We need to figure out how the Origin software processing the data from a Microcal VP ITC calorimeter computes the values of concentrations given in its output. They are not simply computed assuming that total moles of added components are conserved, since part of the solution is released from the working volume as titrant is added to the cell.
Already tried the equations given here: https://www.cif.iastate.edu/sites/default/files/uploads/Other_Inst/ITC/Origin%20Lesson%2010.pdf . It works fine for the concentration of the 'receptor' ligand in the cell, but not yet for the concentration of injected ligand. For this we used,
[L]tot = [L]inyector . Vinjected / (Vcell + Vinjected/2)
The values obtained much perfectly for first injections but diverge from the values given by Origin towards the end of the titration
Thanks.
Jere
MicroCal ITC instruments operate a constant filling volume. It is assumed that the injection results in the ejection of the same amount of liquid from the cell. Several approximations can be made: instantaneous injection (ejection before mixing), instantaneous mixing (mixing before injection), or mixed regime (ejection as the mixing occurs).
I think MicroCal considers the third option, but the equation for the ligand (titrant in the syringe) are not correct:
PT,j=P0x(1–(Σv/2V0))
LT,j=L0x(Σv/V0)x(1–(Σv/2V0))
where PT,j is the concentration of titrand in the cell after the injection j, LT,j is the concentration of titrant in the cell after the injection j, P0 is the initial titrand concentration in the cell, L0 is the titrant concentration in the syringe, V0 is the cell volume, and Σv is the cumulative injected volume until injection j.
In the mixed regime it is assumed that the expelled volume contains a variable concentration of reactants as the mixing is occurring.
In the instantaneous injection it is assumed that the expelled volume contains reactants at concentrations equal to those after the previous injection:
PT,j=P0x(1–(v/V0))j
LT,j=L0x(1–(1–(v/V0))j)
But some people use the following expressions:
PT,j=P0xexp(–jv/V0)=P0xexp(–Σv/V0)
LT,j=L0x(1-exp(–jv/V0))=L0x(1–exp(–Σv/V0))
You can see that the previous expressions arise when expanding the last expressions with the Taylor series up to first order: exp(-x)=1–x
All these expressions provide very similar values when v/V0 is small, which is the usual situation.
Hi Adrian Velazquez-Campoy , thanks a lot.
We tried the expressions for the mixed regime -with the only difference that we have your expression for the concentration of titrand in the cell, PT,j, divided by (1 + Σjv/2V0) as in the expression given in the cited manual, the expression for injected titrant LT,j being identical (in that way PT,j = P0 (1 - LT,j/L0) )
This set of expressions provides a perfect match for PT,j values with the values given by Microcal, whereas they do not perfectly match for LT,j.
The final results of the analysis doesn't change significantly whether we use Microcal or computed values, as the discrepancy is at most 2% in last points of the titration. At the lower values of Σjv/V0 (
Jeremías Incicco Yes, you are right. I was typing too fast... The correct expression from MicroCal user manual for the titrand concentration inside the cell is:
PT,j=P0x(1–(Σv/2V0))/(1+(Σv/2V0))
When you say "...if we need to match 2 consecutive set of injections to the same solution in the cell", do you mean you want to concatenate two series of injections done on the same titrand solution by refilling the syringe?
That is called "concatenate" by MicroCal. I have done this a couple of times and it worked fine if you consider that, after the first set of injections, the initial concentrations inside the cell for the second set of injections correspond to the mixing of the total volume injected of titrant and the volume of titrand (i.e., when you take out the syringe to be refilled, all the previously expelled liquid is mixed with the cell content).
On the other hand, I do not see much necessity for concatenation experiments. It is much better to increase the concentration of titrant in order to cover a larger molar ratio range, while adjusting conveniently the injection volume to get sufficient resolution in the binding isotherm.
Adrian Velazquez-Campoy Thanks again! Yes, it's not our favorite to do the concatenation but allowed us to save some titrations in which ligand concentration in the syringe was smaller than required. Also, yes, we wanted to test some conditions in which a single titrant concentration was not enough to fulfill resolution at low concentrations (with a minimum of 2-2.5 µl aliquots) and a clear definition of saturation (with the ~290 µl of titrant in the syringe).
- Badges
- Science method
- Similar topics
- Biological Science
- Genetics
- Gene Expression
- Protein Expression