Example in biology

Sunday, March 05, 2006


example in biology





 


Introduction:

The aim of this work is to show that by taking an exponential base of
time, one can follow an experimental curve mathematically.

A method deduced from an hypothesis on time is used.

an application of this method in biology makes it possible to describe
a reaction of protease H.I.V.(1)..

My step is to show the general information of this method in various
sciences.



Material and Method

The experimental results of the curve of reaction of the H.I.V.
protease resulting from the data base Scirus(1) were treated
mathematically according to the hypothesis prédente.

The curve tending towards a balance, one can say that it is a naturally
stable system.

Thus (2) is written in the form:

y = K (1-e(-t/jo))

with

y = the final signal

K = the value of the plate (concept of quantity)

jo = a number without dimension defining protease HIV





curve 1:

K = 7,1

jo is deduced at the beginning from balance and is equal to 20.

Y = K (1 - (E (- T/20))

With these values one realizes that the value of jo is smaller at the
beginning of reaction.

Thus the reaction speed depends on what already reacted, which is
written:

Y = K (1 - E (- T/(20 (1 - e(- T/jo')))))



Numerical application:

Y = 7,1 (1 - E (- T/(20 (1 - E (- T/14))))







Curve 2:

Thus K = 11

jo is deduced at the beginning from balance and is equal to 31.

Y = K (1 - (E (- T/31))

With these values one realizes that the value of jo is smaller at the
beginning of reaction.

Thus the reaction speed depends on what already reacted, which is
written:

Y = K (1 - E (- T/(31 (1 - e(- T/jo')))))



Numerical application:

Y = 11 (1 - E (- T/(31 (1 - E (- T/12)))))





curve 3:

K = 18

jo is deduced at the beginning from balance and is equal to 47.

Y = K (1 - (E (- T/47))

With these values one realizes that the value of jo is smaller at the
beginning of reaction.

Thus the reaction speed depends on what already reacted, which is
written:

Y = K (1 - E (- T/(47 (1 - e(- T/jo')))))



Numerical application:

Y = 18 (1 - E (- T/(47 (1 - E (- T/11,27))))









One realizes that on this system product it finished slows down the
reaction speed.



By this equation, the curve signal of protease HIV according to the
substrate is followed in its totality; the experimental data can be
expressed mathematically by taking an exponential base of time.



It is noticed that the value k/jo curve 1 equalizes the value k/jo
curve 2.

The value of k/jo (2,82) appears characteristic of protease HIV. An
exploitation of other curves and a thorough study would make it
possible to better characterize this parameter.






H.I.V. Protease

"Kinetic assay for HIV proteinase subunit dissociation." Kuzmic, P.
(1993) Biochem. Biophys. LMBO. Commun run. 191, 998-1003.

"Stabilization of HIV proteinase dimer by bound substrate." Kuzmic, P.;
Garcia-Echeverria, C; and Rich, D.H. (1993) Biochem. Biophys. LMBO.
Commun run. 194, 301-5.



The experimental results of the curve of reaction of the H.I.V.
denatured protease resulting from the data base Scirus(1) were treated
mathematically according to the preceding assumption.

The curve tending towards a balance, one can say that it is a naturally
stable system.

Thus (2) is written in the form:

y = K (1-e(-t/jo))

with

y = the final signal

K = the value of the plate (concept of quantity)

jo = a number without dimension defining denatured protease HIV





curve 1:

K = 4,9

jo is deduced at the beginning from balance and is equal to 20,5.

Y = K (1 - (E (- T/20,5))

With these values one realizes that the value of jo is smaller at the
beginning of reaction.

Thus the reaction speed depends on what already reacted, which is
written:

Y = K (1 - E (- T/(20,5 (1 - e(- T/jo')))))



Numerical application:

Y = 4,9 (1 - E (- T/(20,5 (1 - E (- T/23))))









curve 2:

K = 5,8

jo is deduced at the beginning from balance and is equal to 24.

Y = K (1 - (E (- T/24))

With these values one realizes that the value of jo is smaller at the
beginning of reaction.

Thus the reaction speed depends on what already reacted, which is
written:

Y = K (1 - E (- T/(24 (1 - e(- T/jo')))))



Numerical application:

Y = 5,8 (1 - E (- T/(24 (1 - E (- T/23))))



H.I.V. Protease Denaturation

Analyze invertase. Source SCIRUS

One reconnait the form of an interaction between the finished product
and the initial product.









Conclusion:

The method makes it possible to build a data base taking of account the
general shape of the curve.

The method makes it possible to model biological reactions.





Bibliography:

1: Source Internet SCIRUS

"Kinetic assay for HIV proteinase subunit dissociation." Kuzmic, P.
(1993) Biochem. Biophys. LMBO. Commun run. 191, 998-1003."Mechanical
effects one the kinetics of the HIV proteinase deactivation." Kuzmic,
P.; Peranteau, A.G.; Garcia-Echeverria, G; and Rich, D.H. (1996)
Biochem. Biophys. LMBO. Commun run. 221, 1-7."Stabilization of HIV
proteinase dimer by bound substrate." Kuzmic, P.; Garcia-Echeverria, C;
and Rich, D.H. (1993) Biochem. Biophys. LMBO. Commun run. 194,
301-5."Mechanical effects one the kinetics of the HIV proteinase
deactivation." Kuzmic, P.; Peranteau, A.G.; Garcia-Echeverria, G; and
Rich, D.H. (1996) Biochem. Biophys. LMBO. Commun run. 221, 313-7.

2: Source Internet letime.net



Author: ANDRE pierre jocelyn





Hypothesis on time