# Global ITC Models¶

## Simple global parameters¶

The first (and simplest) sort of global fit is to declare that parameters from separate experiments should use the same, shared, fitting parameter. The following code takes two experimental replicates and fits them to a single $$K$$ and $$\Delta H$$. The code that actually does the linking is highlighted with ***

import pytc

# Create fitter
g = pytc.GlobalFit()

a = pytc.ITCExperiment("demos/ca-edta/hepes-01.DH",pytc.indiv_models.SingleSite,shot_start=2)

b = pytc.ITCExperiment("demos/ca-edta/hepes-02.DH",pytc.indiv_models.SingleSite,shot_start=2)

# **********************************

# **********************************

# Fit and show results
g.fit()
print(g.fit_as_csv)


The new global parameters are simply assigned a name (global_K and global_dH) that are individually fit. The fitter takes care of the rest. The output of this fit will look like the following. The global parameters appear as global_K and global_dH.

# Fit successful? True
# Fit sum of square residuals: 0.634237669456395
# Fit num param: 8
# Fit num observations: 108
# Fit num degrees freedom: 100
type,name,dh_file,value,uncertainty,fixed,guess,lower_bound,upper_bound
global,global_K,NA,3.84168e+07,1.40582e-06,float,1.00000e+06,-inf,inf
global,global_dH,NA,-4.64104e+03,7.96280e-03,float,-4.00000e+03,-inf,inf
...


This fits a global model to a collection of ITC experiments collected in buffers of the same pH, but different ionization enthalpies.

global_connectors.NumProtons

This is useful for analyzing a binding reaction that involves the gain or loss of a proton. The measured enthalpy will have a binding component and an ionization component. These can be separated by performing ITC experiments using buffers with different ionization enthalpies.

### Model parameters¶

parameter variable parameter name class
association constant $$\Delta H_{intrinsic}$$ dH_intrinsic thermodynamic
binding enthalpy $$n_{proton}$$ num_protons thermodynamic

### Required data for each experiment¶

data variable data
ioinzation enthalpy $$\Delta H_{ionization,buffer}$$ ionization_enthalpy

### Model Scheme¶

$\Delta H_{obs,buffer} = \Delta H_{intrinsic} + \Delta H_{ionization,buffer} \times n_{proton},$

where $$\Delta H_{intrinsic}$$ is the buffer-independent binding enthalpy, $$\Delta H_{ionization,buffer}$$ is the buffer ionization enthalpy, and $$n_{proton}$$ is the number of protons gained or lost.

## Van’t Hoff¶

A standard Van’t Hoff analysis assuming a constant enthalpy.

global_connectors.VantHoff

Fits a collection of ITC experiments collected in identical buffer conditions, but at different temperatures. The temperature of each experiment is taken from the heats file. Allows extraction of the Van’t Hoff enthalpy and binding constant for the reaction at a defined reference temperature.

### Model parameters¶

parameter variable parameter name class
association constant $$K_{ref}$$ K thermodynamic
binding enthalpy $$\Delta H_{vh}$$ dH thermodynamic

### Required data for each experiment¶

data variable data
temperature (K) $$T$$ temperature

### Model Scheme¶

$\Delta H = \Delta H_{vh}$
$K = K(T_{ref})exp \Big ( \frac{-\Delta H_{vh}}{R} \Big (\frac{1}{T} - \frac{1}{T_{ref}} \Big ) \Big )$

By performing experiments at a minimum of two temperatures, one can extract the Van’t Hoff enthalpy $$\Delta H_{vh}$$ and binding constant at the reference temperature $$K(T_{ref})$$.

## Extended Van’t Hoff¶

An extended Van’t Hoff analysis that assumes constant heat capacity.

global_connectors.VantHoff

Fits a collection of ITC experiments collected in identical buffer conditions, but at different temperatures. The temperature of each experiment is taken from the heats file. Allows extraction of the heat capacity, as well as the enthalpy and binding constant at a reference temperature.

### Model parameters¶

parameter variable parameter name class
association constant $$K_{ref}$$ K thermodynamic
binding enthalpy $$\Delta H_{ref}$$ dH thermodynamic
heat capacity $$\Delta C_{p}$$ dCp thermodynamic

### Required data for each experiment¶

data variable data
temperature (K) $$T$$ temperature

### Model Scheme¶

$\Delta H(T) = \Delta H_{ref} + \Delta C_{p}(T - T_{ref})$
$K = K(T_{ref})exp \Big ( \frac{-\Delta H_{ref}}{R} \Big (\frac{1}{T} - \frac{1}{T_{ref}} \Big ) + \frac{\Delta C_{p}}{R} \Big ( ln(T/T_{re}) + T/T_{ref} - 1 \Big ) \Big )$

By performing experiments at a minimum of two temperatures, one can extract the heat capacity $$\Delta C_{p}$$, the enthalpy at a reference temperture $$\Delta H_{ref}$$ and the binding constant at a reference temperature $$K_{ref}$$.