athletes. Contact sports such as football, boxing, wrestling, rugby, hockey, lacrosse, soccer, and skiing have all been implicated. In boxers the term ‘punch drunk’ is frequently used. Notable current cases are Mohammed Ali, former world heavyweight boxing champion, and Jansher Khan, who won the world squash open squash championship eight times. The condition has also been reported in epileptics, head bangers and domestic abuse victims, and former soldiers.

Other boxers who showed symptoms of the condition are. Joe Louis, Rocky Graziano, Tony Zale, Jimmy Ellis, Floyd Patterson, Bobby Chacon, Jerry Quarry, Mike Quarry, Wilfred Benitez, Emile Griffith, Willie Pep, Freddie Roach, Sugar Ray Robinson, Billy Conn, Joe Frazier, Fritzie Zivic and Meldrick Taylor.

The condition has been described at length by McKee at al 2009. Their paper includes an excellent bibliography.

The condition is different from other forms of PD in that it is characterized by atrophy of the cerebral hemispheres, medial temporal lobe, thalamus, mammillary bodies, and brainstem, with ventricular dilatation and a fenestrated cavum septum pellucidum. Microscopically, there are extensive tau-immunoreactive neurofibrillary tangles, astrocytic tangles, and spindle-shaped and threadlike neurites throughout the brain.