Kinetic Models

The kinetic model (specified with the -d or --model option) defines the type of exchange model to be used for data analysis. Available models include:

Model Name	Description
2st	2-state exchange model (default)
3st	3-state exchange model
4st	4-state exchange model
2st_rs	2-state exchange model for residue-specific studies
2st_hd	2-state exchange model for H/D solvent exchange studies
2st_eyring	2-state exchange model for temperature-dependent studies
3st_eyring	3-state exchange model for temperature-dependent studies
4st_eyring	4-state exchange model for temperature-dependent studies
2st_binding	2-state exchange model for ligand binding studies
4st_hd	4-state exchange model for simultaneous normal and H/D solvent exchange studies

In these models, each state in the exchange process is represented with a unique parameter suffix (A, B, C, D, etc.). For example, R1_A denotes the R₁ relaxation rate of the major (ground) state, while R2_B refers to the R₂ rate of the first minor state, and so forth.

note

For any kinetic model, you can add the .mf suffix to create a model that fits model-free parameters directly (e.g., TAUC_A, S2_A), rather than individual relaxation parameters (e.g., R1_A, R2_A). For an example, see CEST_15N_TR/ under Examples/Experiments/.

Temperature-Dependent Eyring Models

The 2st_eyring, 3st_eyring, and 4st_eyring models implement 2-state, 3-state, and 4-state exchange systems (respectively) with temperature-dependent rate constants calculated using Eyring transition state theory. These models are particularly useful for studying exchange processes where thermodynamic parameters govern the temperature dependence of exchange rates.

Theoretical Background

The Eyring equation relates the rate constant to the activation free energy:

k_ij = (k_B * T / h) * exp(-ΔG‡_ij / RT)

where:

• k_ij is the rate constant for transition from state i to j (s⁻¹)
• k_B is Boltzmann's constant (1.380649×10⁻²³ J/K)
• T is temperature in Kelvin
• h is Planck's constant (6.62607015×10⁻³⁴ J·s)
• ΔG‡_ij is the activation free energy (J/mol)
• R is the gas constant (8.314462618 J/mol/K)

The activation free energy is calculated from enthalpic and entropic contributions:

ΔG‡_ij = ΔH‡_ij - T * ΔS‡_ij

2st_eyring Model Parameters

The 2st_eyring model uses the following thermodynamic parameters:

State Energies (relative to state A):

• DH_B: Enthalpy difference (J/mol) for state B relative to A
• DS_B: Entropy difference (J/mol/K) for state B relative to A

Transition Barriers:

• DH_AB: Activation enthalpy (J/mol) for A → B transition
• DS_AB: Activation entropy (J/mol/K) for A → B transition

The model automatically calculates both forward (k_AB) and reverse (k_BA) rate constants from these parameters.

3st_eyring Model Parameters

The 3st_eyring model extends the 2-state model with an additional state:

State Energies (relative to state A):

• DH_B, DH_C: Enthalpy differences (J/mol) for states B, C
• DS_B, DS_C: Entropy differences (J/mol/K) for states B, C

Transition Barriers:

• DH_AB, DH_AC, DH_BC: Activation enthalpies (J/mol) for transitions
• DS_AB, DS_AC, DS_BC: Activation entropies (J/mol/K) for transitions

The model automatically calculates all 6 rate constants (k_AB, k_BA, k_AC, k_CA, k_BC, k_CB).

4st_eyring Model Parameters

The 4st_eyring model implements a full 4-state system:

State Energies (relative to state A):

• DH_B, DH_C, DH_D: Enthalpy differences (J/mol) for states B, C, D
• DS_B, DS_C, DS_D: Entropy differences (J/mol/K) for states B, C, D

Transition Barriers:

• DH_AB, DH_AC, DH_AD: Activation enthalpies (J/mol) for transitions from A
• DH_BC, DH_BD, DH_CD: Activation enthalpies (J/mol) for transitions between B, C, D
• DS_AB, DS_AC, DS_AD: Activation entropies (J/mol/K) for transitions from A
• DS_BC, DS_BD, DS_CD: Activation entropies (J/mol/K) for transitions between B, C, D

The model automatically calculates all 12 rate constants (k_AB, k_BA, k_AC, k_CA, k_AD, k_DA, k_BC, k_CB, k_BD, k_DB, k_CD, k_DC).

note

State A serves as the reference state with ΔH_A = ΔS_A = 0 for all Eyring models. Rate constants are automatically clipped to [0, 1×10¹⁶ s⁻¹] for numerical stability.