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What is a concentration dependence in Molecular
Biophysics?
Practically in every experimental method that is used to study
binding of the small molecules (ligands) to biomacromolecules
(DNA's, RNA's, oligonucleotides, proteins) some dependencies
between recorded values and concentrations of reagents are observed.
In the lecture, I want to describe generally the ways and the models,
which we can use to determine the binding parameters in a ligandbiopolymer system from analysis of these dependencies: affinity.
stoichiometric coefficients, site sizes to chose the best binding
modes.
Analysis of in vitro experiments
Dr. Kruglova E.B.
Why do we still continue to melt NA (DNA) at temperatures more
than 100 0C ?
to add in solutions of biopolymers
NaCl, KCl in such quantity to be more
than 1 M and ions of two charged and
transition metals?
to
expose
of
solutions
of
biomacromolecules to higher doses
either ionizing radiation or
drugs?
If our living conditions are 37 0C, about
0.1 M NaCl and pH7.
So obtainig results in these in
vitro experiments can be fine
and very simple Models
describing different situation
in living cells and organisms
in both real and critical
situation.
Thus we must continue to
work in the same way
What is a concentration dependence?
Solutions of the components
A and B
to A is added B
CA0
Our conclusion:
component A
interacts with
component B –
Why? Colour is
changed
CB0
A (ligand) can be a small molecule of
dyes, drugs, aminoacids, proteins, so
on
B can be in molecular biophysics NA's,
proteins, oligonucleotides so on
If that ibformation is not enougth
What is a concentration dependence?
Spectrophotometer
Spectrofluorometer
CD spectropolarimeter
so on
What is a concentration dependence?
Spectrophotometer,
VIS range
Spectrofluorometer
Can we say that the component A interacts with
component B using only one spectra? - No.
We shoul add to spectra of the mixture A+B, at least,
spectra of free component A at the same concentration.
Thus, good concentration dependencies we can
obtain by titration procedure
A titration is a method of analysis that
There are two basic
will allow to determine the precise
ways that are used
endpoint of a reaction and therefore the
usually in biophysics
precise quantity of reactant in the
experiments
titration ..(Wikipedia).
Case 1
The method can give very
V1 of CA0 is added good results for studies of
to V2 of (CA0 + CB0 ) interaction between dyes
or drugs and NA's and
proteins Why?
CA0
CA0 + CB0
can be shown that at that titration procedure
concnetration of component A does not
change in each (A+B) mixture and to be
CA0 = (CA0 V1 + V2 CA0) /(V1 + V2 )
How
can
we
obtain the
thermodynamic
and
spectral
parameters of a drug to DNA
binding by spectrophotometry?
CL0 =
CAoi = [Cf ]i + [Cb
]i
If one type of complex
is formed only
If omponent B does
not absorb in VIS
range
Ai = f [Cf ]i + b
[Cb ]i
Scatchard isotherm (plot)
r/Cf
Then we can construct
K
[Cf] is equilibrium
concentration of a
free ligand
Scatchard plot without
any
preliminary
knowledge about a mode
of binding A to B and
obtain values of binding
constant and site size as
it is shown in the picture
r
n=1/r
r = [Cb ]/CBO
It is very difficult to obtain good concentration dependence
in biophysical expeiment, which we can analysis to obtain
the thermodynamic parametrs of interaction A+B. Why?
PROBLEMS
Very often in biochemical experiments it is used complicate
buffer systems consisting of some organical components
(TRIS, EDTA), two carged metalloions, so on;
At interaction of many biopolymers with some dyes, drugs,
metal ions heving more than one ionic charge aggregation,
sedimentation of biomacromolecules or condensation of
DNA's (NA) are observed;
Large organic molecules which we study as ligands can
form dimers or some high order structures, can be in
different tautomeric forms and chemical degradeted by
light effect, temperature change and in time.
PROBLEMS (Continuation)
The analysis of the obtaining concentration
dependences in the future needs the known values for
concentrations of both A and B components very
accurately determined.
DNA's
(bp)
Molar extinction coefficients
 (max)
stDNA
12680 M-1cm-1 (260 nm)
Tyr
1,440 M-1cm-1 (274 nm)
Tyrosine
Phe
Phenylalanine
220 M-1cm-1 (257 nm)
Some curious mistakes can be sometimes in your
protocol of an experiment
You want to research the
Next
dimarization of a drug in
example
solution
You are preparing a series of solutions
containing a drug at different concentrations
K
2A d A2
You record, for example, fluorescence
emission spectra of these solutions
And we want to obtain good
result by optimization of
spevtra and ...
+
Kd
Some errors in our concentration dependencies
can be through non calibrated instruments
Relative C/Cint
The
calibration
curve
0.5
is not a linear one
0.4
 For
calibration, we prepare a series of
solutions containing the analyte in the
concentration range expected
 Record the fluorescence emission (FL)
of each solution
 Construct plot the data (relative C/Cint
vs. FL)
 Compare obtained curve with line
0.3
0.2
0.1
0
50
100
150 200
250 300 FL intensity
Thus, good concentration dependencies we can
obtain by titration procedure.
Case 2
CB0 is fixed
In main biophysics
methods this method
of titration is used
more offen.
V1 of CA0 is added to V2 of CB0
CA0
CB0
At
this
method
of
titration,
concentrations of both A and B
components
are
differed
from
mixture to mixture and observed
results are interpreted not so lightly
Hard to understand why
treatment of numerous
experimental data obtained
from biophysical methods to
determine thermodynamic
n=6-8 bp
parametrs
of
complex
formation are done up to
now with the use of the
model of one type of
complex. Of cource, there
are
different
kinds
of
bound
n<1 bp
drugs to DNA (NA), but we
n=2-4 bp can assume that in a drugNA mixture several types of
complexes are formed
model of
one type
of
complex
up to now describes the all
biophysical experimental data
Stern – Volmer
equation
Io/I = 1 - KC
Io/I-1
CL0 =
1
model of
one type
of
complex
fluorescence
0
C
McGhee equation
1.0
1/Tm - 1/T0 = R/m1 - KC)
1/n
model of
one type
of
complex
0.5
T0 – DNA alone Tm
T
Melting of DNA in the prsence of a drug
G= -TS
G= -RT lg K
DSC,
T is
canged
Differential
scanning
calorimetry
ITC,
T is
fixed
Isothermal
titration
calorimetry
model of
one type
of
complex
We compare usually our results
with results detected in another
methods
CD
DSC, ITC
polarimetry
model of
calorimetry
one type of
complex
for a
system
so on
and
values
of
fluorometry
binding
parameters
estimated should
spectrophotometry be the same ones
By titration we obtain the set of spectral data that should be
large enough to be statistically treatment by new algorithms
(for example, either by method of chemometric analysis or by
rather like methods)
actinocin – ctДНК , CA0=2x10-5 M
What is P/D? P/D is the
molar ratio of DNA base
A
1 - P/D =0
1
to drug
0.4
2 - P/D =0,76
2
3
Kruglova E.B., Gladkovskaya
N.A., and Maleev V.Ya. Use of
Spectrophotometric Analysis to
Calculate the Thermodynamic
Parameters of Binding between
an Actinocin Derivative and
DNA. Biofizika 2005. V.50. 253
8
7
4
0.3
6
5
3
4
5
6
7
8
-
P/D =1,98
P/D =3,81
P/D =4,88
P/D =6,9
P/D =12,76
P/D =51,64
0.2
0.1
380
400
420
440
460
480  , nm
Beer-Lambert Law
A = (  l ) c
where:
A  - absorbance at wavelength 
1  - Molar absorptivity at , M-1 cm-
c - concentration, M
Principle of additivity: Absorbance of
mixture at 1 should be the sum of the
absorbances of the components at 1
A(mixture) 1 = A(1) 1 + A(2) 1
Block-scheme of our algorithm

CA,10,
CB,100
CA,2 ,
0
C
. .B,2
......
CA,n0,
CB,n0
1
A1,1
A2,
2
...
An,1
exit
Criteria of
conformity of a
model to
experimental
data
19
block of
calculation of
K,
n
A2,n
equilibrium
concnetrations
...
K, 
An,n
A1,n
block of
comparison
of Aij exp.
and Aij cal.
block calculation
of absorptions
of mixtures, Aij
k [Ck ]i
A + Bn
2( ABn )
ABn K1
CA,n0,
CB,n0
19
A + Bn
A1,1 A1,n
A2,
2
...
An,1
ABn
K
A2,n
...
An,n
n− 1
(2ω− 1)(1− Rn )+R− x
R
=K
Cf
2 (ω− 1 )(1− Rn )
(
A2
Kd
( ABn )2 K2
1
CA,10,
CB,100
CA,2 ,
CB,20
........
2A
McGhee, von
Hippel Model
()
1− (1 +n )R+x
2 (1− Rn )
)(
)
Force-induced stretching DNA elongetion in the
presence of ethidium bromide (EtBr):
concnetration dependences
Temperature
induced
melting
of
DNA
Lipfert J., Klijnhout S., and Dekker N.H.
Torsional sensing of small-molecule
binding using magnetic tweezers. Nucleic
Acids Res. 2010 November; 38(20):
7122–7132.
So, at concentration of EtBr CetBr< CEtBrcrt the
stretching curves exhibit cooperative transition
effect similar to that seen in the absence of the
drug.
r/CEtBr
But we have no peculiarities
in this range of Scatchard
isotherm. Why?
At
CetBr< CEtBrcrt the force
extension curves are simple,
monotonically increasing functions.
This CetBrcrt to be CetBrcrt = 2,5*108M
r
It would be very
interesting to find the
answer to the question
what is
CetBrcrt = 2,5*10-8 M
???
Vladescu I.D., McCauley M.J., Rouzina I. And Williams M.C. Mapping the phase
diagram of single Dna molecule force-induced melting in the presence of ethidium.
2005. Phys Rev. Lett. V.95. .
These questions wait to our
answers
Thank you