Multi-scale Simulations Find Receptor-substrate Kinetics of Binding with Applications for Drug Design
Key to drug design in this context is a concept called the kinetic rate constant of binding, the speed at which a drug binds to a larger molecule. The goal in drug design is to optimize this rate of binding, that is, identify or design a drug that binds to the larger molecule at the desired rate, ensuring a tight lock. Such a lock is critical to drug efficacy. Votapka refers to this rate constant as kon. (The rate for unbinding is referred to as koff but was not part of the work described here.)
Traditionally, such rate constants have been determined experimentally. But there are at least two possible disadvantages to this approach. One is that the experiment itself can affect and distort the natural process of binding. The other is that it’s not always possible to determine the rate constant experimentally. Instead, researchers can turn to computation, which not only enables rate determination that can’t be done in some experimental situations, but may become an easier, faster, and less expensive way to obtain this information. Plus the codes developed and computational strategy can then be used by others to validate the results and adapted to similar types of investigations.
In this research, Votapka and Amaro studied the kon for four molecular systems. These four were chosen as “simple but medically relevant” systems with which they could validate their methodology before extending it to more complex systems. “One system, superoxide dismutase, scavenges toxic byproducts of cellular respiration,” says Votapka. “Another, Troponin C, is used in cardiac muscle contractions and is implicated in heart disease, so it’s a relevant therapeutic target.”
Votapka and Amaro used two long-standing computational simulation techniques: molecular dynamics (MD) and Brownian dynamics (BD). “We use MD to study the physical movements of atoms and molecules,” says Votapka. “We watch how atoms and molecules interact for a fixed period of time to view the propagation of the dynamics of the system. This method is very detailed and accurate for many situations but time-consuming and expensive computationally. BD also models macromolecular diffusion. It’s very fast, but it can be inaccurate when two molecules are in close proximity.” So, in studying the progression of the binding process, they applied BD in situations where the molecules were separated by a larger distance and MD when the two were in closer proximity or even bound together at the binding site.
The innovation of this work is that they combined MD and BD with the more recent theory of “milestoning” (Figures 1 and 2) to create concentric spheres around the receptor through which to track the molecule’s circuitous path as it approached the receptor protein. The rate constants found using this composite method agreed well with experimental and theoretical values.
In particular, Votapka and Amaro predicted the kinetic rate constant of binding of a small charged molecule toward charged and uncharged spherical receptors. They also calculated the rate constant for superoxide dismutase with its natural substrate, O2−, to validate a previous experiment using similar methods but applying several important improvements. Finally, they calculated the rate constant for a new system: the N-terminal domain of Troponin C with its natural substrate Ca2+.
How will this work advance the field? Amaro responds, “Our new methodology will be useful to predict other kinetic rate constants and understand the process of binding between a small molecule and a protein receptor in biologically or pathogenically interesting systems. It will also be useful to study system-specific binding details, such as the direction from which the substrate approaches the binding site, which is applicable to biomolecular modeling and drug discovery.
“What’s key about this new method is that it is truly multi-scale,” Amaro continues. “It combines the best of Brownian dynamics and molecular dynamics methods to gain tremendous efficiency in understanding how molecules come together to interact. Because it’s so efficient, our next step is to use the method to determine how molecules interact in larger-scale, more realistic structural environments.”
The total computational cost of all systems simulated in this study for MD and BD was approximately 65,000 CPU hours. This cost is significantly less per target than the all-atom MD simulations run in past studies to observe kinetic events [1, 2, 3]. And the fact that the milestoning results, the all-atom MD results, and the experimental values are so similar supports the validity of the milestoning methodology.
“Before computers, researchers had to do tasks manually,” says Votapka. “And those tasks were often time consuming, repetitive, and boring. But now computers can help us solve problems more accurately and much, much faster especially when, as in this work, we can parallelize the computations across multiple processors. The icing on the cake is that, once we’ve developed a program for a given task, we have in effect automated it. That provides us a whole new level of power because our productivity is continually increasing.”
- Shan et al., J Am Chem Soc 2011, 133 (24), 9181-9183.
- Shan, et al., Cell 2012, 149 (4), 860-870.
- Ogawa, Y., J, et al., Biochem-Tokyo 1985, 97 (4), 1011-1023.
- Votapka, L. W., & Amaro, R. E. (2015). Multiscale Estimation of Binding Kinetics Using Brownian Dynamics, Molecular Dynamics and Milestoning. PLoS Comput Biol, 11(10), e1004381.
Researchers: UCSD: Lane W. Votapka, Rommie E. Amaro.Figure 1. Cartoon depicting a hypothetical path taken by a substrate as it diffuses in the vicinity of its binding site in an MD simulation. As the substrate travels, it crosses a series of milestones. The “trip” ends when the substrate crosses the “binding surface,” where it is considered bound, or when it crosses the BD surface, thus exiting the MD simulation regime into the BD regime.
Figure 2. Schematic of the project’s workflow illustrating how MD and BD simulations are prepared, run, and unified using milestoning. The number of arrows in this workflow are suggestive and do not correspond to actual numbers of simulations.