Thursday, 12 October 2017

The resurrection of Maxwell's Demon

Sometimes when reading the residence time literature, I get the impression that the off-raters have re-animated Maxwell's Demon. It seems as if a nano-doorman stands guard at at the entrance of the binding site, only opening his nano-door to ligand molecules that want to get in. Microscopic Reversibility? Stop being so negative! With Big Data, Artificial Intelligence, Machine Learning (formerly known as QSAR) and Ligand Efficiency Metrics we can beat Microscopic Reversibility and consign The Second Law to the Dustbin Of History!

There were a number of things that triggered this blog post. First, I saw a recent article that got me thinking about philatelic drug discovery.  Second, some of the off-raters will be getting together in Berlin next week and I wanted to share some musings because I won't be there in person. Third, my former colleague Rutger Folmer has published a useful (dare I say, brave) critique of the residence time concept that is bang on target. 

I'm not actually going to say much about Rutger's article except to suggest that you read it. That's because I really want to examine the article on philatelic drug discovery in a more detail (it's actually about thermodynamic and kinetic profiling but I thought the reference to philately would better grab your attention). My standard opening move when playing chess with an off-rater is to assert that slow binding is equivalent to slow distribution. In what situations would you design a drug to distribute slowly?

Chemical kinetics is all about energy barriers and, the higher the barrier, the slower things will happen. Microscopic reversibility tells us that a barrier to association is a barrier to dissociation and that the ligand will return to solution along the same path that it took to its binding site. Microscopic reversibility tells you that if you got into the parking spot you can get out of it as well although that may not be the experience of every driver. The reason that microscopic reversibility doesn't always seem to apply to parking is that most humans, with the possible exception of tank drivers in the Italian army, are more comfortable in forward gear than in reverse. Molecules, in contrast, have no more concept of forward and reverse than they do of standard states, IUPAC or the opinions the 'experts' who might quantitatively estimate their drug-likeness while judging their beauty. Molecules don't actually do concepts. Put more uncouthly, molecules just don't give a toss.

I've created a graphic to illustrate to show how things might look in vivo when there is a barrier to association (and, therefore, to dissociation). We can think of the ligand molecule having to get over the barrier in order to get to its binding site and we call the top of the barrier the 'transition state'. This is a simplified version of reality (it is actually the system that passes from the unbound state through the transition state to the bound state and for some ligand-protein association there is no barrier) but it'll serve for what I'd like to say. The graphic consists of three panels and the first (A) of these illustrates the situation soon after dosing when the concentration of ligand (L) is relatively high and the target protein (P) has not had sufficient time to respond. If the barrier is sufficiently high, the system can't get to equilibrium before the ligand concentration starts to fall in what a pharmacokineticist might refer to as the elimination phase. Under this scenario the system will be at equilibrium briefly as the ligand concentration falls and I've shown this in panel B. After the equilibrium point is reached, the rate of dissociation exceeds the rate of association and this is shown in panel C. 



There's something else that I'd like you to take a look at in the graphic and that's the free energy (G) of the unbound state (P + L).  See how it goes down relative to the free energy of the bound state (P.L) as the concentration of ligand decreases. When thinking about energetics of these systems, it actually makes a lot of sense to use the unbound state as the reference but you do need to use a reference concentration (e.g. 1 M) to to do this.

When we do molecular design we often think in terms of manipulating energy differences. For example, we try to increase affinity by stabilizing the bound state relative to the unbound state. Once you start trying to manipulate off-rates, you soon realize that you can't change one thing at a time (unless you draft Maxwell's Demon into your project team).  I've created a second graphic which looks similar to the first graphic although there are important differences between the two graphics. In particular, I'm referencing energy to the unbound state (P + L) which means that the ligand concentration is constant in all three panels. Let's consider the central panel as the starting point for design. We can go left from that starting point and stabilize the bound state which is equivalent to optimizing affinity.  Stabilizing the bound state will also result in slower dissociation provided that the transition stare energy remains unchanged. This is a good thing but it's difficult to show that the benefits come from the slower dissociation and not from the increased affinity. If you raise the barrier (i.e. increase the energy of the transition state) to reduce the off-rate you'll find that you have slowed the on-rate to an equal extent.        



Before moving on, it may be useful to sum up where we've got to so far. First, ask yourself why you think off-rates will be relevant in situations where concentration changes on a longer time scale than binding. Second, you'll need to enlist the help of Maxwell's Demon if you want to reduce off-rate without affecting on-rate and/or affinity. Third, if you want to consider binding kinetics in design then it'd be best to use barrier height (referenced to unbound state) and affinity as your design parameters.

Now I'd take a look at the philatelic drug discovery article. This is a harsh term but it does capture a tendency in some drug discovery programs to measure things for the sake of it (or at least to keep the grinning Lean Six Sigma 'belts' grinning).  Some of this is a result of using techniques such as isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR) that yield information in addition to affinity (that is of primary interest) at no extra cost. I really don't want to come across as a Luddite and I must stress that measurements of enthalpy, entropy, on-rate and off-rate are of considerable scientific interest and are also valuable for improving physical models. Furthermore, I am continually awed by the exquisite sensitivity of modern ITC and SPR instruments and would always want the option to be able to measure affinity using at least one of these techniques. However, problems start when the access to enthalpy, entropy, off-rates and on-rates becomes exploited for 'metrication' and drug discovery scientists seek 'enthalpy-driven' binding simply because the binding will be more 'enthalpy-driven'. It is easier to make the case for relevance of binding kinetics although, as Rutger points out, reducing the off-rate may very well make things worse if the on-rate is also reduced. It is much more difficult to assemble a coherent case for the relevance of thermodynamic signatures in drug discovery. Perhaps, some day, a seminal paper from the Budapest Enthalpomics Group (BEG) will reveal that isothermal systems like live humans can indeed sense the enthalpy and entropy changes associated with drugs binding to their targets although I will not be holding my breath.

Unsurprisingly, the thermodynamic and kinetic profiling (aka philatelic drug discovery) article advocates thermodyanamic profiling of bioactive compounds in lead optimization projects. I'm going to focus on the kinetic profiling and it is worrying that the authors don't seem to be aware that on-rates and off-rates have to be seen in a pharmacokinetic context in order to make the connection with drug discovery. The authors may find it instructive to think about how inhibitor concentration would have varied over the course of a typical experiment in their cell-based assays. They are also likely to find Rutger's article to be educational and I recommend that they familiarize themselves with its content.

The following statement suggests that it may be beneficial for the authors to also familiarize themselves with the rudiments of chemical kinetics:


"Association and dissociation rate constants (kon and koff) of compound binding to a biological target are not intrinsically related to one another, although they are connected by dissociation equilibrium constant KD (KD = koff/kon)."

The processes of association and dissociation are actually connected by virtue of taking place along the same path and by having to pass through the same transition states. The difference in barrier heights for association and dissociation is given by the binding free energy. 

Some analysis of relationships between potency in a cell-based assay and  KD, koff and kon were presented in Figure 6 of the article. I have a number of gripes with the analysis. First, it would be better to use logarithms of quantities like KD, IC50, koff and kon when performing analysis of this nature. In part, this because we typically look for linear free energy relationships in these situations. There is another strong rationale for using logarithms because analysis of correlations between continuous variables works best when the uncertainties in data values are as constant as possible. My second gripe is that the authors have chosen to bin their data for analysis and this is a great way to shoot yourself in the foot. When you bin continuous data you both reduce your data analysis options and leave people wondering whether the binning has been done to hide the weakness of the trends in the data.   I have droned at length about why it is naughty to bin continuous data so I'll leave it at that.

It's been a long post and it's time to wrap things up. If you've found the post to be 'cansativo' (sounds so much more soothing in Portguese) then spare a thought for the person who had to write it. To conclude, I'll leave you with a quote that I've taken from the abstract for Rutger's article:
  
"Moreover, fast association is typically more desirable than slow, and advantages of long residence time, notably a potential disconnect between pharmacodynamics (PD) and pharmacokinetics (PK), would be partially or completely offset by slow on-rate."

Wednesday, 20 September 2017

To logP or logD, that is the question

So last week I asked twitter which lipophilicity measure was more relevant of binding of bases to hERG. The poll resulted in a landslide for logD(pH=7.4) (70%; 21 votes) over logP (30%; 9 votes). I did not vote.

So let's take another look at the question and I've cooked up a thought experiment to help you do this. Let's suppose that we have an amine bound to hERG (which your Scottish colleagues may call hairrg). It has a pKa of 10.4 and logP of 6 and the IC50 in the hERG assay is 100 nM (the safety people think that this will lead to an unpleasant torsades de pointes that will hERG a whole lot more than a corrective thrashing by Wendi Whiplasch). Provided that there is no significant partitioning of the protonated form of the amine into the octanol, the logD(7.4) value for the amine will be 3.

Let's imagine that we can change the pKa of the amine while keeping all the other physicochemical and molecular properties the same. Changing the amine pKa from 10.4 to 12.4 will get logD(7.4) down to 1. But how do you think the hERG IC50 will respond?      

Saturday, 1 April 2017

A concentration of scoring functions

Researchers at The Hungarian Institute Of Thermodynamics have published a number of seminal articles on the interplay of enthalpy and entropy in areas ranging from physical chemistry to socioeconomics. For example, the cause of World War 1 (also known as 'The Great War' although I doubt whether any of its participants thought that it was that great) was traced to a singularity in the Habsburg Partition Function. In a nutshell, the problem was shown to be a surfeit of the wrong type of entropy (which led to Franz Ferdinand's driver getting lost) coupled with a deficit in the right type of entropy (which would have prevented Gavrilo Princip's bullets from finding their targets). However, it is unlikely that any amount of the right type of entropy could have saved the hapless Maximilian I of Mexico, who generously volunteered to be Emperor only to be shot by the ungrateful Mexicans.

The most recent study from BEG (Budapest Enthalpomics Group) is little short of sensational. Unfortunately it's not available online and the poor fax quality, coupled with my rudimentary grasp of Hungarian, have made the going hard. The essence of this seminal study is that the performance of scoring functions can be significantly improved by including the concentration unit (in which affinity is expressed) as a parameter in the fitting process. The casual observer of virtual screening may have wondered why scoring functions are trained with affinity but validated by enrichment. By treating the concentration unit as a parameter in the fitting process, the authors were able to achieve unprecedented accuracy of prediction and the phone call from Stockholm would seem to be a foregone conclusion. Commenting on these seminal findings, Prof. Kígyó Olaj, the director of the Institute said, "Now we no longer need to use ROC plots to mask feeble correlations between predicted and measured affinity".     

Tuesday, 24 January 2017

PAINS and editorial policy

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I have blogged previously (1 | 2 | 3 | 4 | 5 ) on PAINS. In this post, I present the case against inclusion of PAINS criteria in the Journal of Medicinal Chemistry (JMC) Guidelines for Authors (viewed 22-Jan-2017) as given below:


"2.1.9. Interference Compounds. Active compounds from any source must be examined for known classes of assay interference compounds and this analysis must be provided in the General Experimental section. Compounds shown to display misleading assay readouts by a variety of mechanisms include, but are not limited to, aggregation, redox activity, fluorescence, protein reactivity, singlet-oxygen quenching, the presence of impurities, membrane disruption, and their decomposition in assay buffer to form reactive compounds. Many of these compounds have been classified as Pan Assay Interference Compounds (PAINS; see Baell & Holloway, J. Med. Chem. 2010, 53, 2719-2740 and webinar at bit.lyj/mcPAINS). Provide firm experimental evidence in at least two different assays that reported compounds with potential PAINS liability are specifically active and their apparent activity is not an artifact."

The term 'known classes of assay interference compounds' must be defined more precisely in order to be usable by both authors submitting manuscripts and reviewers of those manuscripts. Specifically, the term 'known classes of assay interference compounds' implies the existence of a body of experimental data in the public domain for which specific substructural features have been proven to cause the observed assay interference. The JMC Guidelines for Authors (viewed 22-Jan-2017) imply that any assay result for a compound with 'potential PAINS liability' should necessarily be treated as less informative than would be the case if the compound did not have 'potential PAINS liability'. I shall term this as 'devaluing' the assay result.              

The PAINS acronym stands for Pan Assay INterference compoundS and it was introduced in a 2010 JMC article (BH2010) that is cited in the Guidelines for Authors (viewed 22-Jan-2017). The PAINS filters introduced in the BH2010 study are based on analysis of frequent-hitter behavior in a panel of 6 AlphaScreen assays. Each PAINS filter consists of a substructural pattern and is associated with an enrichment factor that quantifies the frequent hitter behavior. Compounds that quench or scavenge singlet oxygen have the potential to interfere with AlphaScreen assays but individual PAINS substructural patterns were not evaluated for their likelihood of being associated with singlet oxygen quenching or scavenging. For example, the BH2010 study makes no mention of studies ( 1 | 2 | 3 | 4 ) linking singlet oxygen quenching/scavenging to the presence of a thiocarbonyl group which is a substructural element present in rhodanines.  

I argue that a high hit rate against a small panel of assays that all use a single detection technology is inadmissible as evidence for pan-assay interference.  I also argue that the results of screening against this assay panel can only be invoked to devalue the result from an AlphaScreen assay. In a cheminformatic context, the applicability domain of a model based on analysis of results from this assay panel is restricted to activity measured in AlphaScreen assays. Furthermore, it is questionable whether it is valid to invoke the results of screening against this assay panel to devalue a concentration response from an AlphaScreen assay because the results for each assay of the panel were obtained at a single concentration (i.e. no concentration response).

The BH2010 study does present some supporting evidence that compounds matching PAINS substructural patterns are likely to interfere with assays. In a cheminformatic context, this supporting evidence can be considered to extend the applicability domain of PAINS filters. However, supporting evidence is only presented for some of the substructural patterns and much of that supporting evidence is indirect and circumstantial. For example, the observation that rhodanines as a structural class have been reported as active against a large number of targets is, at best, indirect evidence for frequent hitter behavior which is characterized by specific compounds showing activity in large numbers of assays. There is not always a direct correspondence between PAINS substructural patterns and those used in analyses that are presented as supporting evidence. For example, the BH2010 study uses substructural patterns for rhodanines that specify the nature of C5 (either saturated or with exocyclic carbon-carbon bond).  However, the sole rhodanine definition given in the BMS2006 study specifies an exocyclic carbon-carbon double bond. This means that it is not valid to invoke the BMS2006 study to devalue the result of every assay performed on any rhodanine.


The data (results from 6 AlphaScreen assays and associated chemical structures) that form the basis of the analysis in the BH2010 study are not disclosed and must therefore be considered to be proprietary. Furthermore, some of the supporting evidence that compounds matching PAINS filters are likely to interfere with assays is itself based on analysis (e.g. BMS2006 and Abbott2007) of proprietary data. The JMC Guidelines for Authors (viewed 22-Jan-2017) make it clear that the use of proprietary data is unacceptable:

"2.3.5.2 Proprietary Data. Normally, the use of proprietary data for computational modeling or analysis is not acceptable because it is inconsistent with the ACS Ethical Guidelines. All experimental data and molecular structures used to generate and/or validate computational models must be reported in the paper, reported as supporting information, or readily available without infringements or restrictions. The Editors may choose to waive the data deposition requirement for proprietary data in a rare case where studies based on very large corporate data sets provide compelling insight unobtainable otherwise.

2.3.6 QSAR/QSPR and Proprietary Data. The following are general requirements for manuscripts reporting work done in this area:

(3) All data and molecular structures used to carry out a QSAR/QSPR study are to be reported in the paper and/or in its supporting information or should be readily available without infringements or restrictions. The use of proprietary data is generally not acceptable."

Given JMC's stated unacceptability of analysis based on proprietary data, to use such analysis to define editorial policy would appear to contradict that editorial policy.

To sum up:

  • Analysis of the screening results for the BH2010 assay panel can only be invoked  invoked to devalue or otherwise invalidate the result from an AlphaScreen assay.
  • Additional supporting evidence is only provided in BH2010 for some of the PAINS filters. In these cases, the evidence is not generally presented in a manner that would allow a manuscript reviewer to assess risk of assay interference in an objective manner.
  • Most of the analysis presented in the BH2010 study has been performed on proprietary data. To base JMC editorial policy on analysis of proprietary data would appear to contradict the Journal's policy on the use of proprietary data.

I rest my case.

Friday, 6 January 2017

Confessions of a Units Nazi

Regular readers of this blog will know that I have an interest, which some might term an obsession, with units. At high school in Trinidad, we had the importance of units beaten into us by the Holy Ghost Fathers and, for some of the more refractory cases, the beating was quite literal. I was taught physics by the much loved, although somewhat highly-strung, Fr. Knolly Knox (aka Knox By Night) who, as Dean of the First Form, used to give 'licks' with a cane of hibiscus (presumably chosen for its tensile properties). You quickly learned not to mess with The Holy Ghost Fathers, especially the Principal, Fr. Arthur Lai Fook (aka Jap), and it was a brave student who responded to the request by Fr. Pedro Valdez to define the dyne by answering, "Fah, it what happen after living". Fr. Pedro was a gentle soul although his brother, Fr. Toba, who taught me Latin, would lob a blackboard eraser with reproducible inaccuracy at any student who had the temerity to doze off during the Second Punic War while Hannibal and his elephants were steamrollering the hapless legions of Gaius Flaminius into Lake Trasimene. At least we didn't have detention at my school. Actually we did have detention only it was called 'penance'. Each and every student also had a Judgement Book in which was entered a mark (out of 10) for each subject each and every week. A mark of 5 (or less) or a failure to return one's Judgement Book, duly signed by parent or guardian, by Wednesday morning earned the transgressor a corrective package of Licks and Penance.  As a thoughtful child, I managed to shield my parents from this irksome bureaucracy and, in any case, it was simply safer that The Holy Ghost Fathers were never given the opportunity to familiarize themselves with the authentic parental signatures.

What we learned from the Holy Ghost Fathers was that most physical quantities have dimensions and if the quantities on the opposite sides of the 'equal sign' in an equation have different dimensions then it is a sign of an unforced error rather than a penetrating insight. For example the dimensions of force are MLT-2 (M = mass; L = length; T = time) and you are free to express forces in newtons, dynes or poundals as you prefer. You can think of a physical quantity as a number multiplied by a unit and, without the unit, the number is meaningless. Units are extremely important but at the same time they are arbitrary in the sense that if your physical insight changes when you change a unit then it is neither physical nor an insight. Here's a good illustration of why dimensional analysis matters.

I have blogged ( 12 | 3 ) about how building the a concentration unit into the definition of ligand efficiency (LE) results in a metric that is physically meaningless (even though it remains a useful instrument of propaganda) and, for the masochists among you, there's also the LE metric critique in JCAMD. The problem can be linked to a lack of recognition of the fact that logarithms can only be calculated for numbers (which lack units). However, LE has another 'units issue' which is connected with the fact that it is a molar energy that is scaled in the definition of LE rather than pIC50 or pKd. This needn't be an issue but, unfortunately, it is. LE is defined by dividing a molar energy by the number of non-hydrogen atoms in the molecular structure and there is nothing in the definition of LE that says that the energy has to be expressed in any particular unit. This means that you can define LE using any energy unit that you want to. Some 'experts' appear to believe that dividing a molar energy by number of non-hydrogen atoms relieves them of the responsibility to report units. I'm referring, of course, to the practise of multiplying pIC50 or pKd by 1.37 when calculating LE. You might ask why people do this, especially given that 'experts' tout the simplicity of LE and they don't multiply pIC50 or pKd by 1.37 when they calculate LipE/LLE. Don't ask me because I'm neither expert nor 'expert'.

Let's take a look at this NRDD article on LE metrics and I'd like you to go straight to Box 1 (Ligand efficiency metrics). Six numbered equations are shown in Box 1 and it is stated towards the end of the first paragraph that "each equation corresponds to a mathematically valid function".  This statement is incorrect because the first equation (1) in Box 1 is not a mathematically valid function. The reason for this is that the logarithm function cannot take as its argument a quantity, such as Kd, that has units. Equation (5), which defines LLEAT, is mathematically valid although it differs from the mathematically ambiguous equation that was originally used to define LLEAT

To be honest, I think that Box 1 is probably beyond repair by conventional erratum and I'll back this opinion with an example:


"Assuming standard conditions of aqueous solution at 300K, neutral pH and remaining concentrations of 1M,
 –2.303RTlog(Kd/C°) approximates to –1.37 × log(Kd) kcal/mol." 

At my school in Trinidad this would have been called a 'ratch' and, once detected, it would have earned its perpetrator a corrective package of Licks and Penance. I don't think even the Holy Ghost Fathers could have exorcised a concentration unit quite this efficiently.

I'd now like to talk a bit about the 'p' operator that we use to transform IC50 and Kd values into logarithms. This makes it much easier to perceive structure-activity relationships and provides a better representation of measurement precision than when the IC50 and Kd values themselves are used. To calculate pKd,, first express Kd in molar concentration units, dump the units and calculate minus the logarithm of the number. I realize that this may come across as arm waving but the process of converting  Kd, to  pKd, can actually be expressed exactly in mathematical terms as follows:

 pKd = –log10(Kd/M)

The 'p' operator has a 1 M concentration built into it. Although this choice of unit is arbitrary, it doesn't cause any problems if you're doing sensible things (e.g. subtracting them from each other) with the pKd values. If, however, you're doing silly things (e.g. dividing them by numbers of non-hydrogen atoms) with the pKd values then the plot starts to unravel faster than you can say 'Brexit means Brexit'. 

I'd like you take a look at another article which also has a Box 1 although I won't bother you with another tiresome 'spot the errors' quiz. The equation that I'll focus on is:

pKd = pKH + pKS 

This equation describes the decomposition of affinity into enthalpic and entropic contributions and you might think this means that you can write:

Kd = KH × KS 

As Prof. Pauli would have observed, this is an error in the 'not even wrong' category and it is clear that a difference in opinion as to the importance of units was as much responsible for the unraveling of the Austro-Hungarian empire as that unfortunate wrong turn in pre-SatNav Sarajevo. The 'p' operator implies that each of KdKH and Khas units of concentration. However, multiplying two such quantities will give a quantity that has units of concentration squared. 

It is actually possible to decompose Kd into enthalpic and entropic contributions a valid manner but you need to be thinking carefully about the meaning of the standard state. As noted previously DG° depends on the concentration used to define the standard state. This is a consequence of the dependence of DS° on the standard concentration and DH is independent of the standard concentration (the standard state is assumed to be a dilute solution). This suggests defining KS as quantity with units of concentration and Kas a quantity without units.

This is probably a good point to wrap things up. My advice to all the authors of the featured NRDD and FMC articles is that they read (and make sure that they understand) the section of this article that is entitled '8. Ligand Efficiency and Additivity Analysis of Binding Free Energy'. This advice is especially relevant for those of the authors who consider themselves to be experts in thermodyamics.

May I wish all readers a happy, successful and metric-free 2017.