This paper synthesizes previous papers with the added twist of explaining the connection between bacteria and nervous system diseases. We make use of familiar AT Math solution as applied to contagions. We will see that E Coli and Cholera which cause watery diarrhea deplete the electrolytes in the body leading to detrimental affects on DNA Adenine. This paper is the key toward understanding the root cause of some major neurological diseases.

Continuing in the vein of what causes major neurological disorders, we have a paper that shows how electrolyte depletion through diarrhea caused by E Coli and Cholera may be the cause of various diseases. Once again AT Math plays a role in the mathematics underlying the phenomena. We begin with the familiar golden mean parabola and the logarithmic and exponential functions. We then move into the chemistry of excess sugar and the impact it has on bacterial growth, such a E coli. Next, we proved some calculations from the chemistry of E Coli which has been well studied. Finally, we consider pH and how acid environments contribute to bacteria growth. We begin with the familiar ln function.

Golden Mean Parabola
Ln t=e^-t
Derivative:
1/t= (-e^-t-1)/ (-1)
1/t=e^-t-1
 Integrate both sides:
Ln (1/t) =Ln e^(-1-t)
Ln (1/t) =-1-t
Aside:
Ln t=e^-t
Derivative:
1/t=-e^-t/-1=e^-t
t=1/e^-t
t=e^t
1/e^t=e^exp(-1-t)
Ln (e^-t)= e^(-1-t)
Ln (-t) =Ln e^(-1-t)
Ln -t=-1-t
t=-1
∫dt/dt=∫1+? =t+?
t+?=1
t=?-1
Let ?=0
t=-1
-t=e^exp(1-t)
Take ln of both sides twice:
-Ln Ln t=(-1+t)
Ln Ln t-t=-1
1/Ln t+1=t
Integrate both sides: 
∫1/Ln t=∫t-1
Ln t=t²-t
From above:
e^-t=t²+t
 Take Ln of both sides:
-t=Ln t²+Ln t
Take derivative: 
?=1/t²+1/t
?=(1+t)/t²
Let ?=1
Golden Mean Parabola
t²-t-1=0
t=1.618; -0.618

Since one cycle is 2π; then:
2π/3=212
M=Ln t
=Ln 212
=1.550
TE=M [0.15915]
= (0.1550)(0.15915)
=246.68
E=1/t=405.38
E=Mc²
405.4=Mc²
M=451
M=Ln t
t=166.99~1.57=π/2
PE=KE=t
Mc²=1/2Mv²
1/2=c/v
1/2=9/v
v=18
t=KE=1/2Mv²
=1/2(Ln π/2) (18)²
=73.156
E=1/t=0.01367
E²+E-2=t
(0.01367)²+0.01367-2
=-1.986~-2
t²-t-1=E
t²-t-1=--1.986
t²-t+1=0
t=1.314; 3.1429=Pi

Proton Motive Force
C_{8H11NO2 + C7H16NO2+ C13H16 N2O2 + C8H ON4O3 + C5H5N5 Fe³⁺ +NaCl +H2O2 →
Dopa. + Ach. + Melatonin + Caffeine and Adenine+ Iron and Chlorine + Hydrogen Peroxide →
C41H48N13O12 + 3 Fe⁺²+2NaCl+5O2 ==>
41CH + 12NO-+Fe2O3 +2NaOH + FeCl2-+ H2NOH +2H2O2^-2}

Methylene (Carbene) Hydroxylamine
a CH+ C₂₂H₃₀O₅+ 10 NO^-+ 22 H₂O → C₂₂H₄₄O₂₂ +10 H₂NOH + 2O₂+OH^-
Carbene +Cortisol (Stress) Sugar Hydroxylamine
The excess sugar makes the bodily system acidic. Bacteria need iron Fe +3 to grow.
amu= (14.016+362.46+30.006+396.33=1072.866
1072.866 x 6.026=6461.87 g
6461.87g x/ 0.994 g/mole of blood=65.008 moles
Normal pH=7.35-7.45 Say 7.4
pH=Ln [H+]
e^-7.4=6.1125
[H+]=moles of H+/moles of solute
6.1125=Mol 0f H+/6500
Mol of H+=3973
H+ =1.008 g/mol x 4 moles=4.00 =|D|
4.00 x 6.023=24120.8
e^0.241208=127.3=4/π=ρ
Moles of Sugar:
C22H44O22=660.33 g/mol x 6.023=397.716 g~4g of Sugar
=Moles of H+
H+1.008 g/mol x 397.716=4.008977~4.00g of H+

So we consider that E Coli is the proximate cause of various disorders including Parkinson’s; Schizophrenia; ALS; Alzheimer’s disease; and Cancer.
We examine E Coli in more detail.
E Coli double in growth every 20 minutes (1/3 hour)
Since it follows exponential growth, we have:
2=a₀e^t
2=a₀e^(1/3)
a₀=1.4335=1/698=1/7 Economic Multiplier.
A full cycle is 2π rads
2π/7=0.8976=c²
GMP: t=1/3
(1/3)²-(1/3)-1=1.22222
E Coli has 20% of its protein in its envelope
M=Ln t
=Ln (1/3)
=1.096
(20%/100%) M=21972/χ
χ=1.0986
M_T=21972
TE=M[0.15915]
=1.0986[0.15915]
=174.842~1 rad
t=E²-E-2
t=30.743
E=1/t=3.2527
100% M=1.0986/30 genes=0.03663 gm/gene
3.2527/0.03662=0.88823
GMP: = E=1.099~11 base pairs
4 mol of sugar=amu x mol x Avg.
=660.33 x 4 x 6.023=1590.86~1591

E Coli and Cholera cause watery diarrhea which depletes the body of electrolytes. Electrolytes such as Salt and Potassium are essential for the functioning of the nervous system as they are the ions that cause a nerve to surge with a signal.

So how does electrolyte depletion cause the genetic mutation that leads to a genetic disposition of r these nervous system diseases? The answer lies in a “special membrane protein that binds to an 11 base-pair sequence (5’-AAGTGCGGTCA-3’) that occurs frequently in Haemophilus DNA....” [17]

Let us consider the A o=Adenine molecule: C5H5N5
The chemical mol balance equation is:
C₅H₅N₅+C₂₂H₄₄O₂₂+22NaCl +3H₂O₂ + 8H₂ ==>
(Adenine+ Sugar +Salt + Hydrogen Peroxide + Proton ==>
27CH+22HCl+22NaOH +5NO+ (1/2) O₂
Carbene + Hydrochloric Acid + Sodium Hydroxide+ Nitrate +Oxygen

Pathways of fermentation of sugars by various microorganisms need protons(Hydrogen atoms). Pyruvic acid C3H4O3 produces Formic acid; Acetyl CoA; Acetic Acid; Ethanol; Acetoacetic acid; Butyric acid; Butanol; Acetone Isopropanol; Butanediol; Propionic acid; Lactic acid; Acetaldehyde; Ethanol requires 16 Hydrogen atoms which is what we have above.[17]

Now, excess sugar causes the body to become acidic. Thus, pH varies from the normal pH=7.4
pH = Moles of [H⁺] /Mol of solute.
pH =7.4
Ln 7.4=2
2 = (8x2)/Moles of Solute
Moles of solute=8
8 x 6.023 =481.8
GMP: E=-1.249~-1.25=E_min

So, we see that these diseases of the nervous system follow AT MATH. E Coli causes depletion of the electrolytes that are necessary for normal A- adenine in the DNA molecules.