Analysis of in vitro experimentsDr. Kruglova E.B.

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 ligand-biopolymer system from analysis of these dependencies: affinity. stoichiometric coefficients, site sizes to chose the best binding modes.

What is a concentration dependence in Molecular Biophysics?

Why do we still continue -Why do we still continue -to melt NA (DNA) at temperatures more to melt NA (DNA) at temperatures more

than 100 than 100 00C ?C ?

If our living conditions are 37 If our living conditions are 37 00C, about C, about 0.1 M NaCl and pH7. 0.1 M NaCl and pH7.

to add in solutions of biopolymers to add in solutions of biopolymers NaCl, KCl in such quantity to be more NaCl, KCl in such quantity to be more than 1 M and ions of two charged and than 1 M and ions of two charged and transition metals?transition metals?

to expose of solutions of to expose of solutions of biomacromolecules to higher doses biomacromolecules to higher doses either ionizing radiation oreither ionizing radiation or drugs?drugs?

So obtainig results in these in So obtainig results in these in vitro experiments can be fine vitro experiments can be fine

and very simple Models and very simple Models describing different situation describing different situation in living cells and organisms in living cells and organisms

in both real and critical in both real and critical situation.situation.

Thus we must continue to Thus we must continue to work in the same waywork in the same way

What is a concentration dependence?What is a concentration dependence?

Solutions of the components Solutions of the components A and B A and B

CCAA00 CCBB

00

A (ligand) can be a small molecule of A (ligand) can be a small molecule of dyes, drugs, aminoacids, proteins, dyes, drugs, aminoacids, proteins, so onso on

B can be in molecular biophysics B can be in molecular biophysics NA's, NA's, proteins, oligonucleotides so onproteins, oligonucleotides so on

to A is added Bto A is added B

Our conclusionOur conclusion: : component A component A interacts with interacts with component B – component B – Why?Why? Colour is Colour is changedchanged

If that ibformation is not enougthIf that ibformation is not enougth

What is a concentration dependence?What is a concentration dependence?

SpectrophotometerSpectrophotometerSpectrofluorometerSpectrofluorometer

CD spectropolarimeter CD spectropolarimeter so onso on

What is a concentration dependence?What is a concentration dependence?

Spectrophotometer,Spectrophotometer,VIS rangeVIS range

SpectrofluorometerSpectrofluorometer

Can we say that the component A interacts with Can we say that the component A interacts with component B using only one spectra? - No.component B using only one spectra? - No.

We shoul add to spectra of the mixture A+B, at least, We shoul add to spectra of the mixture A+B, at least, spectra of free component A at the same concentration.spectra of free component A at the same concentration.

Thus, good concentration dependencies we can obtain by titration procedure

Case 1

CCAA00 CCAA

0 0 ++ CCBB00

VV11 of of CCAA0 0 is added is added

to Vto V2 2 of of (C(CAA0 0 ++ CCBB

0 0 ))

can be shown that at that titration procedure can be shown that at that titration procedure concnetration of component A does not concnetration of component A does not change in each (A+B) mixture and to bechange in each (A+B) mixture and to beCCAA

0 0 = (C= (CAA0 0 VV1 1 + V+ V2 2 CCAA

00) /(V) /(V11 + V+ V2 2 ))

The method can give very The method can give very good results for studies of good results for studies of interaction between dyes interaction between dyes or drugs and NA's and or drugs and NA's and proteins proteins Why?Why?

A titration is a method of analysis that will allow to determine the precise endpoint of a reaction and therefore the precise quantity of reactant in the titration ..(Wikipedia).

There are two basic ways that are used usually in biophysics experiments

How can we obtain the thermodynamic and spectral parameters of a drug to DNA binding by spectrophotometry?

CL0 = If one type of complex

is formed only

CAo

i = [Cf ]i + [Cb ]i

If omponent B does not absorb in VIS

range

Ai = f [Cf ]i + b [Cb ]i

Scatchard isotherm (plot)

r/Cf

r [Cf] is equilibrium concentration of a free ligand

Then we can construct 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

n=1/r

K

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?

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

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)

TyrTyrosine

1,440 M-1cm-1 (274 nm)

PhePhenylalanine

   220 M-1cm-1 (257 nm)

Some curious mistakes can be sometimes in your protocol of an experiment

Next example

You want to research the dimarization of a drug in solution

You are preparing a series of solutions containing a drug at different concentrations

You record, for example, fluorescence emission spectra of these solutions And we want to obtain good

result by optimization of spevtra and ...

Kd

2A A2

Kd

++

Some errors in our concentration dependencies can be through non calibrated instruments

50 100 150

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

The calibration curve The calibration curve is not a linear oneis not a linear one

0 200 300250

0.1

0.20.2

0.3

0.5

0.4

Relative C/Cint

FL intensity

Thus, good concentration dependencies we can obtain by titration procedure.

CCAA00 CCBB

00

VV11 of of CCAA0 0 is added to Vis added to V2 2 of of CCBB

0 0

At this method of titration, At this method of titration, concentrations of both A and B concentrations of both A and B components are differed from components are differed from mixture to mixture and observed mixture to mixture and observed results are interpreted not so lightlyresults are interpreted not so lightly

Case 2Case 2CCBB

0 0 is fixedis fixed

In main biophysics In main biophysics methods this method methods this method of titration is used of titration is used more offen.more offen.

Hard to understand why treatment of numerous experimental data obtained from biophysical methods to determine thermodynamic 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 drugs to DNA (NA), but we can assume that in a drug-NA mixture several types of complexes are formed

n=2-4 bp

n=6-8 bp

n<1 bp

model of one type

of complex

up to now describes the all biophysical experimental data

CL0 =

Stern – Volmer equation

Io/I = 1 - KC

model of one type

of complex

Io/I-1

0

1

Cfluorescence

McGhee equation

1/Tm - 1/T0 = R/m1 - KC)

model of one type

of complex

T Melting of DNA in the prsence of a drug

model of one type

of complex

1/n

T0 – DNA alone Tm

0.5

1.0

G= -RT lg K

model of one type

of complexDifferential

scanning calorimetry

model of one type

of complex

DSC,T is

cangedITC,T is

fixed

G= -TS

model of one type

of complex

Isothermal titration

calorimetry

model of one type of

complexfor a

system

DSC, ITC calorimetry

We compare usually our results with results detected in another

methodsCD polarimetry

spectrophotometry

fluorometry and values of binding

parameters estimated should be the same ones

so on

380 400 420 440 460 480

0.1

0.2

0.3

0.4

832

5

76

4

1A

, nm

1 - P/D=02 - P/D=0,763 - P/D=1,984 - P/D=3,815 - P/D=4,886 - P/D=6,97 - P/D=12,768 - P/D=51,64

What is P/D? P/D is the molar ratio of DNA base to drug

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

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

Beer-Lambert LawBeer-Lambert Law

Principle of additivity: Absorbance of mixture at 1 should be the sum of the absorbances of the components at 1

A = ( l ) cwhere:A - absorbance at wavelength - Molar absorptivity at , M-1 cm-

1

c - concentration, M

A(mixture) 1 = A(1) 1 + A(2) 1

Block-scheme of our algorithm Block-scheme of our algorithm

CCA,1A,100, C, CB,1B,1

00 1 19

CCA,2A,200, C, CB,2B,2

00

CCA,nA,n00, C, CB,nB,n

00 . . . . . . . . . . . . . . . .

AA1,11,1 AA1,n1,n

AA2,22,2 AA2,n2,n

AAn,1n,1 AAn,nn,n

. . . . . . . . . . . . . . . . . .

block of block of calculation of calculation of equilibrium equilibrium concnetrations concnetrations

K, n K, n

block calculation block calculation of absorptions of absorptions of mixtures, Aij of mixtures, Aij

k [Ck ]i

block of block of comparisoncomparisonof Aij exp. of Aij exp. and Aij cal.and Aij cal.

K, K,

exitexitCriteria of Criteria of conformity of a conformity of a model to model to experimental experimental datadata

n−1R

C f = K( (2ω−1) (1−Rn ) +R−x

2 (ω−1 ) (1−Rn ) )()

(1− (1 +n ) R+x 2 (1−Rn ) )

1 19 CCA,1A,1

00, C, CB,1B,100

1 19

CCA,2A,200, C, CB,2B,2

00

CCA,nA,n00, C, CB,nB,n

00 . . . . . . . . . . . . . . . .

AA1,11,1

AA2,22,2

AAn,1n,1

. . . . . . . . . . . .

AA1,n1,n

AA + B+ Bnn AB ABnn

McGhee, von McGhee, von Hippel ModelHippel Model

AA + B+ Bnn AB ABnn

2( AB2( ABn n ) ( AB) ( ABn n ))22

2A A2A A22

AA2,n2,n

AAn,nn,n

KKdd

KK

KK11

KK22

Lipfert J., Klijnhout S., and Dekker N.H.Lipfert J., Klijnhout S., and Dekker N.H.Torsional sensing of small-molecule Torsional sensing of small-molecule binding using magnetic tweezers. Nucleic binding using magnetic tweezers. Nucleic Acids Res. 2010 November; 38(20): Acids Res. 2010 November; 38(20): 7122–7132.7122–7132.

Force-induced stretching DNA elongetion in the Force-induced stretching DNA elongetion in the presence of ethidium bromide (EtBr): presence of ethidium bromide (EtBr):

concnetration dependencesconcnetration dependences

Temperature Temperature induced induced melting of melting of DNADNA

So, at concentration of EtBr CetBr< CEtBrcrt the

stretching curves exhibit cooperative transition effect similar to that seen in the absence of the drug.

At CetBr< CEtBrcrt the force extension

curves are simple, monotonically increasing functions. This CetBr

crt to be CetBr

crt = 2,5*10-8 M

r/CEtBr

r

But we have no peculiarities But we have no peculiarities in this range of Scatchard in this range of Scatchard isotherm. isotherm. Why?Why?

Vladescu I.D., McCauley M.J., Rouzina I. And Williams M.C. Mapping the phase 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. diagram of single Dna molecule force-induced melting in the presence of ethidium. 2005. Phys Rev. Lett. V.95. .2005. Phys Rev. Lett. V.95. .

It would be very It would be very interesting to find the interesting to find the

answer to the question answer to the question what is what is

CetBrcrt = 2,5*10-8 M

???

These questions wait to our These questions wait to our answersanswers

Thank you