Calculating binding energy is one of the most important applications of biomolecular simulations. Binding energy simulation is arguably the most efficient and promising method for estimating the binding free energy of ligands to macromolecules. Binding energy simulations have been employed recently to describe the solvation characteristics of many compounds. They have now established themselves as a crucial resource for evaluating, enhancing, and testing the force fields of biomolecules.

Molecular dynamics (MD) simulations can be used by Alfa Chemistry to determine the free energy of binding tiny ligands to proteins, and the results are in good agreement with the experiments. In the near future, it is anticipated that this physics-based methodology will significantly advance the drug discovery and optimization process.

### Our Theory and Method

The following are the main methods we use to calculate binding free energies from MD simulations.

#### A. Statistical mechanics and equilibrium binding constants

A relationship needs to be established between macro-observables and micro-variables. Specifically, a protein macromolecule (P) is assumed to be in thermodynamic equilibrium with a dilute solution containing a ligand molecule (L). The equilibrium constant Kb for the binding reaction L+P ⇌ LP is defined as Kb = [LP]/([L][P]), where [L], [P] and [LP] are the unbound ligand, unbound ligand, respectively Bound proteins and bound complexes. The standard binding free energy is defined by the equilibrium constant as ΔG^{□}b=-k_{B}Tln(C^{□}k_{B}), where C^{□} is the standard concentration, k_{B} is the Boltzmann constant, and T is the absolute temperature.

According to classical statistical mechanics, it can be shown that the equilibrium constant can be expressed as:

where U is the total potential energy of the system, β≡1/k_{B}T, L and X represent the coordinates of the ligand and all remaining atoms, respectively, r_{L} is the position of the centroid of the ligand, and r* is the distance relative to the protein in the bulk region any location. The binding process can be described as the ligand leaving the host region and moving to the binding site based on the equation.

#### B. Standard binding free energy from alchemical perturbations

Alchemical methods calculate the reversible thermodynamic work used to decouple a ligand from its surroundings. The free energies associated with decoupling the ligands in the bulk solvent are as follows:

where U0 represents the total potential energy of the system with non-interacting (uncoupled) ligands. The solvation free energy in the equation can be calculated using alchemical free energy perturbation (FEP) or thermodynamic integration (TI).

#### C. Binding Free Energy from a PMF

Equilibrium association constants and binding free energies can also be calculated using PMF without the alchemical decoupling step as in DDM. In simple cases, strategies based on one-dimensional (1D) radial PMF may work.

where r* is a reference position far away in the bulk.

**Fig 1**. Shown in the figure is path for the free energy computation using a PMF-based method with restraining potentials. (Deng Y, *et al*. 2009)

### Our Service

Project Name | Binding Energy Calculation Service |

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Alfa Chemistry provides global customers with fast, professional and high-quality binding energy calculation services at competitive prices. The service is a customized innovative scientific research service. We need to evaluate each project before we can determine the corresponding analysis plan and price. Customers can contact our staff directly and provide timely feedback on their inquiries. If you are interested in our services, please contact us for more details.

Reference

- Deng Y,
*et al*. (2009). "Computations of Standard Binding Free Energies with Molecular Dynamics Simulations."*J. Phys. Chem. B*. 113(8): 2234-2246.