By Wesley Errington
How do the trillions of cells that make up our bodies maintain the complicated orchestration required for us to stay healthy? What causes this finely-tuned cell orchestra to break down? And if breakdown occurs, how do we create effective treatments for the resulting diseases?
We can answer these questions by studying the programming code that instructs cell behavior. Whether directing a stem cell to grow and divide or activating an immune cell to fight an infection, the software that operates our cells is written entirely in the ways with which molecules bind to one another.
All molecules that are present in our cells or that send messages between them (such as DNA, proteins, and growth hormones) exist in a state of dynamic interaction. In order for a cellular program to run properly, specific molecules must identify their correct partners and bind to them at the right moment, in the right location, and for the necessary amount of time. Diseases can ensue when this process breaks down, requiring therapeutics that can bind and correct the molecular mistake.
We have recently developed a mathematical framework and computer model that simulates the key parameters that control an elegant type of molecular binding, referred to as multivalency [1].
At its simplest, a molecule (referred to here as the ligand \(L\)) binds to its partner (the receptor \(R\)) to form a ligand-receptor complex \(LR\). In this most basic case, the ligand and receptor bind through just a single binding site. This mode of binding is called monovalent, and can be described by the equilibrium expression
\[ L + R ⇌ LR. \]
Figure 1. A few of the 78 unique, structural configurations that a molecular interaction can sample when both the ligand (yellow) and receptor (blue) have three binding sites (i.e., they are trivalent) tethered through linkers. More configurations arise as more binding sites are added. These configurations become more accessible with increasing linker flexibility. Image courtesy of Errington et al., University of Minnesota.
The
forward direction represents the kinetic rate of association between \(L\) and \(R\), and the
reverse direction represents the kinetic rate of the \(LR\)
complex’s dissociation in this reversible interaction.
Through "copy and paste" duplications and other cellular processes, ligands and receptors can accumulate multiple binding sites along their lengths, and use these sites to interact with each other. This molecular elaboration is known as multivalency. While a monovalent interaction can only occur in a single way and therefore adopt just one configuration, multivalent interactions can exist in a multitude of configurations, the number of which increases factorially with growing amounts of binding sites (i.e., the valency). For example, when a ligand and receptor each have three binding sites (i.e., they are trivalent), the \(LR\) complex can exist in 78 unique configurations. Figure 1 diagrams a small subset of these.
The immense utility of the multivalent mode of binding is its ability to achieve binding affinities and selectivities that are not possible with monovalent counterparts, due to the fact that multivalent molecules can dynamically sample this plethora of available configurations (rather than being limited to just one). However, the way in which the sampling of these states specifies multivalent binding dynamics has previously been difficult to model.
Our mathematical framework and computer simulation represent each multivalent configuration as a node in a network, and the connections between those nodes as the structural rearrangements that enable two configurations to interconvert. The following animation depicts the dynamic sampling of the full configuration network for a trivalent ligand-receptor interaction.
A mathematical framework modeling multivalent interactions as a network of configurations. This animation diagrams a network for a trivalent ligand-receptor interaction. Each of the 78 binding configurations are represented as a node. Connections between nodes signify structural transitions between configurations. The model demonstrates that a multivalent interaction is entirely determined by the network’s size (number of nodes), each configuration’s population (color of the nodes), and the rate of interconversion between configurations. The animation shows how the 78 states are dynamically populated when a trivalent ligand and receptor first encounter each other.
Through modeling and experimentation, we demonstrate that a ligand’s ability to selectively bind to a receptor is determined by three properties of the network:
- The number of configurations in the network, which is a function of the molecule valency
- The favorability of each of these configurations, which is a function of the molecular structure
- The rates of interconversion among these configurations, which is a function of the molecule kinetics.
Our network model of multivalent binding enables researchers to apply these three network properties as a set of tunable dials that can be used to fully program the type, strength, and duration of any multivalent molecular interaction. In doing so, our computational resource aims to assist scientists in deciphering the molecular code of cellular programming and speed the development of new possible therapeutics.
This work was published in the December 17 issue of the Proceedings of the National Academy of Sciences by a team at the University of Minnesota and at the Budapest University of Technology and Economics. To read the full research paper, entitled “Mechanisms of noncanonical binding dynamics in multivalent protein-protein interactions,” visit the PNAS website.
Acknowledgments: The work was supported by the National Institute of General Medical Sciences, the National Institute of Biomedical Imaging and Bioengineering, a shared instrument grant from the Office of Research Infrastructure Programs at the National Institutes of Health, and the Higher Education Excellence Program of the Ministry of Human Capacities in Biotechnology at the Budapest University of Technology and Economics.
References
[1] Errington, W.J., Bruncsics, B., & Sarkar, C.A. (2019). Mechanisms of noncanonical binding dynamics in multivalent protein-protein interactions. Proc. Natl. Acad. Sci. USA, 116(51), 25659-25667.
Wesley Errington is a postdoctoral researcher in the Department of Biomedical Engineering at the University of Minnesota. He specializes in understanding biological complexity through the study of molecular structure and dynamics.