ThANNCs for kinetically optimizing ITC

For decades, isothermal titration calorimetry (ITC) has been an indispensable tool for determining the thermodynamics of macromolecular binding equilibria. Stoichiometry, binding constants (affinity), free energy, enthalpy, and entropy differences between bound and free states can readily be obtained through the measurement of the heat of association. Most modern ITCs operate on the principle of power compensation between a reference cell and a sample cell containing the titrand (i.e., a protein) into which the titrant (i.e., a small-molecule ligand, inhibitor, or another macromolecule) is injected. Upon binding, a small amount of heat is released or absorbed, and the calorimeter compensates for the temperature change by applying or withdrawing heat to the sample cell in order to maintain a constant temperature throughout the reaction time. This gives rise to a differential power trace over time that is integrated to directly determine the enthalpy of binding. Subsequent analysis of a series of injections at different mole ratios of the interacting species in solution can provide binding affinities and the stoichiometry of the association.

For basic scientists simply wanting to know a binding affinity, most often expressed as an equilibrium dissociation constant (K_D), ITC already provides a wealth of additional information that enables a comprehensive thermodynamic understanding of binding mechanisms. Scientists that are also interested in how fast reactions occur generally turn to other methods perhaps more suitable to determining kinetic rates of association and dissociation, such as surface plasmon resonance (SPR) or stopped-flow rapid mixing methods coupled with spectroscopy (1,2). In principle, the kinetics of macromolecular binding equilibria may also be ascertained with calorimetry because ITC is a time-based measurement, but access to kinetic information in ITC experiments is complicated by slow mixing times in the titrations, instrument response times, electrical power gain settings, data-sampling rates, and unknown mechanical/frictional contributions due to stirring.

It has long been known that calorimeter response times must be accounted for and that mixing of the titrant with the titrand is not instantaneous. These instrumental properties have been determined by titrations of known reaction standards or instrumental heater pulses (3) and by convoluting the linear injection rate with an exponential delay using Laplace transforms. In a manuscript entitled “The feasibility of determining kinetic constants from isothermal titration calorimetry data,” Tso et al. have arrived at a refined experimental and analytic procedure that kinetically optimizes ITC by taking these factors and others into consideration within a numerical and analytical framework (4).

These methods, implemented into the Thermogram Generation via Analytical and Numerical Calculation and Concatenation (ThANNC) algorithm, are calibrated specifically to the calorimeter through direct measurements of mono- and bi-exponential response times by fitting heater pulses to the ITC sample cell, which can be performed at each of the instrumental gain settings defined by the user. Data-acquisition rates are sampled at high frequencies commensurate to the instrumental electronics and then down-sampled to the calorimeter’s data-report rate. A non-instantaneous mixing of titrant with the titrand is also accounted for to optimize numerical simulations with respect to analytical calculations of the component concentrations. Mechanical heats of injection are derived from titrations at the end of the thermogram where the macromolecule is saturated with ligand. Others have modeled dilution and frictional heats into the thermograms (2,5), but it is possible, or perhaps prudent, to determine actual dilution heats of the titrant as a separate experiment lacking the titrand and manually subtract it out (6), leaving only the very small frictional heats due to the mechanics of the injection. Prior to the ThANNC analysis, an unbiased baseline within the injection peaks can be initially determined by singular value decomposition with NITPIC (7,8). Finally, an error surface protocol utilizes non-linear least squares to determine confidence intervals on all the derived parameters. All of these methods are wrapped as modules into a graphical user interface that collectively comprise the Simulation Engine and Software for the Kinetic Analysis of ITC Power-traces (SEASKAIP) software for simulation and data fitting.

Tso et al. have benchmarked these methods against SPR experiments for the binding of inhibitors to bovine carbonic anhydrase and of anti-lysozyme nanobodies that each follow simple bimolecular mono-exponential kinetics. They find a substantial agreement, although the rate constants are slightly lower for ITC than for SPR. Other comparisons have also observed discrepancies between the rates obtained from both methods (5,9,10). SPR is generally not without its own experimental issues, such as the need to immobilize the macromolecule on a surface that restricts the stochastics of binding in solution to an interface. ITC has long been heralded for the lack of requirement for chemical modification because it directly measures the enthalpy of binding (11). In its current iteration, ThANNC only includes a simple bimolecular kinetic model with k_on and k_off rates defining the equilibrium constant, K_D. Due to the analytical equations used (12), ThANNC is much more efficient at solving bimolecular equilibria imbedded into ITC traces than using traditional ordinary differential equations. Simple kinetics will not reflect more complex mechanisms involving polyfunctional linkage (13), conformational selection, or induced fit (14, 15, 16); however, simulations of more complex models and the observed k_on- and k_off-dependent shapes of ITC traces using ODEs may open the door to these expanded applications.

It is expected that SEASKAIP will continue to develop to include additional kinetic models as well as the inclusion of other calorimeter manufacturers. The scientific community, as a whole, would benefit from the methods and procedures discussed by Tso et al. calibrated specifically to their calorimeter of choice. Having this in a single software platform that can be calibrated to your lab’s calorimeter is a notable improvement to the field.

Editor: Elizabeth Rhoades.