00:00:00 For Jeff Blaney, there's a rumor that your version of the distance geometry code will

00:00:07 be released by Quantum Chemistry Program Exchange.

00:00:10 Is there a deadline or a date?

00:00:13 Yeah, as a matter of fact, there is.

00:00:16 We will have that submitted to QCP sometime within the next couple of weeks,

00:00:21 which is longer than we'd expected, but things often take longer than you'd expect.

00:00:26 So it will be available.

00:00:29 That was a good question, Al.

00:00:32 These are the real questions that people want to know.

00:00:34 How can I get the code and how do I run it?

00:00:37 I wanted to ask a follow-up on the distance geometry approach in general,

00:00:41 and that is that its strength is also, in some sense, its weakness.

00:00:46 It's unbiased in terms of the areas of conformational space that it explores,

00:00:52 but that also means that you're spending computation in unproductive areas of

00:00:57 conformational space that you know, through other information, might not be reasonable.

00:01:03 Do you have a way around that problem?

00:01:07 Well, I don't think you really do spend much time in conformational space that's unreasonable.

00:01:11 It depends entirely on how much information you know about the problem in advance.

00:01:16 Any information you know you can provide in the form of distance constraints.

00:01:20 It could be NOE distances in the pharmacophore modeling,

00:01:23 constraints that would overlap atoms on top of each other.

00:01:26 In the latter case, you clearly don't spend time generating conformers that can't possibly overlap.

00:01:31 You generate solutions directly.

00:01:33 In straight conformational analysis,

00:01:36 where you might use distance geometry to generate purely random conformations,

00:01:40 then clearly we may be wasting time generating structures that are high energy

00:01:45 or degenerate by symmetry, for example, in the case of highly symmetric ring structures.

00:01:52 I want to interrupt just a second.

00:01:54 Callers, when you call us, please do not hang up.

00:01:57 Stay on the line. We're not going to hang up on you.

00:02:00 We will tell you if we can't take your question.

00:02:03 But please don't hang up. I'm sorry. Please continue.

00:02:07 I guess as a practicing medicinal chemist, I can ask you this question.

00:02:11 Which methods do you use most in terms of trying to answer a scientific question

00:02:19 that relates to a product or some goal outside of your fundamental research?

00:02:26 My interests are both in lead generation,

00:02:29 trying to come up with brand new structures that we think would be active

00:02:33 and worth synthesizing, and also in optimizing leads.

00:02:36 The two problems are somewhat different.

00:02:39 In the latter case of optimizing a lead, I think it's a less ambitious problem,

00:02:44 therefore it's quite a bit easier.

00:02:46 So we tend to use a mixture of the more traditional QSAR methods,

00:02:50 regression analysis-based methods, and also modeling approaches,

00:02:55 the ensemble distance geometry, pharmacophore modeling.

00:02:58 Occasionally we will use dynamics, particularly if we're looking at peptides.

00:03:03 We've done a lot of work in the last few years on trying to come up with organic mimics of peptides,

00:03:08 and we found dynamics very useful for that.

00:03:11 Jeff, on line 5 we have Lakshmi. What is your question, please?

00:03:15 Hello. Dr. Blaney, could you expand on how you go from your initial matrix of distance bounds

00:03:25 when you randomly select discrete distances and then put them together to make a molecule.

00:03:32 Now, how can you prevent structures that are chemically infeasible being arrived at?

00:03:41 In that distance bounds matrix, there are constraints that force reasonable stereochemistry.

00:03:47 So for all the bond lengths and the bond angles, they are constrained exactly to,

00:03:52 in the case of the program we use, their input value from the coordinate file we give the program.

00:03:57 But these are just standard bond lengths and bond angles.

00:04:00 And we allow the torsion angles to be freely rotating,

00:04:03 with the exception of double bonds or amides or aromatic systems.

00:04:07 In the course of generating the structures, these obviously different random combinations of distances

00:04:13 aren't all going to produce a realizable three-dimensional structure.

00:04:19 Most of the CPU time actually spent in distance geometry is in the very last stage

00:04:23 where we refine a projection of the distances into Cartesian coordinate space

00:04:29 against our initial distance bounds so that we in fact guarantee that we have a structure

00:04:33 that satisfies the original covalent constraints.

00:04:42 I spoke with the two previous speakers about the types of computation that they do

00:04:47 and whether it's vectorizable or parallelizable in one way or another.

00:04:53 Have you looked into that for distance geometry calculations?

00:04:57 We have to some extent.

00:04:59 At DuPont we run it on a Cray and on that machine it's vectorized and it vectorizes quite nicely.

00:05:07 I know that Scott Dixon at SmithKline has put quite a bit of effort into making it run parallel

00:05:12 on a four-processor machine.

00:05:17 It's not clear to me that it's worth a lot of effort to make it run in parallel

00:05:20 and that typically when we run distance geometry we're generating multiple structures or multiple conformers.

00:05:25 And so it tends to be most efficient to simply divide the problem by the number of processors we have.

00:05:31 If we were going to generate 100 random conformers and we have 10 processors,

00:05:35 we'd run 10 structures per processor.

00:05:38 It's much easier than parallelizing the code.

00:05:41 On a vector machine we can get speedups of on the order of 25, maybe 30 times the speed of a VAX 8800.

00:05:49 This is on a Cray XMP.

00:05:52 In fact, it's very easy to parallelize your approach to distance geometry.

00:06:04 From the point of view of a user, we always have the question of do we use academic code,

00:06:12 the latest that's come out of Peter Coleman's lab or wherever,

00:06:18 do we use commercial code that's supported but maybe doesn't have the latest hooks?

00:06:25 Could I jump in right here?

00:06:28 We have so many callers lined up for Jeff and I want to make sure that we take this.

00:06:32 Perhaps Jeff could address that at the panel discussion or at the end of this discussion.

00:06:35 Steve is on line 6. Steve, would you go ahead, please?

00:06:39 Hello, Jeff?

00:06:41 Yes.

00:06:42 I'm here.

00:06:43 We are here. Please talk, Steve.

00:06:44 Okay.

00:06:45 I was curious.

00:06:46 You talked about screening large databases and the length of time it would take.

00:06:50 Have you tried prescreening by other methods such as using similarity searching

00:06:54 and then seeing how well that works as a prescreen method for molecules

00:07:00 then going to distance geometry fitting programs?

00:07:04 Yes, in fact, we have.

00:07:07 That's unfortunately the subject of probably a whole other talk,

00:07:10 but something we just completed at DuPont in the last few weeks

00:07:14 is using a similarity searching approach followed by cluster analysis

00:07:18 to actually take our database of several hundred thousand structures

00:07:22 and cluster them into structurally related families.

00:07:25 This is done at just a two-dimensional level of the structure, the chemical graph,

00:07:30 but the idea behind that is that that way we can choose one or more representatives from each cluster

00:07:35 for a three-dimensional search or a docking program, what have you,

00:07:39 but it's clearly not practical at this point to test one molecule at a time

00:07:43 by any of these computational approaches out of such a huge database.

00:07:47 Conrad on Line 5, what is your question for Jeff?

00:07:50 Yes, this is Conrad from Chicago.

00:07:53 I wanted to ask, for the 3D database searching problem,

00:07:58 what do you see as the best long-term solution,

00:08:01 either generations of conformations on the fly using some distance geometry technique

00:08:06 or storing conformations, perhaps selecting representative conformations using cluster analysis?

00:08:18 That's a tough one.

00:08:20 My bias would be to try and generate them on the fly,

00:08:25 given that with a few distance constraints I think we can answer fairly quickly

00:08:29 whether a structure is likely to match a given site, a pharmacophore model or a binding site.

00:08:34 We actually haven't proved that that can work, though, on a large scale.

00:08:37 The methods that are available right now fall so far just in the class of storing

00:08:42 a predefined three-dimensional structure for each molecule in your database,

00:08:46 perhaps by using CONCORD or perhaps by using a new program called COBRA.

00:08:51 In each case, though, they'll require that you're searching a database of predefined conformers.

00:08:56 I need to step in here and thank you very much for your segment.

00:09:00 We'll take any other questions you might have for Jeff during the panel discussion.

00:09:04 When we return from this break, we'll hear once again from Dr. Peter Coleman,

00:09:08 and then for the first time, we'll hear from Dr. David Case.

00:09:12 During this break, we'll show promotional spots from our sponsors.

00:09:16 We want to give a special thanks to the San Diego Supercomputer Center,

00:09:20 Digital Equipment Corporation, San Diego State University,

00:09:24 as well as the American Chemical Society for their support of this program.

00:09:28 We'll see you again in 20 minutes.

00:09:31 This program was made possible by support from Digital Equipment Corporation.

00:09:37 Additional support was provided by Tripos Associates.

00:09:43 Question.

00:09:45 What computer company has the largest number of software applications for chemists?

00:09:50 Answer.

00:09:52 Digital Equipment Corporation.

00:09:55 Question.

00:09:57 What company is the leader in providing integrated solutions for research scientists?

00:10:02 Answer.

00:10:04 Digital Equipment Corporation.

00:10:06 Question.

00:10:08 What company recently added vector processing to their family of computer systems?

00:10:13 Answer.

00:10:15 Digital Equipment Corporation.

00:10:18 Still, things are not so black and white in today's world of computational chemistry,

00:10:24 and digital knows that.

00:10:26 For years, we've been working closely with scientists,

00:10:29 helping them search for the unknown and make new discoveries.

00:10:33 In fact, the first VAC system ever sold was purchased

00:10:36 to perform advanced computational chemistry applications.

00:10:40 And digital is collaborating with the Quantum Chemistry Program Exchange,

00:10:44 as well as with other software suppliers that provide chemistry-related software.

00:10:49 Presently, digital is working with Dr. Peter Coleman and associates

00:10:52 at the University of California, San Francisco,

00:10:55 to optimize AMBER for the VAX 9000 and VAX 6000 computers with vector processing options.

00:11:01 The university will make this version available to the scientific community.

00:11:05 The VAX 9000 systems with vectors deliver supercomputer performance,

00:11:10 and like other VAXs, the VAX 9000 is fully compatible

00:11:13 with our entire family of VAX computers and workstations.

00:11:17 All offer a choice of either digital's VMS or Ultrex operating systems.

00:11:22 Our risk-based deck system family of high-performance workstations and systems running Ultrex

00:11:27 demonstrates our continuing commitment to open systems.

00:11:31 And there is more to come.

00:11:34 We know how important visualization technologies are to molecular biology.

00:11:38 Digital VAX and RISC workstations, along with leading public and commercial visualization software,

00:11:44 provide a broad set of scientific visualization tools.

00:11:48 Our commitment in this area is strong and active.

00:11:52 For presentation of research results, digital's compound document architecture

00:11:56 integrates text and graphics, even from different systems, into scientific documents.

00:12:02 Scientific collaboration and communication depend on network technology,

00:12:06 which links the research community locally and worldwide.

00:12:11 Digital is the leader in supporting network standards and in providing advanced network technology.

00:12:17 Digital products are designed for use in a distributed environment,

00:12:21 with systems from other vendors connecting resources, including supercomputers.

00:12:26 From the lab bench to the supercomputer, from your desk to information sources worldwide,

00:12:32 digital has the integrated computing solutions for your research environment.

00:12:37 Digital Equipment Corporation. Make that discovery.

00:13:07 The San Diego Supercomputer Center, located on the campus of the University of California at San Diego,

00:13:31 is a co-sponsor of this conference.

00:13:35 The Center, or SDSC, was established in 1985 with funding from the National Science Foundation

00:13:43 and the State of California to assist academic and industrial researchers across the nation.

00:13:50 SDSC has focused on providing supercomputing capability

00:13:55 and accompanying user services to widely distributed researchers.

00:14:00 Over 3,000 users at 170 institutions access the Center by both satellite and terrestrial links.

00:14:10 The heart of the computing facilities at the Center is the Cray YMP864,

00:14:16 the most powerful general-purpose computer available at this time.

00:14:21 The Cray XMP48 is also used by researchers.

00:14:25 Both are supported by a wide variety of peripheral equipment.

00:14:30 Computer visualization tools are very important for understanding the science of a complex macromolecular system.

00:14:38 The facilities here at the San Diego Center enable researchers to generate and store thousands of images

00:14:45 and to make animated movies or videotapes.

00:14:52 Hello, and welcome to the San Diego Supercomputer Center.

00:14:57 Biochemists and molecular biologists have made extensive use of our supercomputer facility.

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00:15:10 As the technical advisors for this teleconference,

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00:15:20 Together with you, today they will work to push ahead the frontiers of computational biochemistry.

00:15:27 I know that you'll feel the same excitement that I feel after seeing the results that are now achievable.

00:15:40 Hello, I'm John Crum, a chemist and one of your colleagues.

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00:15:48 You and I already know the future of society in general is very closely tied

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00:29:33 Welcome back to Molecular Modeling for Biological Systems.

00:29:37 Dr. Peter Coleman is with us again to talk about current simulations using molecular dynamics

00:29:43 and free energy perturbation applications to study large molecules.

00:29:49 The free energy techniques that Peter will now discuss have generated a lot of interest lately,

00:29:53 not the least of which is from the supercomputer vendors.

00:29:57 As Peter himself likes to point out, free energy is actually pretty expensive.

00:30:01 Moreover, the calculations produce just a single number or just a few numbers

00:30:07 as opposed to the lengthy trajectories that have to be analyzed from normal dynamics runs.

00:30:13 This allows even more computations to be run.

00:30:17 Peter, is it worth it?

00:30:21 Thanks, Art.

00:30:23 Well, we'll let the audience decide whether these calculations are really worth it,

00:30:27 but I would point out to the audience that perhaps today's Cray is tomorrow's Macintosh on everyone's desk,

00:30:35 so hopefully what we'll see in the next few years is the capability to do such calculations on every bench chemist's desk.

00:30:43 The other point I want to make in response to your comment, Art,

00:30:47 is that whether there is one number or five numbers or millions of numbers that come out of the calculations,

00:30:54 if they give someone an insight into the problem, then it's worth it,

00:30:59 and if they don't, no matter how many numbers you get out, it's not.

00:31:03 So what I hope is that the calculations I will present today will give you some idea of whether or not one can get insight from these calculations.

00:31:13 In this presentation, I will highlight some recent molecular modeling efforts in my own research group.

00:31:19 The focus of our research efforts continues to be to develop and apply methods that can simulate the structures

00:31:25 and free energies of covalent and non-covalent associations of complex molecules.

00:31:31 These studies use mainly molecular mechanics, dynamics, and quantum mechanics,

00:31:35 but selected applications have used distance geometry and graphical representations of results,

00:31:40 are an essential feature of macromolecular simulations.

00:31:44 The three classes of molecules that have been the major players in our research have been proteins, nucleic acids, and ionophores,

00:31:51 although model studies on smaller molecules are often critical to develop approaches for these three classes of complex molecules.

00:31:58 In this talk, I will focus mainly on applications whose goal it is to calculate the free energies for a process.

00:32:05 Slide one summarizes the subject I will cover today.

00:32:09 One, solvation.

00:32:11 And there's a reference to the Bash et al. 1987 science paper.

00:32:15 There's a complete bibliography that is available for the papers I will mention.

00:32:21 The second area of applications are protein inhibitor binding, which include applications to thermolysin and ribonuclease T1 inhibitors.

00:32:32 Thirdly, I will describe combined applications of quantum and molecular mechanical approaches to study enzyme catalysis and tautomer stability.

00:32:41 Fourth, I will describe sequence-dependent macromolecular stability.

00:32:47 Fifth, studies of potential of mean force or absolute free energies of association.

00:32:53 And finally, a brief word on the development of non-additive potential functions.

00:33:00 In the second slide, we summarize the basic ideas behind the methods to calculate free energy differences between related systems.

00:33:09 The derivation is simple, but the implementation complicated.

00:33:13 One can write an expression for the Helmholtz free energy in terms of a classical partition function, as shown on the slide.

00:33:20 But since this involves an integration over all degrees of freedom, this absolute free energy is difficult to evaluate for any complex system.

00:33:28 However, if a free energy difference is required, the problem becomes more tractable, as shown by Singh et al., 1987, and in this slide.

00:33:37 The bottom line is that the method requires a molecular mechanics potential function for the two systems for which the free energy difference is being calculated.

00:33:47 And one must generate an ensemble average of the two systems, as well as hybrid systems, partway between the two real systems.

00:33:54 Either Monte Carlo or molecular dynamics methods can be used to generate this ensemble average.

00:34:01 The relative free energies of aqueous solvation were among the first properties studied by free energy calculations,

00:34:08 featuring studies of the absolute free energy of noble gases in water, Postma et al., 1982,

00:34:14 and the relative solvation free energy of methanol and ethane, Rabi-Mohan and Jorgensen, 1985.

00:34:21 Bash et al. showed that one could study solvation properties of a variety of molecules, and slide 3 summarizes the study.

00:34:29 For instance, you can calculate the free energy of solvation of amino acids in excellent agreement with experiment.

00:34:37 Previous to that, only a few model calculations using the free energy perturbation method had been done.

00:34:44 There was a dramatic difference between the ability to calculate free energies and enthalpies of solvation,

00:34:50 and the calculations on many systems required many hours of Cray XMP time,

00:34:57 which was critical not only to the development of the methodology, but also in the application.

00:35:03 The next slide has the conceptual basis for using the free energy calculation approaches

00:35:10 to study non-covalent association between two related inhibitors of a given macromolecule.

00:35:16 On the slide, you can see that what is shown is the interaction between a protein and inhibitor 1,

00:35:23 and a protein and inhibitor 2, and the two horizontal arrows correspond to the experimentally derivable quantities.

00:35:33 The two vertical processes correspond to those that you can do in the computer, and they are ΔG2 and ΔG1.

00:35:43 ΔG1 corresponds to mutating one inhibitor into the other in solution,

00:35:49 and ΔG2 corresponds to mutating one inhibitor into the other in the enzyme active site.

00:35:56 The difference in the calculated free energy should be equal to the difference in the experimentally measured one.

00:36:03 In the next slide, we show a representation of the protein ligand system to which we first applied the free energy method,

00:36:10 a thermolysin phosphoramidate inhibitor.

00:36:13 The green and red parts are allowed to move during the molecular dynamic simulation.

00:36:17 The blue parts are frozen at the X-ray crystal structure.

00:36:21 In the following slide, a close-up of the active site is presented,

00:36:25 in which both phosphoramidate, NH, and phosphonate ester, oxygen, inhibitors are shown interacting with the protein.

00:36:34 This view, taken from crystal structure determined by Brian Matthews of Oregon,

00:36:38 shows how these inhibitors bind nearly identically in the enzyme active site.

00:36:44 When we began these simulations, we also knew that the NH inhibitor bound 10 to the third more strongly to the enzyme,

00:36:50 corresponding to a change in binding free energy, ΔΔG sub-bind, of approximately 4 kilocalories per mole.

00:36:58 In the next slide, we summarize our findings.

00:37:01 In 1987, our calculations did reproduce this ΔΔG binding,

00:37:06 but suggested an interpretation of the results, which would make it very interesting to study the phosphinic acid,

00:37:12 CH2 analog, of the other two inhibitors.

00:37:16 So we set up a joint study with Paul Bartlett of Berkeley,

00:37:19 in which we would do the calculations on this inhibitor,

00:37:22 and B. Morgan and he would make the molecule to determine its free energy of binding experimentally.

00:37:29 This was an important test of the free energy approach,

00:37:32 because it would be a prediction with no knowledge of experiment during the calculation.

00:37:37 The results of the calculation were quite surprising,

00:37:39 in that the CH2 inhibitor was calculated to bind nearly as tightly as the NH.

00:37:44 Despite the H bond, the NH group apparently forms with the carbonyl of alanine-113 in the enzyme active site.

00:37:52 The ΔΔG was subsequently determined by Morgan and Bartlett,

00:37:55 and confirmed the calculations nearly quantitatively.

00:37:59 I must stress that this level of agreement is probably fortuitous,

00:38:02 and determining the free energy within one kilocalorie per mole could be classified as success.

00:38:07 Matthew's group also confirmed the similar mode of binding of the CH2 molecule to the enzyme.

00:38:13 The theoretical studies were carried out by Bash, Brown, and Singh, NH versus O,

00:38:17 and Kenny Murs, now of Penn State, on the CH2 analog.

00:38:22 One of the questions asked of free energy calculations is,

00:38:25 how large of a mutation can be studied reasonably?

00:38:28 The bottom line is that one must be able to generate a representative ensemble for the systems,

00:38:33 at both ends of the mutation and in the middle.

00:38:36 The thermolysin system was chosen first,

00:38:39 because it was about the simplest mutation one could imagine,

00:38:42 yet had a substantial ΔΔG.

00:38:46 Recently, Suiti Hirono of my research group has calculated the ΔΔG

00:38:50 for 2'-GMP versus 2'-ANP inhibitors of ribonuclease T1,

00:38:56 and also found good agreement with experiment,

00:38:59 with both calculations and experiment leading to a value of about 3 kilocalories per mole.

00:39:05 But the calculations suggest that this value comes about

00:39:09 from a difference in 10 kilocalories per mole in the binding interactions in the enzyme site,

00:39:14 and a compensating 7 kilocalories per mole difference in solvation,

00:39:19 the latter of which is like the value calculated by Bash et al. for the bases themselves.

00:39:24 These results are summarized in the next slide.

00:39:27 As we can see on the right-hand side of the slide,

00:39:30 the calculated 2.76 ± 0.67 experimental 3.07.

00:39:37 The 10 kilocalories per mole difference in binding can be understood

00:39:41 by comparing schematic representations of the interactions in the active sites in the next two slides.

00:39:47 For the 2'-R ribonuclease T1 complex,

00:39:51 the inhibitor forms the 7 H-bonds to the base observed crystallographically.

00:39:56 If you look at the base there, you can see there are 7 hydrogen bonds to its groups.

00:40:01 The next slide shows a representation of a 2'-ANP in the site,

00:40:07 and we predict that there will be only 3 H-bonds to the base in the corresponding complex with 2'-ANP.

00:40:15 The other encouraging feature about the calculations is in the structures generated.

00:40:20 As one mutates the 2'-GMP into the 2'-ANP, the structure changes.

00:40:26 But then, as one mutates the 2'-ANP back into the 2'-GMP,

00:40:31 the structure's changes should, in principle, reverse themselves.

00:40:35 Although this does not happen completely, there is significant structural reversibility in the calculations,

00:40:41 something that provides an important validation for them.

00:40:45 Does one conclude that the free energy approach can be applied to changes in a substantial number of atoms?

00:40:50 The key point is that guanine and adenine are the same shape.

00:40:54 It would be much more difficult to carry out mutations on groups that change shape substantially in the interior of a macromolecule.

00:41:01 The importance of solvation effects has been clear from the results presented in the first two sections of this talk.

00:41:08 In particular, results suggest that completely hydrophobic and nonspecific binding sites

00:41:15 would bind adenine nucleotides about 7 kcal more tightly than guanine nucleotides.

00:41:20 Thus, it is a much greater challenge to design active sites specific for guanine or cytosine than adenine or thymine.

00:41:28 We now move to the next section, in which we illustrate the combined use of quantum and molecular mechanical dynamical methods

00:41:34 to study enzyme catalysis and base tautomerase.

00:41:38 In the next slide, we show a thermodynamic cycle, which is a modified and elaborated version of the one shown earlier.

00:41:45 First, this slide illustrates mutation of the enzyme, E to E' rather than the ligand.

00:41:51 And secondly, an additional cycle is added to represent the process of going from the non-covalent enzyme substrate complex, ES,

00:41:58 to the transition state, ETS, for a reaction.

00:42:02 Quantum mechanical methods must be employed to create models for this transition state,

00:42:07 and these have been incorporated into the molecular mechanics dynamic studies by making this transition state a local minimum in the energy surface.

00:42:15 Rao et al. have used this approach to study the mutation of acin-155 to alanine in sutilicin,

00:42:22 in which we did not know the ΔΔG values prior to the simulation.

00:42:27 The calculated values for both relative binding and catalysis are compared with experiments by Jim Wells of Genentech in the next slide,

00:42:34 and the agreement is satisfactory.

00:42:36 Huang and Warshall found similar results in independent simulations.

00:42:40 Our calculations were not only able to reproduce experiment reasonably,

00:42:44 but led to structural insights illustrated in the next slide.

00:42:48 Does threonine-220 stabilize the oxyanion oxygen in the transition state, or just function as an anchor for acin-155?

00:42:56 The results of this analysis has led to a joint ongoing study involving Scott Braxton and Jim Wells of Genentech,

00:43:01 and David Spellmeyer, Naoki Mizushima, and myself of UCSF.

00:43:07 A second application of combined quantum and molecular mechanical dynamical approaches has been the study of base tautomerism in the gas phase and solution.

00:43:16 The next slide has drawings of the three tautomeric equilibria Chaplock et al. have studied.

00:43:22 To determine the intrinsic difference in free energy of these tautomers require accurate quantum mechanical studies at the ab initio level.

00:43:28 To these energies, one must use the free energy approach to calculate the relative solvation free energies of these molecules.

00:43:35 The comparison between calculated and experimental values both in the gas phase and solution suggests very good agreement in both phases,

00:43:44 and validates the application of state-of-the-art quantum and molecular dynamical free energy approaches to chemical equilibria.

00:43:52 If we could have the next slide, please.

00:43:55 You can see on the left, the values on the left are the gas phase energies with the values in parentheses, experimental values,

00:44:04 and on the right are the free energies in solution with the experimental values in parentheses.

00:44:10 Again, the agreement is really excellent.

00:44:12 Jorgensen has carried out related studies also with excellent results.

00:44:17 Another interesting implication of our studies is that the active site of the enzymes which synthesize DNA must not be gas phase-like

00:44:25 in order not to have too many errors in base replication caused by the wrong tautomeric form of the bases.

00:44:32 The next section of our talk deals with free energy approaches to study sequence-dependent stabilities of proteins and nucleic acids.

00:44:39 In the area of proteins, one can set up a thermodynamic cycle illustrated in the next slide.

00:44:45 Experimentally, one studies the relative stability of a protein, delta G1, and its site-specific mutant, delta G2.

00:44:51 The theoretical studies focus on mutating the protein in its native conformation, delta G3, and its denatured conformation, delta G4.

00:44:59 The key question is, what should one use for the denatured conformation?

00:45:03 In the study of Dang et al. on the threonine-157 devalium mutation in T4 lysozyme,

00:45:08 they used a blocked tripeptide containing the sequence of residues 156 to 158 as a model for the denatured protein.

00:45:16 The results of this study are summarized in the next slide.

00:45:20 The agreement with the experimental delta G is good, and more recent studies using another model for the mobile residues confirm this agreement.

00:45:30 Interestingly, the differential stability of threonine-157 and valine enzymes appears to be more a van der Waals than electrostatic effect,

00:45:38 a result we have supported by mutations in which we have mutated only the charges on the atoms, not the van der Waals properties.

00:45:45 This and other calculations are examples of calculations in which one can use the free energy approach to gain insight,

00:45:51 as well as to calculate free energies to relate to experiment.

00:45:55 In our opinion, this is one of the most exciting applications of the methods,

00:45:58 as we describe further in the paper by Dang et al. that's in your references.

00:46:04 The next slide describes a corresponding thermodynamic cycle for studies of sequence-dependent stabilities of nucleic acids.

00:46:10 To study relative stabilities to denaturation, one has the analogous problem as in protein stabilities,

00:46:16 that is, what to choose for the structure of the single-stranded denatured form.

00:46:21 Again, a choice of an isolated base or nucleotide model should give an upper bound to the denaturation-free energy.

00:46:27 However, viewing the cycle on the right, one can also study the relative sequence-dependent free energies of two different DNA structural forms,

00:46:35 such as A, B, and Z DNA.

00:46:37 We have done this successfully in three cases, see the references,

00:46:41 and the results for the relative stability of two sequences,

00:46:44 in which a single CG-based pair in an alternating CG run is mutated to TA by Dang and Perlin,

00:46:51 is given in the next slide.

00:46:53 I apologize for the quality of this slide,

00:46:56 but the bottom line is that this mutation destabilizes Z DNA relative to B

00:47:01 by about the right order of magnitude as observed experimentally.

00:47:05 Here the agreement is not quantitative, but it is still in the right ballpark, and it is still quite good.

00:47:12 It is harder to sort out the underlying molecular causes in this case,

00:47:16 but it is clear that base-base and base-phosphate interactions are the key to determining the Z-phobicity of AT-based pairs.

00:47:26 A new recent development has been the capability to calculate free energy as a function of geometrical coordinate,

00:47:33 as outlined in the next slide.

00:47:36 This implementation has been carried out by both Perlman,

00:47:40 whose focus is on the study of nucleic acid conformational free energies,

00:47:43 and by Dang, whose focus has been free energies for molecular association.

00:47:48 Chaplock and Coleman had earlier calculated the relative free energies in the gas phase and solution

00:47:54 using the mutation method I mentioned at the beginning,

00:47:57 in which bases and base pairs disappeared to nothing.

00:48:01 Although the calculated values were in reasonable agreement with experiment

00:48:05 in suggesting a greater stability of the stacked form in solution and the hydrogen-bonded form in the gas phase,

00:48:12 with the free energy of association in solution near the experimental value of minus 1.15 kcals per mole in aqueous solution,

00:48:20 the error bars on such an approach were very large.

00:48:25 Now, this slide has the hydrogen-bonded form.

00:48:28 You can see it's calculated to have a free energy of association on the bottom of minus 0.42 kcals per mole.

00:48:35 Next slide has the corresponding cycle for the stacked form,

00:48:39 which has a free energy of association of minus 1.86, both with very large error bars.

00:48:45 Liam Dang has implemented the approach to calculate the free energy as a function of base-base separation

00:48:50 and studied the interaction of base pairs in water, either in a stacked or hydrogen-bonded form.

00:48:55 The next three slides describe the result.

00:48:58 The first shows the potential energy in the gas phase, where a hydrogen-bonded form of the base pairs is clearly more stable.

00:49:05 The next slide shows the potential of mean force, PMF, in solution, in which the stacked form is the more stable one.

00:49:15 The final slide shows the result of turning the potential of mean force into a ΔG association that can be compared to experiment.

00:49:23 That's the number 1.22, sorry, or minus 1.15 is the experiment,

00:49:30 and the best estimate is minus 0.86 for the stacked form,

00:49:34 and the free energy for the hydrogen-bonded form, as you can see from the slide, is minus 0.12 kcals per mole.

00:49:41 As one can see, the calculated value varies some depending on cut-off radii,

00:49:46 but the agreement with experiment is quite encouraging.

00:49:49 It suggests that our potential functions for water-water, water-base, and base-base interactions are balanced.

00:49:55 Dang has also applied the PMF, potential of mean force, approach to cation-crown interactions,

00:50:01 specifically the interaction of 18-crown-6 with potassium in solution.

00:50:05 The next two slides illustrate the gas phase energies, this is in this slide,

00:50:10 and solution-free energies for the association process.

00:50:14 So here in this slide you see the gas phase free energies,

00:50:17 and now you see the potential of mean force in solution.

00:50:21 Again, the calculated ΔG is minus 3.5 plus or minus 0.4 in a good agreement with the experimental value of 2.9 kcals per mole.

00:50:30 But even more interestingly, the free energy minimum occurs, as you can see on the slide,

00:50:35 with the cation displaced from the center of the crown in contrast to the crystal structure.

00:50:41 Examining the conformations as a function of crown-cation separation is also instructive.

00:50:47 As the cation dissociates from the crown, it induces a high energy conformation,

00:50:53 which allows multiple crown-cation interactions at the same time water is interacting with the potassium.

00:51:01 This leads to a conformation, a so-called C2 conformation,

00:51:06 which turns out to be the lowest energy conformation for this complex as the cation is dissociating from the crown.

00:51:14 This conformation is interesting because it places all the oxygen on the same side of the crown

00:51:21 to allow the maximizing of crown-cation interactions.

00:51:26 A final application presented is from the studies by Chaplock et al.,

00:51:31 and concerns the development of non-additive potentials for molecular interactions.

00:51:37 The next generation of force fields should have non-additive effects built in

00:51:41 to allow quantitative simulation of polar and ionic systems.

00:51:46 Chaplock et al. have developed such a potential, and the next slide presents the good news and the bad news

00:51:52 with respect to its capabilities to simulate gas, liquid, and solid water,

00:51:56 and solutions of lithium and sodium, cations in water.

00:52:01 The good news, you can see that you can represent the energy and the volume of water-liquid well,

00:52:08 its second virial coefficient as a function of temperature,

00:52:11 and extremely well representation of the delta H of hydration of lithium and sodium.

00:52:18 In the next slide, the bad news is that the OO radial distribution function has no second peak,

00:52:24 and the ice densities, we did simulations on ice 1 and 7, are about 10% too small.

00:52:31 Although the above studies use Monte Carlo methods, Jim Caldwell and Liam Dang of my group,

00:52:36 Liam is now at IBM San Jose, have implemented molecular dynamics with analytical derivatives

00:52:41 for inducible dipoles, and are applying this to generate new models for water and ionic interactions,

00:52:46 which include non-additive effects.

00:52:50 Let us put a general perspective on the successes and problems with free energy approaches.

00:52:55 Our view is that if the molecular mechanical potential, Hamiltonian, is accurate,

00:53:00 and secondly, if one samples sufficiently, one should be able to calculate free energies

00:53:05 in good agreement with experiment consistently.

00:53:08 For many systems, current molecular mechanical parameters are sufficiently accurate,

00:53:13 with the exception of ionic systems where cutoff effects are significant.

00:53:17 Thus, one can carry out mutations with changes in the net charge of the system,

00:53:22 with no changes in the net charge of the system, with little hysteresis and reliable,

00:53:30 which are reliable statistically, but the need for cutoff corrections is clear,

00:53:35 and effective two-body potentials often give quite inaccurate representation of the energetics of these systems.

00:53:41 The sampling issue is nothing more than the local minimum problem,

00:53:45 i.e., in a realistic amount of simulation time of the order of tens or hundreds of picoseconds,

00:53:51 one can carry out large mutations in water where the rotational diffusion time is of the order of picoseconds,

00:53:56 but one cannot do such in an enzyme-active site where reorientation times might be of the order of nano or microseconds.

00:54:04 As noted above, one can successfully carry out free energy calculations with reasonably large mutations,

00:54:09 for example, adenine to guanine in protein-active sites,

00:54:12 but for mutations that involve changes in shape as well as partial charges,

00:54:17 the chances of success, both from a structural and energetic point of view, are much more problematic.

00:54:23 But the future is bright for ever-increasing and more effective applications

00:54:27 of free energy approaches to molecular systems of all varieties.

00:54:32 We would like to conclude with a slide that highlights our own studies

00:54:37 in the use of computer simulation to genuinely predict molecular properties in advance of experiment.

00:54:44 Prediction 1 corresponds to the prediction of a new anisole spherand,

00:54:48 which we suggested would have a higher lithium-ion affinity than any that had been characterized.

00:54:53 This prediction was confirmed by Cram and co-workers.

00:54:56 Predictions 2 and 3 were discussed above, and 2 has been confirmed by experiments,

00:55:00 with experiments on 2 in progress.

00:55:03 We think the future is bright for computer simulations making ever more accurate

00:55:07 quantitative predictions of new molecules and their properties.

00:55:11 Thank you very much.

00:55:26 While we're waiting for your calls, we're going to take our first call from the studio audience.

00:55:31 Yes, what is your question, please?

00:55:33 Ernest Villafranca from Agron Pharmaceuticals here in San Diego.

00:55:37 Peter, you mentioned, as did Dr. Blaney, that the molecular size limitations of the free energy calculations,

00:55:48 you know, you're running into some limitations, of course.

00:55:52 I have a two-part question.

00:55:54 What do you consider to be the current limitations in terms of size and in terms of atom type?

00:56:00 And also, how do you see us overcoming these limitations?

00:56:04 Are they going to be hardware, software, theory?

00:56:09 Thanks, Ernie.

00:56:12 My feeling is that I gave some examples of the large mutation,

00:56:19 or the large mutation in terms of the number of atoms involved in the mutation of adenine to guanine,

00:56:27 and that is a mutation that involves a change of many atoms.

00:56:31 But I didn't mention some mutations that have been done, which have been pushing the limits of the technology.

00:56:39 For instance, Jim Caldwell tried to grow a group that was too large into the alpha-lytic protease active site,

00:56:47 and it bumped into a protein.

00:56:50 And during 40 picoseconds of molecular dynamics, there was a huge repulsive interaction generated.

00:56:56 So the point I alluded to in my talk is that if one studies macromolecular systems,

00:57:03 that is, protein-ligand complexes, that it's not clear.

00:57:08 We don't know the answer how long one has to simulate to get the groups in the active site to relax,

00:57:13 to allow a isoleucine to fit there.

00:57:16 Maybe it wouldn't ever fit there. We don't know.

00:57:19 Another interesting example was done by Kenny Murs, who is now at Penn State,

00:57:23 where in some carbonic anhydrase inhibitors, he mutated a hexyl group to nothing.

00:57:30 And there you get rather different answers depending on whether you shrink the atoms,

00:57:35 the bond lengths of the hexyl group, and so on.

00:57:39 So there are a lot of problematic difficulties when one changes the shape of the molecule.

00:57:46 Now, the question, your second question, is it going to be an algorithmic or computer time issue

00:57:51 that will solve some of these problems?

00:57:54 I think it's, at this point, there are a lot of things where a factor of 100 more computer time power

00:57:59 would be very useful in letting us really understand on a nanosecond timescale

00:58:05 how protein-active sites relax on response to different ligands.

00:58:10 So there may be other, you know, algorithmic improvements which help us along,

00:58:14 but I think this is an area where a couple more orders of magnitude would be very useful.

00:58:19 Thank you, Peter.

00:58:20 We now have Herschel on line 5.

00:58:22 Herschel.

00:58:23 Hello, Peter.

00:58:24 This is Herschel Weintraub at Merrill Dow in Cincinnati.

00:58:27 There's been some controversy that variations in windowing and other parameters

00:58:33 will allow prediction of any either sign or value at the delta delta G.

00:58:37 If this is the case, that would limit the predictive value of the method,

00:58:42 although it would still allow retrospective analysis.

00:58:45 Is this a result of the inability to calculate a small enough window or a long enough simulation,

00:58:52 or is it something inherent in the instability of the technique?

00:58:56 That's a very good question, Herschel.

00:58:58 Nice to hear from you.

00:59:00 I think that with suitably chosen potential functions,

00:59:04 one can get very reliable numbers, as I tried to illustrate,

00:59:08 particularly for polar molecules.