replacing affinity with binding kinetics in qsar studies resolves otherwise confounded effects

JOURNAL OF CHEMOMETRICSJ. Chemometrics 2006; 20: 370–375Published online 5 February 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/cem.1010
Replacing affinity with binding kinetics in QSARstudies resolves otherwise confounded effects

Karl Andersson and Markku D. Hamalainen*

Biacore AB, Uppsala, Sweden

Received 3 March 2006; Revised 3 July 2006; Accepted 15 July 2006

*CorrespoSE-75450E-mail: M

Steady-state binding affinity is a commonly used response variable in quantitative structure-activity

relationship (QSAR) studies. In this paper we show that affinity alone may introduce unnecessary

noise to the model or even cause model failure. Binding affinity is a ratio between the dissociation

rate and association rate. Mathematical modeling of a ratio with unknown variation structure of

nominator and denominator is difficult and the interpretation of the resulting model might be

meaningless under certain circumstances. Commercially available biosensors can be used for

measurement of binding kinetics enabling separate modeling of association and dissociation rates.

In this paper we discuss the problems caused by the confounded effect in the compiled response

affinity and show examples where separate modeling of the rate constants improves the interpret-

ation of QSAR models. Copyright # 2007 John Wiley & Sons, Ltd.

KEYWORDS: quantitative structure-activity relationship; biosensor; surface plasmon resonance; Biacore; on-rate; off-rate

1. INTRODUCTION

In quantitative structure-activity relationship (QSAR) stu-

dies, biological activity is often represented by the binding

affinity of the binders to the selected target [1–3]. This is an

understandable choice, since the binding affinity represents

the average degree of drug-populated targets at equilibrium,

and a large number of successful QSAR models have been

reported using this strategy. Furthermore, the assays used

for the characterization of the binders are often only suitable

for affinity measurements.

However, in recent years it has become increasingly

obvious that binding affinity alone may not always be a

suitable descriptor of biological activity. Binding affinity is

composed of an association and a dissociation event

according to the equation

KD ¼ kdka

(1)

whereKD is the binding affinity (M), kd is the dissociation rate

(s�1) and ka is the association rate (M�1 s�1). In cases where

the association or the dissociation rate dictates biological

activity, affinity alone may be a directly misleading measure

of activity.

When modeling the relationship between the settings of

influential factors and responses, it is vital that the responses

ndence to: M. D. Hamalainen, Biacore AB, Rapsgatan 7,Uppsala, [email protected]

accurately describe the desired function of the system under

study. Quotients can only be used with confidence in cases

where either the denominator or nominator is known to have

limited variation, or when they are proportional to each

other. For example, the frequent use of signal to noise ratios

in quality modeling has been heavily criticized [4]. In the

field of QSAR, it is commonly but erroneously believed that

the association rate is approximately constant due to

diffusion limitation and that the affinity reflects the

dissociation rate of the interaction.

The kinetic properties of drug-target interactions for

compounds belonging to one or more scaffold class can be

visualized using an on-off-rate map as shown in Figure 1.

Such amap comprises an association rate versus dissociation

rate plot, in which iso-affinity lines become diagonals

(Figure 1A). Strong binders appear in the upper left corner.

The common assumption that the association rate is close to

constant [5] would yield a map as shown in Figure 1 subplot

B and in such cases, affinity-based QSAR modeling is

appropriate. It is clearly possible to have a constant affinity

and variable kinetic properties (Figure 1C), a pattern that has

been observed in the temperature dependency of drug-target

interactions [6]. The most common on-off-rate map appear-

ance encountered to date, however, resembles the one shown

in Figure 1D, with a significant spread in association rate,

dissociation rate and affinity. In such situations, the

assumption that the association rate is constant is obviously

false and standard QSAR methodology may fail to establish

an interpretable model of activity as a function of structure.

Copyright # 2007 John Wiley & Sons, Ltd.

Figure 1. Schematical on-off-rate maps visualizing (A) that

the binding affinity forms iso-affinity lines in the space

spanned by the dissociation and association rates, (B) a

situation when association rate is constant, (C) an association

and dissociation rate ratio variation giving nearly constant

affinities and thereby hiding the effect of structural variation on

the interaction and (D) a typical situation when the structural

variation influences both association and dissociation rates.

Binding kinetics resolves confounded effects in QSAR 371

In this mini-review, we present a collection of findings that

together demonstrate the benefit of replacing affinity with

kinetics in QSAR studies.

Figure 2. The kinetic profiles of 37 different HIV-1 protease

inhibitors presented in an on-off-rate map. Commercially

available drugs in the map are Saquinavir (Saq), Nelfinavir

(Nelf), Indinavir (Ind), Ritonavir (Rit), Ampenavir (Amp). The

remaining compounds were selected from a lead series. For

B376, only affinity could be determined due to extremely fast

kinetics.

2. KINETICS AND BIOLOGICALACTIVITY IN THE LITERATURE

In multiple reports, biological activity has been shown to

correlate better to binding kinetics than to affinity. To the best

of our knowledge, Hall and co-workers [7] first published

this observation in a study of saxitoxins. Their structure-

activity relationship discussion required use of the associ-

ation rates of the toxin interactions as description of activity.

Several authors have noted that biological activity correlates

better to other binding properties than affinity, even though

they have not developed QSAR models. Elg et al. [8] found

that the association rate of thrombin inhibitors correlated

better than affinity with the in vivo pharmacological effect in

a rat blood coagulation model. Using affinity as an

approximation of pharmacological effect would therefore

be detrimental in this case. Park et al. [9] showed that for

anti-cancer peptides derived from a pharmacologically

active antibody, the peptides and the antibodies had similar

activity in a cell-based growth inhibition assay provided that

the dissociation rates were similar. Rich et al. [10] found that

estrogen receptor agonists had 100-fold higher association

rates than antagonists, irrespective of the dissociation rate.

Krogsgaard et al. [11] showed that dissociation rate and heat

capacity, rather than affinity are responsible for T-cell

activation. Finally, Wu et al. [12] developed dedicated

screening methods for the detection of antibodies with high

association rate, since results from a virus neutralization

assay correlated best with association rate of the virus-

antibody interaction.


Within drug discovery, there is an emerging awareness on

the fact that different compounds may have widely varying

association rates. In a report by Huber [13], compounds

belonging to three different scaffold classes binding to

dipeptidylpeptidase IV had widely varying kinetic profiles.

Most notably, the association rates varied by at least two

orders of magnitude within each scaffold class. In a similar

experiment, the kinetic profiles of a range of compounds

binding to CD80 were obtained using biosensor technology

[14]. The compounds originated from five different scaffold

classes, and both the association and the dissociation rate

varied by three orders of magnitudes. Although apparently

unremarkable based on theirmoderate affinities alone, one of

the classes had a significantly slower dissociation when

compared to the others, implying a prolonged mode of

action.

Another well-characterized model system within drug

discovery is the HIV-1 protease. Inhibitors binding to this

protease showed significant spread in kinetic profiles [15]. As

seen in Figure 2, association rates vary by more than three

orders of magnitude and dissociation rates vary by four

orders of magnitude. Furthermore, a SAR was developed

based on kinetic information [15], in which it was shown that

some of the more structurally rigid cyclic scaffolds were

limited by the instability of the complex formed (i.e. rapid

dissociation). In a follow-up study Schaal [16] made a full

scale CoMFA QSAR analysis using association and dis-

sociation rates as activity. In brief, a QSAR model could be

developed for the dissociation rate but not for the association

rate, implying that the dissociation rate was the better

predictor of activity.

All these reports indicate that in many cases, the kinetic

profile of the binder may be vital for prediction of biological

activity. In each unique QSAR study, it is therefore rational to

J. Chemometrics 2006; 20: 370–375DOI: 10.1002/cem

372 K. Andersson and M. D. Hamalainen

verify the accuracy of affinity as predictor of biological

response and consider use of kinetic rate constants.

3. AMBIGUOUS RESPONSE VARIABLESIN MODELING

It is not uncommon to use compiled responses within

chemometrics. This is perhaps most frequently seen in the

use of closure in chromatography, where the peaks are

expressed as percentage of all peaks areas, and in the use of

signal/noise ratio in quality modeling. Such responses may

be perfectly acceptable for use in modeling, but certain

caution must be taken to ensure that the underlying

mechanisms are not masked in the process of compiling

the response. For example, if the signal of a system is related

to the factors in a completely different way than the noise, the

quotient signal/noise may have a quite complex relationship

to the factors that could be resolved more easily if they were

modeled as separate responses.

By analogy, affinity is the quotient of the dissociation rate

and the association rate and if the kinetic rate constants are

related to structural factors in different ways, themodeling of

the compiled response (i.e. affinity) will become problematic.

4. KINETICS-BASED QSAR: EXAMPLES

Two QSAR studies have been performed explicitly to show

that kinetic rate constants are beneficial for the QSAR

modeling process and for the interpretation of the model

[17–19]. These two studies were easily designed and dealt

with peptides or proteins binding to antibodies. In brief, the

experiments were designed in the following manner:

� S

Co

election of a set of molecules. In both cases, the sequence

of a polypeptide was modified. Two or three positions in

the polypeptide were mutated simultaneously. In order to

achieve maximal span in sequence space, the amino acid

substitutions were selected according to a multivariate

experimental design using three tabulated amino acid

properties as factors: hydrophilicity (ZZ1), size (ZZ2)

and electronic characteristics (ZZ3) [20].

Figure 3. Left: Amino acid (aa) sequence

conclusions from the QSKR model. Righ

dissociation rate for the interaction of Fab

height of the markers in the plot indicates

observed values.

pyright # 2007 John Wiley & Sons, Ltd.

� C

o

t:

5

th

haracterization of the activity of the molecules. The

binding kinetics for the interaction with the target mol-

ecule as measured by Biacore analysis was selected as

activity measure in both studies. This resulted in separate

models for association and dissociation rate.

� M
athematical description of the molecules. The same
tabulated values of amino acid properties used during

the design of the mutated polypeptides were used as

description. In one of the studies, a fourth descriptor,

helix-forming tendency (HFT) was also included [21].

� I
dentification of a mathematical model that relates the
description to the characterization. Since the design of the

polypeptides was statistically sound, the modeling part

became simple, with a linear model providing accurate

predictions.

The first QSAR study involved peptides binding to a

fragment of the recombinant antibody 57P (Fab 57P) [17]. The

wild-type peptide was originally derived from a viral

antigen, the tobacco mosaic virus protein (TMVP) [22].

The interaction of Fab 57P with the wild-type peptide had

been extensively characterized prior to the present study

[22]. Importantly, the wild-type peptide had been point

mutated at a number of positions [23]. It was therefore

possible to select three positions to mutate (142, 145 and 146),

which were all known to influence but not severely disrupt

the interaction, see Figure 3. After design, kinetic character-

ization, description andmodeling, the resulting models were

simply

ka ¼ 106 � ð1:175� 0:511 � ½142HFT�þ 0:0822 � ½145ZZ3�ÞðQ2 ¼ 0:49Þ

logðkdÞ ¼ � 1:052� 1:11 � ½145HFT�� 0:186 � ½146ZZ3�ðQ2 ¼ 0:73Þ

where [142HFT] denotes the value of the HFT descriptor for

the amino acid present at position 142. As seen from the

model equations, association and dissociation rate were

controlled by different properties of the peptide. For

obtaining a fast on–slow off binder (i.e. a high affinity

binder), the amino acid at position 142 should have a small

f the wild-type TMVP peptide and

Plot of observed versus predicted

7P with the different peptides. The

e pooled standard variation of the


Figure 4. Left: CDR3 loop structure (for the wild-type antibody TS) and list of

mutant single domain camel antibodies available for the study. Right: Plots of

observed versus predicted kinetic constants. Mutants used for deriving model are

depicted as circles, mutants used for validation as plus signs. The upper plot

describes predictive ability for association rate and the lower plot predictive ability

for dissociation rate.


HFT value, 145 should have a large HFT value and a large

positive ZZ3 value and 146 should have a large positive ZZ3

value. To obtain high affinity, glycine should be put at

position 142, serine or phenylalanine at 145 and aspartic acid

or serine at position 146. The validity of the model for log(kd)

has been verified in a follow-up study using eight novel

peptides [24], of which the kd of seven could be accurately

predicted by the model.

The second QSAR study included single and double

mutated proteins, namely single domain camel antibodies

(cAb) binding to lysozyme [18]. In this case, two residues

present in the CDR3 loop of cAb were mutated according to

the experimental design outlined in Figure 4. The experiment

was performed essentially as for the TMVP peptides,

yielding the predictive models

logðkaÞ ¼ 3:60� 0:0016 � ½101ZZ1� � 0:25 � ½101ZZ2� � 0:18

� ½101ZZ3� þ 0:16 � ½105ZZ1� � 0:097 � ½105ZZ2�

� 0:19 � ½105ZZ3�ðQ2 ¼ 0:88Þ

logðkdÞ ¼ �2:0þ 0:051 � ½101ZZ1� þ 0:092 � ½101ZZ2� þ 0:23

� ½101ZZ3� þ 0:091 � ½105ZZ1� þ 0:0095 � ½105ZZ2�

� 0:57 � ½105ZZ3�ðQ2 ¼ 0:85Þ

where [101ZZ1] denotes the value of the ZZ1 for the amino

acid present at position 101. Fourteen cAb were used for

deriving the models, while another four were used for model


validation. A graphic presentation of the predictive ability of

the models is given in Figure 4. As can be seen, the validation

mutants were predicted within the noise of the model,

indicating that the models were valid. They predicted that a

small and non-electrophilic amino acid (e.g. glycine) at

position 101 would increase binding strength both via

increased association rate and decreased dissociation rate. At

position 105 there was a conflict, since it was impossible to

find an amino acid giving both high association rate and low

dissociation rate. If the highest possible affinity is required,

the best compromise was predicted to be aspartic acid,

serine, glycine or proline.

The results from the De Genst [18] paper were later

re-analyzed using a completely different strategy [25]. The

method for describing the mutated single domain antibodies

was extended to allow for 3D-QSAR analysis. Using the

measurements in De Genst et al. and the 3D structure of the

wild-type camel antibody [26], a detailed 3D-QSAR model

was derived. Estimated structures of the mutated antibodies

were obtained by using commercial molecular modeling

software. The amino acids at positions 101 and 105 in the

wild-type antibody were replaced in silico according to the

mutation scheme. For each mutant, the software calculated

the 3D structure with lowest energy. These 3D structure

estimates were then used for developing a QSARmodel. The

spatial co-ordinates for backbone and side-chain for all

amino acids in the CDR3 loop and the ZZ3-scales for each of

the two mutated positions were used as structure descrip-


374 K. Andersson and M. D. Hamalainen

tions of the antibody. Interestingly, co-ordinate changes for

amino acids that were not mutated correlated with changes

in binding characteristics. Thus, if the 3D structure of a

protein is available, not all positions in the binding site region

need to be mutated to get information about how each

position near the binding site influences the interaction. The

information on non-mutated amino acid movements was not

as detailed as the information available for the mutated

amino acids. However, enough information was obtained for

detecting which amino acids contributed to the binding,

providing guidance for which residues to mutate in

follow-up studies.

5. CONCLUSION

Contrary to common belief, both the association rate and the

dissociation rate of drug-target interactions vary signifi-

cantly, even within what appears to be fairly homogenous

sets of molecules (drugs of the same scaffold class and

peptides of similar lengthwith large homology). The fact that

binders to the same protein with opposite function (agonist/

antagonist) have been discriminated by kinetics and not

affinity strengthens the arguments for inclusion of kinetic

rate constants in QSAR studies. Furthermore, it has been

shown that simple, separate QSAR models for association

and dissociation rates could be developed for the TMVP

peptides and the cAb. In both cases the models were clearly

different for association and dissociation rate, indicating that

different mechanisms govern the creation and the stability of

a molecular complex. Therefore, it is most likely beneficial to

replace commonly used affinity-assays to get access to kinetic

profiles, proven to be valuable in QSAR by improving the

accuracy and simplifying the interpretation of the model.

The habit of using a compiled response, affinity, in QSAR

may have led to unnecessary failures in modeling and

significant confusion when interpreting results. Simpler

models and more straightforward interpretation are anticip-

ated with the use of unambiguous kinetic rate constants.

Given the collection of proof on the importance of binding

kinetics for explaining biological activity, combined with the

shown benefits of kinetically resolved QSAR, binding

kinetics should be the preferred response in QSAR studies.

AcknowledgementsProfessor Olav Kvalheim is acknowledged for hosting the

post doc visit of M. D. H. 1992 and for acting opponent

during the dissertation of K. A. 2004. We also thank Dr Gary

Franklin for commenting on the manuscript.

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replacing affinity with binding kinetics in qsar studies resolves otherwise confounded effects

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