The cockpit of a Boeing 777, the first airplane to be designed entirely on a computer (Image: Bing)

Werner Heisenberg was once asked what questions he thought were worth asking God. He is said to have quipped, "I would ask God two questions: "Why quantum mechanics?" and "Why turbulence?" I think he will have an answer for the former". Almost a hundred years later turbulence still remains an unsolved problem, although we have gained many insights into the general phenomenon from fields like chaos theory and computational fluid dynamics. One would think that given our still incomplete understanding of turbulence, we would have a lot of trouble designing airplanes.

Not so. Here's a fact that continues to amaze me: the Boeing 777 was the first aircraft completely designed on a computer. And that too way back in 1995. This was when computational modeling still suffered from inadequate computing power and predictive capability, and yet here was as complex a piece of machinery as you could imagine being built on a computer. And when it was built and tested, it flew into the sky and into potentially turbulent airflow, turned around and landed safely to thunderous applause and immense relief. All without crashing. No wonder the regulatory hurdles for approving airplanes are so much less stringent than ones for approving drugs.

Computational fluid dynamics can simulate the airflow around this Space Shuttle (Image: Commons)

This brings to me to an equally amazing fact: more than fifteen years after we designed an airplane on a computer, we still face enormous challenges in designing a small molecule made out of only fifty or sixty atoms that will bind to a protein with high affinity, block its function and halt the progress of the disease which it causes. Since almost all drugs work their magic by binding to and often blocking the action of rogue proteins whose normal activity has been disrupted, this goal would seem pretty important. But I am not even talking here about designing an actual drug, a substance which in addition to binding to a protein also has to contend with getting across cell membranes, reaching its target organ, staying around long enough to do its job, and then gracefully exiting the body through natural processes, all without binding to other proteins and causing side effects. No, all I am talking about is a small molecule that binds an arbitrary protein in a test tube. Fifteen years later I find it both fascinating and disconcerting that we can routinely design airplanes, bridges and skyscrapers on a computer but are still light years behind when it comes to designing even "simple" drugs. The two problems would seem to be of a similar order. Why the difference?

At first sight there indeed don't seem to be too many differences between the two processes. Proteins and drugs (which are usually called "small molecules" in the trade) are machines with many moving parts, just like airplanes. They are buffeted by surrounding water molecules in the body just like airplanes are buffeted by airflow. And just like airplanes, their parts are dependent on each other's motions. Of course, airplane design seems to depend on classical mechanics while drug design would probably need quantum mechanics, but that seems to mainly translate to a question of computational expense. If we can really conceptualize the concerted motion and concomitant functions of tens of thousands of gauges, valves, nuts and bolts, measuring instruments, flaps, wheels and innumerable pieces of metal and plastic in a Boeing 777, what stops us from similarly conceptualizing the interaction of myriad amino acids, water molecules and one small molecule in a test tube?

The answer to this question is something we are still working out, but the short answer is "biological complexity". Accurate drug design from scratch will only be possible when we can realistically simulate and understand the structure and function of both small molecules and proteins in the body. A few months ago there was an article in a drug design journal by Walter Woltosz from a company called Simulations Plus which tries to model the metabolism of drugs. Woltosz wondered why we are not as good at designing drugs as we are at designing airplanes, and I blogged about his article here. My guess is that while computational drug design is certainly going to get better, I am not holding my breath before it has the predictive power of airplane design. What exactly makes the difference?

Think again about that confounding turbulence that seems to thwart airplane design. The basic equations governing the motion of fluids around a rigid body are the Navier-Stokes equations. These equations have been known for years, and many clever approximations have been used to solve them. The actual solution of these equations for turbulent airflow can get hideous, but notice that it may at least be possible to write down the equations for the airflow surrounding an airplane. Now contrast this with even a single small molecule trying to bind a protein bathed by a sea of solvent water. That last variable is enormously important and we will come back to it later; the fact is that even now, water remains a hugely enigmatic substance in terms of modeling its exact behavior. But even if we were to do this, what fundamental equation would describe this protein-small molecule-water system? Ultimately it seems like Schrodinger's equation which governs the behavior of all microscopic entities might do the trick. But firstly, try writing out this equation for the almost unimaginable large number of atoms in a test tube.

More importantly though, what ultimately governs the behavior of a drug binding is a quantity called "free energy" a thermodynamic variable that's ubiquitous in dictating the tendency to reach equilibrium of every physical process that we know. Free energy is in principle computable from quantum mechanics and statistical mechanics, but at the level of binding it's really a hybrid microscopic-macroscopic variable which is more dependent on relatively large scale events like the motion of amino acid side-chains and the average viscosity of solvent combined with all the microscopic forces and bonds that attach the small molecule to the protein. In addition the level of accuracy with which free energy governs protein-small molecule binding is exquisite; a difference of just 1 kilocalories per mole (for reference, a normal carbon-carbon bond is about 80 kilocalories per more) arising from any number of small changes in the system can reduce or improve the binding of a drug to a protein by 90% or more. We are simply not good enough to capture these kinds of tiny changes. But a fundamental difference between airplane and drug design emerges from this understanding; in case of an airplane you can separately simulate a wing, latch it on to the rest of the machine and not notice too much difference in the end product. In case of a protein and small molecule the different parts are far more dependent on each other, and perturbing one can sometimes greatly perturb other. You cannot detach a single amino acid from a protein, simulate its behavior and expect it to function the same way inside the protein. This means that you have perform the simulation on many different levels for a real understanding.

The complexity of a molecular system is illustrated by this simulation of a membrane protein embedded in a lipid membrane and surrounded by water molecules and ions (Image: Bert de Groot)

The bottom line is that quantum mechanical attempts to model the interaction of molecules with proteins have not worked out for all but the smallest systems. In fact more empirical, parameterized computational approaches have worked out better in many cases. But these approaches necessarily involve approximations which make them oblivious to some of the finer details of the process. In addition there's the ubiquitous tradeoff between computational expense and expertise which always makes simulating these systems something of a compromise. The deeper point though is something that I have talked about before, the limits of reductionism and the manifestation of emergent properties. Protein-molecule binding is of course an atomic-level event, but the details of the binding process depend on many "higher-level" phenomena. These include the motions of large loops of proteins, the inflow and egress of water molecules in the exact binding site as well as the average interaction of water around the protein and the flexible interconversion of the organic molecule between several conformations. Each of these interactions is difficult to model at an atomic level, and we still don't understand how the interactions add up, although we do believe that their whole is not the sum of the parts. In addition there's an elephant in the room which has almost always been neglected when modeling these interactions: entropy. The free energy that we mentioned before is a combination of two variables, enthalpy and entropy. Enthalpy refers to the direct energy of interaction between different atoms, and this is a quantity that at least in principle can be calculated. Entropy is a fuzzier and more subtle concept and can come from events like the displacement of water molecules in the protein by the small molecule leading to their greater disorder, and the constraining of protein motions when the small molecule binds. Unlike enthalpy entropy can be a more global variable with effects spread across the entire system, and we don't as of yet have a robust general way of calculating this key quantity.

And then there's water. On one level we should be ashamed that we still don't understand a substance which is absolutely essential for life as we know it. The problem is that water is a very special substance, with its own peculiar hydrogen bonding network that allows it to anomalously expand when cooled, its unusual heat capacity which allows it to absorb large amounts of heat without heating up and many other properties like its polarity and the generous spaces between its constituent molecules which enable it to dissolve a wide variety of organic and inorganic matter. All these life-sustaining properties are special compared to similar properties of many other solvents. Compared to this the air around an airplane is downright well behaved. It's quite clear that unless we are able to simulate these special properties of water we will not be able to design drugs the way we design airplanes. The rather alarming fact is that many simulations of protein-drug systems even now don't even represent water as a discrete substance. Instead they implicitly simulate water as a "continuum solvent" which basically means that they surround the system with an electrostatic field which reproduces the known properties of water. While this greatly cuts down on the computational cost, it means that we are blinded to the behavior of specific water molecules which may play targeted roles in mediating the binding of the drug to the protein. The airplane analog of specific water molecules would be pockets of air which suddenly appear and disappear inside the airplane's electronics and mechanical parts and significantly influence its movements.

The fact of the matter is that all the strenuous efforts we have put into simulating the behavior of proteins and small molecules have not resulted in a real system. They have resulted in a model. A biochemical model just like other models depends on the exact kind of data used for parametrization, the various approximations and fudge factors included to match experiment and the personal preferences of the modelers. In one sense it's fiction. And the real problem may not even be the model, it may be the lack of accuracy in the data itself. There are many kinds of data which would be potentially useful in drug design which we still don't have a good handle on. For instance it's still hard to accurately measure that entropy which we were talking about. It's hard to find out which water molecules are essential inside the binding site and which ones are around for the ride. For crying out loud, it's challenging to get small error bars (and by small I mean less than 100%) even in simple assays which test the potency of drugs in cells. Finally, what we see in experiments are necessarily average effects, and the data don't provide information on the kinds of rare events which can significantly impact the end product of the experiment. Contrast this with airplane design where we are able to rather accurately get data on the behavior of individual parts and feed this into the model. And of course we don't have to worry about probing the insides of living organisms where our experimental manipulations themselves might perturb the system into an unnatural state.

Until now I haven't even really talked about designing drugs which takes the problem to a whole different level. The flight analog of a small molecule which is finally put into the body as a potential drug would be an airplane that is constantly rearranging and maybe even completely replacing parts. This would be a counterpart to the metabolism that the body imposes on a drug which modifies it and breaks it up. Next time, try stabilizing an airplane whose parts are constantly getting modified even as you are struggling to calm the passengers.

In spite of the gloomy outlook and the superlative challenges, the good news is that we have come a long way. Some techniques like molecular dynamics which simulate a molecular system entirely using Newton's classical laws of motion can give remarkably useful answers. Continuum solvation often works. Software and hardware developments have enormously contributed to our facility with such techniques. In addition, partial black box approaches which rely on a combination of "physics-based" first-principles calculations and "knowledge-based" parameterizations seem to be working well in many areas. We are slowly getting there, but the inconvenient fact is that we need to first understand and then simulate far too many more details than we are right now to get anywhere close to the accuracy of airplane design.

Contemplate this fact the next time you are on a Boeing 777 and reach for that blood pressure-lowering pill.