# Global Fitting¶

## 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 something like the following. The global parameters appear as global_K and global_dH.

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

## Global connectors¶

pytc also defines global connectors that link titrations to one another. For example, one might perform the same binding experiment at different temperatures and use that information to perform a Van ‘t Hoff analysis.

### Example 1: van ‘t Hoff fit¶

The following code takes two experiments, done at $$5\ ^{\circ}C$$ and $$10\ ^{\circ}C$$ and then uses them to extract the van’t Hoff enthalpy. (In practice, this would require more than two temperatures, but it illustrates the approach). The code that actually does the linking is highlighted with ***

import pytc
from pytc import global_connectors

# Create fitter
g = pytc.GlobalFit()

t5 = pytc.ITCExperiment("temp-dependence/5C.DH",
pytc.indiv_models.SingleSite,
shot_start=1)

t10 = pytc.ITCExperiment("temp-dependence/10C.DH",
pytc.indiv_models.SingleSite,
shot_start=1)

# **********************************
# Create a van't hoff GlobalConnector, assigning the prefix "vh" to each parameter
vh_conn = pytc.global_connectors.VantHoff("vh")

# Link 5 C experiment into connector

# Link 10 C experiment into connector
# **********************************

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


The new global parameters are assigned the name “vh_K_ref” and “vh_dH_vanthoff”. The output of this fit will look something like the following.

type,name,exp_file,value,stdev,bot95,top95,fixed,guess,lower_bound,upper_bound
global,vh_K_ref,NA,9.06284e+03,2.66839e+02,8.53780e+03,9.64146e+03,False,1.00000e+00,-inf,inf
global,vh_dH_vanthoff,NA,-6.23127e+03,1.15980e+02,-6.46163e+03,-5.96134e+03,False,0.00000e+00,-inf,inf

Note the similarity to the simple global fit. The main difference is that we have defined a connector (vh_conn) that we link variables to as opposed to a name: for example, vh_conn.K rather than "K_global".

### Example 2:¶

The following code takes two experiments, one in Tris and another in Imidazole, and uses them to extract the buffer-independent binding enthalpy and number of protons released (or taken up) upon binding. The code that actually does the linking is highlighted with ***

import pytc
from pytc import global_connectors

# define buffer ionization enthalpies.
# goldberg et al (2002) Journal of Physical and Chemical Reference Data 31 231,  doi: 10.1063/1.1416902
TRIS_IONIZATION_DH = 47.45/4.184*1000
IMID_IONIZATION_DH = 36.64/4.184*1000

# Create fitter
g = pytc.GlobalFit()

# Load in an experiment done in tris buffer
tris = pytc.ITCExperiment("demos/ca-edta/tris-01.DH",
pytc.indiv_models.SingleSite,
shot_start=2)
tris.ionization_enthalpy = TRIS_IONIZATION_DH

# Imidazole buffer experiment
imid = pytc.ITCExperiment("demos/ca-edta/imid-01.DH",
pytc.indiv_models.SingleSite,
shot_start=2)
imid.ionization_enthalpy = IMID_IONIZATION_DH

# **********************************
# Create a NumProtons GlobalConnector, assigning the prefix "np" to each parameter
num_protons = global_connectors.NumProtons("np")
# **********************************

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


This will spit out:

type,name,dh_file,value,uncertainty,fixed,guess,lower_bound,upper_bound
global,np_num_H,NA,-9.79065e-01,1.15256e+00,float,1.00000e-01,-inf,inf
global,np_dH_intrinsic,NA,-4.63537e+02,1.08227e-02,float,0.00000e+00,-inf,inf

The major difference between this code and the van’t Hoff analysis is the line in which we assign the ionization enthalpy for each experiment (for example, tris.ionization_enthalpy = TRIS_IONIZATION_DH). This provides the information required by the NumProtons class do perform the fit. If you are using a different global connector, you could set different properties in this way (pH, competitor concentration, etc.). Note: experiment.temperature is always defined in ITC output, so it should never have to be set manually.