Free Energy Basis Supporting Antibody-Antigen Bond Formation

Introduction

Antibody-antigen complex formation is defined as a spontaneous chemical reaction. For a reaction to occur spontaneously (no additional energy input required for reaction to occur), the sum of all chemical interactions must result in a negative change in free energy (-ΔG). In this review article, we intend to introduce the notion that thermodynamic energy interactions occurring over the course of a typical antibody/antigen binding event, serve to drive antibody-antigen complex formation in a spontaneous manner. As a part of this discussion, we will briefly review some of the macromolecular interactions occurring between hypervariable antigen binding regions of the antibody (paratope structure) and the targeted epitope structure present on antigen surfaces. We conclude this article explaining how chemical reactions associated with formation of interfacing paratope/epitope molecular surfaces results in a net negative change in free energy (-ΔG) for the binding reaction. This -ΔG free energy change parameter enables the overall antibody-antigen binding reaction to occur spontaneously without input of any additional energy in the form of heat.

Gibbs Free Energy component of antibody – antigen complex formation

As we begin our review of the free energy (G) basis responsible for driving the chemical reaction mechanism that is antibody-antigen (Aby-Agn) complex formation, we briefly discuss in general terms, the thermodynamic energy requirements that must be in place for a spontaneous reaction to occur. The energetics involved with Aby-Agn complex formation or in fact, any chemical reaction, are governed by the Gibbs Free-Energy (GFE) equation (ΔG = ΔH – TΔS)1.  ΔG in thermodynamic reaction equations represents the sum change in free energy for any chemical reaction. ΔH represents the change in enthalpy upon completion of any chemical reaction (in our case, the Aby-Agn complex formation). Enthalpy is a unit of measure defining the amount heat given off or absorbed upon completion of any generic chemical reaction. “Spoiler Alert”, formation of Aby-Agn complexes is an exothermic reaction. When heat is released during the Aby-Agn binding event, ΔH has a negative sign (-ΔH). Studies clearly indicate that the spontaneity of antibody-antigen complex formation is enthalpy driven.

ΔS in the Gibbs Free Energy (GFE) equation represents the change in entropy that occurs over the course any chemical reaction. Entropy is a measure of the randomness of molecular structure or order2. In nature, molecules seek to go from a more organized state to a less organized state. Anytime during a chemical reaction when the net result of the reaction is the creation of a more ordered molecular state, entropy is reduced. In other words, the sign of ΔS is negative. The molecular transition to a more ordered state can manifest itself as the creation of an environment where there is less freedom (reduction in degrees of freedom) for the molecules to rotate about their chemical bond linkage or move about within the protein scaffolding. This is also the case when the product of the reaction leads to a more concentrated organized molecular state than was the case before the chemical reaction occurred. This activity translates into a negative change in entropy (-ΔS). A -ΔS event detracts from the degree to which a spontaneous chemical reaction can occur. Looking at our situation involving Aby-Agn complex formation, ΔS represents the change in overall entropy upon Aby-Agn complex formation. Does the overall molecular structure upon completion of Aby-Agn complex formation exhibit a net increase or decrease in molecular organization or freedom to rotate about its chemical bond linkage? If the answer is a decrease in organizational structure, then this change is compatible with natures desire to go from an organized state to a less organized state. This equates to a positive entropy change (+ΔS) and serves to enhance the desire of the reaction to spontaneously go to completion. When referring to the Gibbs free energy equation, the ΔS energy unit is modified by an absolute temperature (in degrees Kelvin) multiplier (T). Greater reaction temperatures, as in an increase in molecular motion, elevates the desire of molecules to disperse equating to a higher state of entropy3.

The GFE equation provides a reliable prediction of the future stability of any given biochemical binding complex. For any chemical reaction to occur spontaneously, the ΔG in the GFE equation (ΔG = ΔH – TΔS) must have a negative value4. Putting this explanation within the context of Aby-Agn binding reactions, spontaneous Aby-Agn complex formation occurring in the absence of additional energy input would never occur unless the ΔG value for complex formation was negative.

Molecular interactions preceding Aby-Agn complex formation

Reaffirming what was stated above, formation of an Aby-Agn complex is a spontaneous reaction implying no outside energy input is required for complex formation. At this point we should define some of the different noncovalent Aby-Agn recognition interactions by which the direct interfacing event between antigen and antibody occurs. Antigen combining sites on antibody (paratope regions) through random interaction with antigen (a complex of epitopes) leads to formation of a network of noncovalent interactions between the epitope (Agn) and paratope (Aby). Aby-Agn interactions can be categorized into three different binding interaction categories: (1) Classic lock and key antibody binding mechanism. Smaller sized hydrophobic molecular antigen targets are recognized, bound, and retained within paratope pocket structure5,6; (2) Oligopeptides bound via induced-fit binding interactions; and (3) Protein antigens bound in a face to face manner on a relatively flat surface allowing only a small degree of movement.

Formation of the Aby-Agn complex typically proceeds through the following noncovalent interactions. These non-covalent forces consist of; hydrophobic bonds, hydrogen bonds, Van der Waals forces, and electrostatic forces. These non-covalent interaction forces play a prominent role in the antigen recognition process7. Once random molecular collision events bring potential antigen-epitope near antibody-paratope sites on hypervariable regions, longer range electrostatic (ionic) and hydrophobic attraction forces bring the paratope/epitope structures close enough to overcome the respective water of hydration energies of the two molecules. This mutual merging action expels surface water molecules on the respective paratope/epitope surfaces enabling the two surfaces to close the distance to a point where Van der Waals and hydrogen bonding forces become a very strong attraction factor. Ionic salt-bridge forces continue to play a strong attractive role even at these short distances4.

Enthalpy Driven Antibody-Antigen Complex Formation

Aby-Agn complex formation is enthalpy driven1,4,7. Because this critical reaction occurs spontaneously, the ΔG of the GFE equation must be negative. In more specific terms, in the ΔG = ΔH – TΔS equation for Aby-Agn complex formation, the enthalpy change component of the equation, ΔH, must also be negative. Though we don’t usually think of commonplace Aby-Agn binding interactions as exothermic (heat releasing reactions), this is in fact the case.  Several Aby-Agn complex formation events contribute to the final net negative ΔH character of these reactions. Since Aby-Agn binding events do not occur in a vacuum, it would be expected that there is a great deal of interactive-overlap amongst the list of chemical reaction participants8.

Total binding free-energy (ΔG) is the sum of the following events and forces

  • + neg ΔH of H-bonding forces
  • + neg ΔH of Van der Waals forces
  • + neg ΔH of electrostatic/ionization forces
  • + neg ΔH of bulk hydration events à >>> H-bonding networks
  • + pos ΔS of hydration of polar and non-polar groups
  • +++ pos ΔS from burial of water-accessible surface area during binding event
  • + negative ΔS from loss of degrees of freedom around torsion angles and ligand sidechains

Considering all the above interactive binding forces and entropy change events, the heat enthalpy derived from bulk hydration of the Aby-Agn complex provides the greatest exothermic process leading to the – ΔG for the Aby-Agn complex formation reaction8,9.

Relationship between ΔG and binding affinity values

Having discussed the chemical basis defining each thermodynamic energy element making up the GFE equation, we should conclude with a brief of commentary on the influence that ΔG has on a typical Aby-Agn binding event. One of the very first concerns you should have when getting in a new batch of monoclonal (to a lesser degree) or affinity purified polyclonal antibodies is, are these antibodies exclusively specific for the target antigen that you are trying to quantitate?  When you miss the mark on getting correct the all-important antibody specificity question, any further concerns over antibody affinity features are wasted brain-power. The second most important topic that usually comes up upon receipt of a new batch of monoclonal or affinity purified polyclonal IgG antibodies is, how strong are the antibody binding affinity values for the target antigen that is to be quantitated in your assay? That said, the binding affinity properties of any given batch of monospecific antibodies are completely dependent upon the magnitude of the negativity properties of the free energy (ΔG) component of the GFE equation. As stated earlier in this discussion paper, the spontaneity of any antibody-antigen complex formation reaction is entirely reliant on the free energy change (ΔG) for said reaction. ΔG must have a negative value! The more negative the change in the ΔG value the greater the stability of the Aby-Agn complex product. This can also be restated as saying that the more negative the ΔG value of the binding reaction, the higher the binding affinity of the antibody for its specific target antigen10,11.

Summary

Our main objective in this review article is to substantiate the fact that Aby-Agn complex formation is just another example of a spontaneous chemical reaction. Thermodynamic energy parameters such as enthalpy (H) and entropy (S), come into play when antigenic-epitopes contact antigen specific paratope structures within the antibody hypervariable regions. The greater the exothermic, negative enthalpy changes (-ΔH) arising out of interfacing contact between epitope and paratope structure, the greater the likelihood of a net negative free energy change (-ΔG) for the GFE equation. If the loss of entropy status (-ΔS) does not exceed the negative change in enthalpy (-ΔH), the free energy change (ΔG) sign will be negative and the Aby-Agn binding reaction can occur spontaneously. As the magnitude of negative change in ΔG becomes greater, so goes the tightness of binding or increase in binding affinity properties of the antibody for the antigen. Because the intimate association between antibody and antigen involves a multitude of noncovalent molecular attraction forces plus potential for increases or decreases in entropy, the ΔG potential values are seemingly endless.

References

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