Kinetic analysis of biosensor data: elementary tests for self-consistency

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Biochem. Sci. 20, 102-103 7 Doyle, D. A. et al. (1996) Cell 85, 1067-1076 8 Morais Cabral, J. H. et al. (1996) Nature 382, 649-652 9 Harrison, S. C. (1996) Cell 86, 341-343 10 Kim, E. et al. (1995) Nature 378, 85-88 11 Kornau, H-C., Schenker, L. T., Kennedy,M. B. and Seeburg, P. H. (1995) Science 269, 1737-1740 12 Kim, E., Cho, K-O., Rothschild,A. and Sheng, M. (1996) Neuron 17, 103-113 13 M(Jller,B. M. et al. (1996) Neuron 17, 255-265 14 Niethammer, M., Kim, E. and Sheng, M. (1996) J. Neurosci. 16, 2157-2163

15 Hemming, N. J. et al. (1995) J. Biol. Chem. 16 17 18 19

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22 Itoh, N. and Nagata, S. (1993) J. Biol. Chem.

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268, 10932-10937 23 Sato, L, Irie, S., Kitada, S. and Reed, J. C. (1995) Science 268, 411-415 24 Gomperts, S. N. (1996) Cell 84, 659-662 25 Brenman, J. E. et al. (1996) Cell 84,

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JAN SARAS AND CARL-HENRIKHELDIN Ludwig Institute for Cancer Research, Box 595, Biomedical Centre, S-751 24 Uppsala, Sweden

Dissociation:

Kinetic analysis of biosensor data: elementary tests for self-consistency

R(t) = R~,d + (Ro, d - Roo,d)exp (-k_t) (2)

Peter Schuck and Allen P. Minton The validity of t h e m o s t c o m m o n kinetic interpretation of b i o s e n s o r data can be quickly a s s e s s e d with t h e aid of two s i m p l e t e s t s for self-consistency, requiring only back-of-the-envelope calculations. A search of the recent literature reveals t h a t many published results fail t h e s e t e s t s qualitatively.

THE USE OF evanescent wave biosensors to study associations between soluble macroligands and immobilized acceptors has increased greatly during the last five years, following the introduction of commercially manufactured instruments (BIAcore AB, Mfinity Sensors IAsys). The kinetic data obtained from the biosensor is most frequently interpreted in the context of the simple binding model:

k+ L + A ~ LA k_ where L denotes mobile ligand and A represents immobilized acceptor. We1,2 and others 3-6 have suggested a variety of chemical and instrumental reasons why it might not be valid to account for a particular set of data

P. Schuck and A. P. Minton are at the Section of Physical Biochemistry, Laboratory of Biochemical Pharmacology, National Institute of Diabetes, Digestive and Kidney Diseases, National institutes of Health, Bethesda, MD 20892, USA. Emaih [email protected] or [email protected]

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using this model, including neglect of mass transport, steric hindrance and/or the possibility of more-complex binding schemes. The purpose of the present communication is twofold: (1) to describe two simple tests for the internal self-consistency of results obtained from analysis of biosensor data in the context of this elementary model; and (2) to argue that all such analyses be subjected to these tests before either submission or acceptance for publication. Assume that the concentration of free ligand remains constant at a value of L0 throughout the time course of the association phase of the experiment, and at a value of zero throughout the time course of the dissociation phase of the experiment. With the additional conventional assumption that the difference between the biosensor signal, R, and the baseline signal, R0, is proportional to the time-dependent concentration of LA, the reaction scheme above leads to the following descriptions of the time course of the observed signal R (Ref. 7): Association: R(t) = R0,a+ (R~a- R0,a) [1 - exp(-kobst)]

(1) Published by ElsevierScienceLtd

where R0a denotes the signal at the start of tfie association experiment; R a denotes the signal at infinite time in th~ association experiment O.e. at attainment of association equilibrium); R0, d denotes the signal at the start of the dissociation experiment; and R, d denotes the signal at infinite time in the dissociation experiment (i.e. when reversibly bound ligand has been fully dissociated) and: kobs = k+L0 + k

(3)

Typically, association experiments are carried out at several different values of L0. For each experiment, the values of kobs and R a can be evaluated either from linear regression of a plot of dR/dt vs R (Ref. 8) or by directly fitting an expression of the form of Eqn 1 to the raw data 7. The values of k and k_ are then determined by linear regression of the dependence of kobs on L0. The value of k_ might be obtained from the dissociation experiment by directly fitting an expression of the form of Eqn 2 to the raw dissociation data 7, or by fitting a straight line to a logarithmic first-order dissociation plot 8. If the simple binding model is correct, then the values of R a obtained at different values of L0 ~hould be related by a simple Langmuir isotherm s* . L0 R~,a(L0) = RO,a + [Rsat - Ro,a]~ (4) K~"§ L o The values of K~q,the equilibrium dissociation constant, and Rsat, the signed

*The Langmuirisotherm describes the dependence of reversiblybound ligand upon free ligand concentration at equilibrium that is expected for multiple identical sites binding ligand independentlyof each other.

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corresponding to complete saturation of immobilized acceptor with ligand, might be evaluated by direct fitting of Eqn 4 to the observed dependence of R on L0, or by an equivalent Scatchard analysis8,9. If Eqns 1--4 are approximately correct descriptions of the kinetic and equilibrium properties of the system, as measured by the biosensor, then the following two tests of internal consistency must be approximately obeyed. Consistency test 1. The value of the equilibrium constant K~q calculated from the dependence of R a on L0 according to Eqn 4 must be approximately equal to the value of the equilibrium constant Kkin calculated according to the thermodynamic relationship: k_ =

-

-

k+

Table I. Examples of published interpretations of biosensor data failing consistency test 1 Mobile species

Immobilized species

~ ~ (nM)

K~q (riM)a

Ref.

CrylA(c)

8BMV from susceptible P. xylostella larvae BBMV from resistant P. xylostella larvae Phosphopeptide Y751P rhlL-5

7.10

>6 x 102

11 (Fig. 5)

8.93

>3.6 x 102

11 (Fig. 6)

42 9

~1.3 ~ 5 x 102

12 (Fig. 1) 13 (Fig. 7)

CrylA(c) p85~ N-SH2 SI-~RED FLAG

aSignals are extrapolated from given signals R(t) to equilibrium values with binding rate constants kobs (Lo) as given in the publications according to Reo= R(t) x [1-exp(-kobs • t)] -1. According to these rate constants and the observation time interval, br~ding equilibria were virtually reached for the highest applied ligand concentrations, and for the lowest ligand concentration, the plateau equilibrium value was less than 25% higher than the last observed data point of the association phase. Although this method does not take into account possible small baseline offsets that contribute to the observed signals, calculations show that this effect does not qualitatively alter the magnitude of the inconsistencies between K~Qand K~in.

(5)

Table I shows results, taken from several recent papers, that qualitatively fail this consistency test. Consistency test 2a, The value of k calculated using linear regression of the dependence of kobs on L0 according to Eqn 3, denoted by k~s, should be approximately equal to the value of k determined directly from the dissociation experiment, denoted by kdi'. Consistency test 2b. It has been argued that owing to uncertainty in the values of kobs, the value of k_~s~ might be poorly defined 7,8. However uncertain this value is, it must still be greater than zero. Moreover, both kobs and kd~ss are readily measurable. It follows from Eqn 3 that kobs > k_ for all values of L0. Thus selfconsistency requires, at a minimum, that kobs > kd_iss for all L0. Table 1I shows results, taken from several recent publications, that qualitatively fail these consistency tests.

Discussion Given that all experimental results are subject to some degree of uncertainty, one might ask the following question: by how much can the various quantities compared in the consistency tests described above differ without invalidating the underlying assumption of the validity of the simple binding model? A rigorous answer to this question would involve statistical tests of significance1~ a discussion of which is beyond the scope of this brief note. However, as a rough guideline, we suggest that if the quantity A is measured with a precision of AA and the quantity B is measured with a precision of ~B, then the values of A and B could be regarded as significantly, different, if the ratio of the greater to the lesser of the two quantities exceeds one by substantially more than AA/A + AB/B. It should be noted that all of the compared quantities in Tables I and II exhibit much larger discrepancies, amounting to one or more orders of magnitude. We emphasize that satisfaction of the self-consistency requirements listed above is a necessary, but not sufficient, condition for the establishment of the validity of the simple binding model

described above. For example, we have found that under mass-transport limited conditions, apparent values of k+ and k derived from analysis of data in the context of the elementary model might be reduced from their actual values by large factors (up to several orders of magnitude) that are the same, or nearly the same, for the association and dissociation phases of the experiment I. Under such conditions, the ratio of the two rate constants would be approximately equal to the true equilibrium constant, even though each rate constant was qualitatively incorrect. The results shown in Tables I and If do not represent an exhaustive list of all inconsistencies found in our search of the recent literature, but rather a sampling of the most obvious. It is our view, based upon the results of this search, that the results of analysis of biosensor data according to the elementary model described above be subjected to one or preferably both of the simple self-consistency tests presented here before submission for publication. If the rate and equilibrium constants derived from analysis of the biosensor data in the context of Eqns 1--4 do not approximately

Table II. Examples of published interpretations of biosensor data failing consistency test 2 Mobile species

Immobilized species

rML ZAP-70 SH2 p85e N-SH2

glycopeptide CD3e ITAM phosphopeptide Y751P protein R2 PDGFR 1009 1-13 pY peptide HS(CH2)11(NANP)6 Y

protein R1 GST-SH2 mAb

Smallest observed kobs [sec -1]

kdiss [sec-1] a <<10 ~4d

kass [sec-1] b

kdiss [sec-1]c

Fails test

2.6 x 104 ~-0.001 ~0.003

0,13

2a 2b 2b

<0.001 0.005

0.14

~0.04 ~0.004

0.055 0.015

-0.08 ~-0.001

2b 2b

~0.0008

0.0077 e

~-0.001

2b

Ref. 14 (Fig. 7) 15 (Rg. 2) 12 (Fig. 1 and Table 1) 16 (Fig. 5) 17 (Fig. 2 and Table 1) 18 (Fig. 7)

a kd_iss given in the publication, b kass determined using the linear regression of kobs(Lo)given in the publication and extrapolation to Lo = O. CDetermined using

Kd as reported from Scatchard analysis of the equilibrium-plateau-binding levels and k = Kd • k+. dObvious from plot of raw data of the dissociation phase (see Fig. 7 in Ref. 14), but ka_ss identified as dissociation rate constant, eFaster dissociating component of double exponential, identified as k .

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satisfy these tests, then this model is shown to be inappropriate and the parameter values derived therefrom of dubious value. We recommend that reviewers of submitted manuscripts containing such analyses insist on self-consistency as one criterion for acceptability for publication. Finally, we suggest that readers apply these extremely simple tests to already published results as one way (but not the only way2) of evaluating their trustworthiness.

Acknowledgments We thank D. Margulies for helpful comments.

References 1 Schuck, P. (1996) Biophys. J. 70, 1230-1249 2 Schuck, P. and Minton, A. P. (1996) Anal. Biochern. 240, 262-272 3 Glaser, R. W. (1993) Anal. Biochern. 213, 152-161 4 Karlsson, R., Roo,s, H., F&gerstarn,L. and Persson, B. (1994) in Methods: A Companion to Methods in Enzymology 6, 99-110 50'Shannessy, D. J. and Winzor, D. J. (1996) Anal. Biochern. 236, 275-283 6 Nieba, L., Krebber, A. and Pl(Jckthun,A. (1996) Anal. Biochern. 234, 155-165 70'Shannessy, D. J. et al. (1993) Anal. Biochern. 212, 457-468 8 Kadsson, R., Michaelsson, A. and Mattson, L. (1991) J. Irnrnunol. Methods 145, 229-240 9 Kalinin, N. L., Ward, L. D. and Winzor, D. J. (1995) Anal. Biochern. 228, 238-244

Tripping the switch fantastic: how a protein kinase cascade can convert graded inputs into switch.like outputs IIIIIIIII

James E. Ferrell, Jr Recent experimental work has shown that the mitogen-activated protein (MAP) kinase cascade can convert graded inputs into switch-like outputs. The cascade could therefore filter out noise (signals of insufficient magnitude or duration) and still respond decisively to supra-threshold stimuli. Here, we explore the biochemical mechanisms likely to be at the root of this behavior. THE MAP KINASE cascade is a set of three protein kinases - a MAP kinase kinase ldnase (MAPKKK), a MAP kinase kinase (MAPKK) and a MAP kinase (MAPK) - that function as a signal-relaying module 1-s (Fig. 1). MAPKKKs activate MAPKKs through the phosphorylation of two residues (usually serines); the active MAPKKs activate MAPKs through phosphorylation of a threonine and a tyrosine residue. MAP kinase cascades often receive inputs from plasma membrane-associated signaling molecules in response to extracellular stimuli. The cascades might also monitor the internal status of the cell. For example, MAP ldnase-like activities have been J. E. Ferrell, Jr is at the Department of Molecular Pharmacology,Stanford University School of Medicine, Stanford, CA 94305-5332, USA. Emaih [email protected]

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implicated in the spindle assembly checkpoint 7. MAP ldnase cascades have been found in animals, plants, fungi and protists. Many cells possess a number of MAP kinase cascades operating in parallel budding yeasts possess at least five, and mammalian cells at least three 1,s,6,8. Even a single MAP kinase cascade might bring about different changes in a cell's function in different contexts. For example, the well-studied cascade comprising Raf-1 (a MAPKKK), Meks 1 and 2 (MAPKKs), and Erks 1 and 2 (MAPKs) can trigger mitogenesis in many tissue culture ceils, transdifferentiation or mitogenesis in PC12 cells, cell-fate induction in developing embryos, and activation of Cdc2-cyclin B complexes in oocytes 4,9,10. Thus, MAP kinase cascades are evolutionarily conserved and biologically versatile; evidently the three-kinase scheme has been a successful way of 9 1996, Elsevier Science Ltd

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10 Remington, R. D. (1970) in Statistics with Applications to the Biological and Health

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transmitting information. But why are three kinases employed rather than one? The adenylate cyclase-cAMP signaling system transmits signals from the membrane to the nucleus using a single protein kinase, protein kinase A. The JAKSTAT systems also use a single kinase. Why are there so many intermediaries in the MAP kinase system?

The magnitude of the response: signal amplification One attractive possibility is that a three-kinase system provides the cell with a high degree of signal amplification, in the same way that a photomultiplier tube converts a small pulse of photons into a large photocurrent. If each kinase rapidly phosphorylates, for example, 1000 target molecules, then the cascade would produce a heroic 109-fold amplification. This degree of amplification is probably unnecessary and, in fact,

Input

Output Figure 1 The mitogen-activated protein kinase (MAPK) cascade. MAPKKK denotes MAP kinase kinase kinase; MAPKK denotes MAP kinase kinase. PII: S0968-0004(96)20026-X