UNDERSTANDING BIOCHEMICAL SYSTEM FOR PATHWAYS RECONSTRUCTION

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UNDERSTANDING BIOCHEMICAL
SYSTEM FOR PATHWAYS
RECONSTRUCTION

Hiren

Karathia

(
Ph.D
-

System Biology and Bioinformatics)

Supervisor: Dr.
Rui

Alves

Ref from: Prof. Michael A.
Savageu

and Dr. Claudio
cobelli
, David Foster
and
Gianna

Toffolo


14
th

January 2010

System


System

is a set of interacting or interdependent
entities forming an integrated whole.


The concept of an '
integrated whole'

can also be
stated in terms of a set of relationships which are
differentiated from relationships of the set to
other elements, and from relationships between
an element of the set and elements not a part of
the relational regime.


System dynamics

is an approach to
understanding the behavior of system over time.

Most systems share common characteristics,
including:


Structure:

defined by parts and their
composition;


Behavior:

which involves inputs, processing and
outputs of material, energy or information;


Interconnectivity:

the various parts of a system
have functional as well as structural
relationships between each other.


Biological System


In Biology, a
Biological system

is a group of
biological entities that work together to
perform certain task.


ENERGY

COMPLEXITY

LEVEL OF CLASSIFICATION

System complexity at the scale of size
& time


Atom coordinate at

0.1
-

1.0 nm

Atoms are interact at

0.1
-

10 ns

Molecules coordinate at

0.1
-

1.0 nm

Molecules interact at

10ns
-

10 ms

Cellular Scale

Concentration of molecules

10
-

100 nm

Diffusion rate

10ms


1000 s

System complexity at the scale of size
& time


Tissue Scale

Metabolic input can be provided

0.01m
-

1.0 m

Metabolic output can be obtained

1 s


1 hr

Tracer Kinetics

Organism scale

Behaviors of animal could be
studied for

0.01m


4.0 m

Habitats could be studied for

1 hr


100
yrs

ENERGY CONCEPT IN BIOLOGICAL
SYSTEM


Organisms must deal with many form of
energy to do functions but the basic unit of
energy is by mean of exchange
CHEMICAL
ENERGY.


All other types of energies, i.e., mechanical
energy, are inter
-
convertible with the
chemical forms by means of specialized
energy transduction process.

What are the chemicals in cellular
systems

Common chemical basis in all
form of life in a cell are

-
Proteins

-
Nucleic Acids

-
Minerals

-
Vitamins

-
Metabolites

Major functional unit of cells, which gives
dynamicity to cell is Proteins:


Proteins are functionally classified as

-
Enzymes

-
Regulators

-
Interactors

-
Transcription factors

-
Receptors

-
Ligands


Understanding of How protein made
as a functional molecule in a cell:

Amino Acid:
Atomic change

Secondary structure
of Poly peptide:
Molecular change

Primary sequence of Poly peptide:

Molecular change

Tertiary structure:
Molecular change

Quaternary structure:
Molecular change

Understanding multi component
systems interaction at cellular level

Free
molecules

Binary
interactions

Multiple and
complex
interactions:
Pathway

Multiple and
complex
pathways
interactions

Multiple
pathways
interaction
between two
Cells:

Inter

Pathways
interactions

What types of chemical changes
characterize functions in cells

1.
Numbers and types of atoms or functional
groups undergoing change.

2.
Alteration in geometry or steric configuration of
reacting molecules.

3.
Number of nature and bonds that are made and
broken.


UNDERSTANDING PROPERTIES OF ENERGY WITH
EACH CHEMICAL SPECIES, DETERMINE
CHARACTERISTICS OF FUNCTIONS AT
MOLECULAR LEVEL.

Analysis of chemicals at ENERGY level
to characterize Systems functions


Qualitative and Quantitative analysis gives
information about

1.
What extent a function normally take place.


STUDY OF MOLECULAR THERMODYNAMICS

2.
How fast a function proceeds.


STUDY OF MOLECULAR KINETICS

THERMODYNAMICS


A collection of laws
and principles
describing
the flow
and interchange
of
heat
,
energy

and
matter

in a system
of interest
.


Thermodynamics
allows us to
determine
whether
a chemical process or reaction
will
occur
spontaneously
in specific direction
(either forward or reverse).


But it doesn’t tell about the speed at which
the reaction take place.

Two laws of Thermodynamics


First Law:


The
total amount of energy in an
isolated
system

is conserved, though the form
of the
energy may change
.


Second Law:


In
all natural processes, the entropy
of the
universe increases.


SYSTEM AND ENVIRONMENT IN
UNIVERSE


Thermodynamic Concepts:


The
SYSTEM

is the portion
of the
universe we
are concerned with; everything else is
the
surroundings (
ENVIRONMENT
).
The system +
surroundings =
UNIVERSE

CLOSED SYSTEM

ENVIRONMENT

UNIVERSE

NO EXCHANGE OF
ENERGY OR MATTER

CLOSED SYSTEM

ISOLATED SYSTEM

ENVIRONMENT

EXCHANGE OF ONLY
ENERGY OCCURS

ISOLATED SYSTEM

OPEN SYSTEM

ENVIRONMENT

EXCHANGE OF
ENERGY AND MATTERS
OCCUR

OPEN SYSTEM

What Functions could be study at
system level


A


V

[A]

B

U

U

=

De novo production of molecule

U’ = Disposal of a molecule

[A] or C = Concentration of A
(mass/volume) either increase or
decrease

T = Transformation of molecule (A
-
> B)

T’ = Reverse Transformation of
molecules (B
-
> A)


U’

T

T’

QUANTIFICATION OF FUNCTION WITH
RESPECT TO ENERGY





Δ
G =
Δ

H
-

T
Δ

S


Δ
G :
Gibbs free
energy
:
The amount of energy capable of
doing work
during a reaction at
constant temperature
and
pressure.



Δ
H :
Enthalpy

:
The heat content of
a system
(H). When a
chemical
reaction releases
heat, it is exothermic and has
a
negative
Δ

H
.



Δ
S:
Entropy

:
Randomness or disorder of
a system
(S).
When the products of a
reaction are
less complex and
more disordered
than the
reactants, the reaction proceeds
with
a gain
in entropy (positive
Δ
S
).



























X1

X2

E1

H1

S
1

E2

H2

S2

S1


S2 =
Δ
S
is positive i.e.,

Randomness increases in X1
and function is forward
(Spontaneous)

H1


H2 =
Δ
H
is negative

Heat is released and
function is forward
(Spontaneous)

F

F’

What happen in simple Enzymatic
reaction


In simple reaction, where molecule X1
(Substrate) is activating molecule X2 (Product)
is expressed as two states in an energy level
diagram.






If the level of energy is grater in Substrate (X1) than
product (X2) then the reaction is favorable and it proceed
towards lower energy state of by releasing amount of energy
to make possible function F (here reaction between X1 and
X2).



But the reaction is proceed in both the direction (imbalance
of energy level after passing one state) at the same time
(resolution of time here is limited factor to separate the two
events).



In this situation only small number of molecules out of total
molecules, obtain enough thermal energy to overcome the
energy barrier.

What happen to energy, when the
population of molecule is high


Since there are more than one molecules in a
system and each molecules in system will have
different levels of energy at different time, that
define their states of functions.


The E per molecule is proportional to Boltzmann
factor [exp(
-
e/
kT
)],


where, T is absolute temperature




k is Boltzmann constant (related to Gas
constant R and Avogadro’s number A
o
[R = k A
o
]).


In standard level to analyze in chemistry groups of molecules are
characterized as general, this standard is called mole (M).


At mole level molecules energy E is expressed as





exp(
-
E/RT)

Where E = A
0
e (Energy per mole of molecules, each with energy ‘e’).


Thus number of molecules having E is given by




where a is proportionality constant


Proportionality constant ‘a’ is determined by integrating all possible
energies that are associated with total number of molecules N
t.




Equilibrium


Equilibrium is when the rates
of forward
and reverse
reactions are equal and no
further change
in the
system occurs
.


Equilibrium constant is when the rate of forward and
reverse reaction is taken as ratio (K
eq
)


When a system
is not at equilibrium, the
tendency to
move toward equilibrium represents
a driving
force,
the magnitude of which
is
Δ
E (E
R
).


Δ
E
O

is called Standard free energy, when free
energy
change under
standard conditions
: 298K; reactants
and
products present
at 1M.

Biochemical reactions occur
at pH
= 7 so we define
Δ
Eo

.


Relationship
between
Δ
Eo

and
K
eq
:



Δ
Eo

=
-
2.303RT log
K
eq


T
= temperature in K;

R = gas
constant
(8.314 J/mol x K
)






Who can perform function?


As previously described, out of total number
of molecules, the number of molecule which
have energies greater than some critical
energy (E
c
), can perform respective function.

This expression is used to estimate the
number of product molecule, in total
number of molecules, which has
sufficient thermal energy to overcome
the energy barrier (E
1



E
2

=


E
R
) and
perform specific function.


The product formed from this function
again perform reverse reaction to
make substrate

If,


K
eq

= 1.0 (reaction at equilibrium) then
Δ
E

(E
R
) is = 0

K
eq

> 0 (function is spontaneous) then
Δ
E

(E
R
) is negative

K
eq

< 0 (Function in reverse direction) then
Δ
E

(E
R
) is positive

STUDY OF MOLECULAR KINETICS


Kinetics (Dynamics) are roughly synonymous
terms referring to the study of functions of
chemical systems (interaction, concentration,
self production etc.) that change with time.





dF
/
dt

Transition state

E

E

X1

X3

X4

X1

E

X2

TRANSITION STATE

(Unstable state)

E
A

= ACTIVATION ENERGY

Rate of function


Rate of function for chemical (proteins) is
proportional to the number of substrate (X1)
molecules possessing sufficient thermal
energy to overcome the activation energy
barrier.


So, the rate is proportional to
exp(
-
E
A
/RT).

Understanding of Kinetic study at
molecule or interaction of molecule level


Monomolecular function: Intra molecular
rearrangement


probability that certain
molecules in population is having sufficient
activation energy at constant temperature (T)
and gas constant (R), then that number of
molecules undergoing conversion from one
state to other state per unit time is:

The conversion rate in terms of concentration is obtained by
dividing volume V in both side of the equation.



-

d
X
/
dt

=
k
X


Where
X

is concentration of substrate
X
and
k

is called rate
constant.




Understanding of Kinetic study at
molecule or interaction of molecule level


Bimolecular function:




X1 + X2 X3

F1: Probability of
individual molecules
have enough energy to
be stable

F2: Probability of two molecules collide and perform specific
function. (Joint probability of two molecules at the same place,
same time with appropriate orientation.)

The probability of finding given X1 molecule at given time in a given position within a
volume V is



pX1(r, t)
α

σ
X1/V,



where r = three
dimentional

position vector



t = time




σ
X1 = effective volume of cross section for considering orientation




optimization.



V = volume of whole reaction.

Therefore the net probability of X1
-
X2 pair form X3 is proportional to


Px1x2(r, t)
α

exp(
-
E
A
/RT)[(
σ
X1/V x
σ
X2/V)]





or




Px1x2(r, t) = k/V
2

In unit volume X3 is formed depending on how number of X1
-
X2 (N1xN2) pair forms,

Thus,
(1/V)d(N3/
dt
) = k/V
2
N1N2,

In term of concentration,



dX3/
dt

= kX1X2 =
-
dX1/
dt

=
-
dX2/
dt



Kinetic Order in chemical functions


In system there are not single copy of chemical, rather
there are multiple copies of identical chemicals.


for example in tri molecular reaction:


X1 + X1 + X2 X4,


So,



dX4/
dt

= kX1
2
X2



(superscript 2 is kinetic order of molecule X1)




=
-
dX2/
dt

=
-
1/2(dX1/
dt
)





(1/2 is
stoichiometric

factor)

(X1 disappears twice at the rate compare to X2)


A reaction defining as a function of a
particular time


Kinetic equation, together with
stoichiometric

constraints and set of initial concentration
values, determines a reaction as a function of
time.




dX
/
dt

= X(0)exp(
-
kt
)

Understanding Non linearity of
Biological system


A


V

[A]

B

U

U’

T

T’

If U = U’
-
> de novo synthesized A
enter into a system at time t1 is
disposal at time t2. if, Rate of
concentration at entry dU1/
dt

=
Rate of concentration at disposal
dU2/
dt
, then A is not utilized in
system and results can be
reproduced several time.

If T = T’
-
> Rate of transforming
from A to B (
dA
/
dt
) = rate of
transformation of B to A (
dA
/
dt
)
then both A and B remain
constant at the system level.



But fortunately (unfortunately for us to
make research easy), neither of these cases
happen in biological systems.

If it could happen, then thermodynamically,
biological system could not have been
existed in universe.

Why Biological system is Non linear


Biological system has thousands of molecules.


Each molecule has its own law of function


Complexity get worsen when two molecules interacts with
their own laws.


There is feedback control mechanisms, which controls,
biological reactions between two molecules


More than one identical molecules interacting with other
to perform reaction (Kinetic order problem).


Same molecules are distributed in various compartments of
a cell (Cell as a system).


Various reactions are influenced by various physiological
parameters (PH, Osmolarity, Temperature etc.)

Biochemical system as Non linear


X0


X1


X2


X3

X0

X1

X2

X3

t0

t1

-

t3

X4

X5

+

t4

Power law Approximation


In general the flux from X
i

to X
j

is a non
-
linear
function of all the X's, that is


Vij = vij(X1, X 2 . . . . . Xn)


The form of this non
-
linearity for a broad class of
enzymatic mechanisms is a
ratio of polynomials
in the reactant and modifier concentrations
. The
degree of the numerator is always less than or
equal to the degree of the denominator, and all
the coefficients are positive real.

Power Law


If we hold all the variables constant (X1, X2,
X3….) except one, we can write the rate law as
a simple rational function and factor the
numerator and denominator polynomials to
identify the poles and zeros.




vij = co(X1+c1)(X2+C2)….(
Xl+Cm
)







Such a rate law can be analyzed in a log
-
log
plot of velocity vs. concentration

(X1 + d1)(X2 + d2).... (Xl + dl)



log v = log k + p log X




or





v = kX
p

Here, p = apparent kinetic order of the reaction


with respect to the variable





concentration

The values for the parameters "p" and "k" are to
be minimize the mean squared error in velocity
over the experimentally determined
concentration range

Power Law


Experimentally determined concentration
range are thus functions of the operating
point Xo in general. Xo may be considered the
mid
-
range value of X, or the steady
-
state value
when we are concerned with small variations
about this state.

General Term of Power Law


Consider
v
ij

as a function of n variables. The
approximation of
v U by a sum of linear terms
in the n
-
dimensional log space is equivalent
to
an approximation that is a product of power
-
laws in the corresponding Cartesian space.

Thus,





v
ij
=
kij

X
l
pij

(where
pij

may be any real




number)



l = 1

n

General Formula for Power law





dX
i
/
dt

=
α
i

X
k
gik



β
i

X
j
hik



i

= 1, 2, 3,…….n variables

k = 1

n

j= 1

n

X0


X1


X2


X3

Constant

dX
1
/
dt

=
α
1 X
0
g10

X
3
g13

β
1 X
1
h11

dX
2
/
dt

=
β
1 X
1
h11

β
2 X
2
h22

dX
3
/
dt

=
β
2 X
2
h22

β
3 X
3
h33

X
4
h34

END OF CHAPTER
-
1

Following is subsequent chapter’s goal
to discuss