@article{zhang_ahn_lin_park_2006, title={Gene selection using support vector machines with non-convex penalty}, volume={22}, ISSN={["1460-2059"]}, DOI={10.1093/bioinformatics/bti736}, abstractNote={With the development of DNA microarray technology, scientists can now measure the expression levels of thousands of genes simultaneously in one single experiment. One current difficulty in interpreting microarray data comes from their innate nature of 'high-dimensional low sample size'. Therefore, robust and accurate gene selection methods are required to identify differentially expressed group of genes across different samples, e.g. between cancerous and normal cells. Successful gene selection will help to classify different cancer types, lead to a better understanding of genetic signatures in cancers and improve treatment strategies. Although gene selection and cancer classification are two closely related problems, most existing approaches handle them separately by selecting genes prior to classification. We provide a unified procedure for simultaneous gene selection and cancer classification, achieving high accuracy in both aspects.In this paper we develop a novel type of regularization in support vector machines (SVMs) to identify important genes for cancer classification. A special nonconvex penalty, called the smoothly clipped absolute deviation penalty, is imposed on the hinge loss function in the SVM. By systematically thresholding small estimates to zeros, the new procedure eliminates redundant genes automatically and yields a compact and accurate classifier. A successive quadratic algorithm is proposed to convert the non-differentiable and non-convex optimization problem into easily solved linear equation systems. The method is applied to two real datasets and has produced very promising results.MATLAB codes are available upon request from the authors.}, number={1}, journal={BIOINFORMATICS}, author={Zhang, HH and Ahn, J and Lin, XD and Park, C}, year={2006}, month={Jan}, pages={88–95} }
 @article{kaur_park_lewis_haugh_2006, title={Quantitative model of Ras-phosphoinositide 3-kinase signalling cross-talk based on co-operative molecular assembly}, volume={393}, ISSN={["1470-8728"]}, DOI={10.1042/bj20051022}, abstractNote={In growth-factor-stimulated signal transduction, cell-surface receptors recruit PI3Ks (phosphoinositide 3-kinases) and Ras-specific GEFs (guanine nucleotide-exchange factors) to the plasma membrane, where they produce 3′-phosphorylated phosphoinositide lipids and Ras-GTP respectively. As a direct example of pathway networking, Ras-GTP also recruits and activates PI3Ks. To refine the mechanism of Ras–PI3K cross-talk and analyse its quantitative implications, we offer a theoretical model describing the assembly of complexes involving receptors, PI3K and Ras-GTP. While the model poses the possibility that a ternary receptor–PI3K–Ras complex forms in two steps, it also encompasses the possibility that receptor–PI3K and Ras–PI3K interactions are competitive. In support of this analysis, experiments with platelet-derived growth factor-stimulated fibroblasts revealed that Ras apparently enhances the affinity of PI3K for receptors; in the context of the model, this suggests that a ternary complex does indeed form, with the second step greatly enhanced through membrane localization and possibly allosteric effects. The apparent contribution of Ras to PI3K activation depends strongly on the quantities and binding affinities of the interacting molecules, which vary across different cell types and stimuli, and thus the model could be used to predict conditions under which PI3K signalling is sensitive to interventions targeting Ras.}, number={1}, journal={BIOCHEMICAL JOURNAL}, publisher={Portland Press Ltd.}, author={Kaur, H and Park, CS and Lewis, JM and Haugh, JM}, year={2006}, month={Jan}, pages={235–243} }
 @article{park_schneider_haugh_2003, title={Kinetic analysis of platelet-derived growth factor receptor/phosphoinositide 3-kinase/Akt signaling in fibroblasts}, volume={278}, ISSN={["0021-9258"]}, DOI={10.1074/jbc.M304968200}, abstractNote={Isoforms of the serine-threonine kinase Akt coordinate multiple cell survival pathways in response to stimuli such as platelet-derived growth factor (PDGF). Activation of Akt is a multistep process, which relies on the production of 3′-phosphorylated phosphoinositide (PI) lipids by PI 3-kinases. To quantitatively assess the kinetics of PDGF receptor/PI 3-kinase/Akt signaling in fibroblasts, a systematic study of this pathway was performed, and a mechanistic mathematical model that describes its operation was formulated. We find that PDGF receptor phosphorylation exhibits positive cooperativity with respect to PDGF concentration, and its kinetics are quantitatively consistent with a mechanism in which receptor dimerization is initially mediated by the association of two 1:1 PDGF/PDGF receptor complexes. Receptor phosphorylation is transient at high concentrations of PDGF, consistent with the loss of activated receptors upon endocytosis. By comparison, Akt activation responds to lower PDGF concentrations and exhibits more sustained kinetics. Further analysis and modeling suggest that the pathway is saturated at the level of PI 3-kinase activation, and that the p110α catalytic subunit of PI 3-kinase contributes most to PDGF-stimulated 3′-PI production. Thus, at high concentrations of PDGF the kinetics of 3′-PI production are limited by the turnover rate of these lipids, while the Akt response is additionally influenced by the rate of Akt deactivation. Isoforms of the serine-threonine kinase Akt coordinate multiple cell survival pathways in response to stimuli such as platelet-derived growth factor (PDGF). Activation of Akt is a multistep process, which relies on the production of 3′-phosphorylated phosphoinositide (PI) lipids by PI 3-kinases. To quantitatively assess the kinetics of PDGF receptor/PI 3-kinase/Akt signaling in fibroblasts, a systematic study of this pathway was performed, and a mechanistic mathematical model that describes its operation was formulated. We find that PDGF receptor phosphorylation exhibits positive cooperativity with respect to PDGF concentration, and its kinetics are quantitatively consistent with a mechanism in which receptor dimerization is initially mediated by the association of two 1:1 PDGF/PDGF receptor complexes. Receptor phosphorylation is transient at high concentrations of PDGF, consistent with the loss of activated receptors upon endocytosis. By comparison, Akt activation responds to lower PDGF concentrations and exhibits more sustained kinetics. Further analysis and modeling suggest that the pathway is saturated at the level of PI 3-kinase activation, and that the p110α catalytic subunit of PI 3-kinase contributes most to PDGF-stimulated 3′-PI production. Thus, at high concentrations of PDGF the kinetics of 3′-PI production are limited by the turnover rate of these lipids, while the Akt response is additionally influenced by the rate of Akt deactivation. Platelet-derived growth factor (PDGF) 1The abbreviations used are: PDGF, platelet-derived growth factor; PI, phosphoinositide; PtdIns, phosphatidylinositol; PH, pleckstrin homology; PDK, 3-phosphoinositide-dependent protein kinase; DMEM, Dulbecco's modified Eagle medium; BSA, bovine serum albumin; PBS, phosphate-buffered saline; ELISA, enzyme-linked immunosorbent assay; TIRF, total internal reflection fluorescence.1The abbreviations used are: PDGF, platelet-derived growth factor; PI, phosphoinositide; PtdIns, phosphatidylinositol; PH, pleckstrin homology; PDK, 3-phosphoinositide-dependent protein kinase; DMEM, Dulbecco's modified Eagle medium; BSA, bovine serum albumin; PBS, phosphate-buffered saline; ELISA, enzyme-linked immunosorbent assay; TIRF, total internal reflection fluorescence. is a polypeptide mitogen of broad specificity, one of the earliest and most potent serum factors to be isolated (1Heldin C. Westermark B. Physiol. Rev. 1999; 79: 1283-1316Crossref PubMed Scopus (1932) Google Scholar). Beyond signaling of proliferation, PDGF acts as a strong chemoattractant during wound healing and can mediate protection from apoptosis in response to serum withdrawal and certain stress stimuli (2Deuel T.F. Kawahara R.S. Mustoe T.A. Pierce G.F. Annu. Rev. Med. 1991; 42: 567-584Crossref PubMed Scopus (176) Google Scholar, 3Harrington E.A. Bennett M.R. Fanidi A. Evan G.I. EMBO J. 1994; 13: 3286-3295Crossref PubMed Scopus (732) Google Scholar). Three forms of PDGF have been studied extensively. They are composed of disulfide-bonded homo- and heterodimers of A and B chains, of which PDGF-BB is the best characterized. There are two structurally related PDGF receptors, α and β, which exhibit different affinities for the A chain but roughly equivalent affinities for the B chain (4Östman A. Thyberg B. Westermark B. Heldin C. Growth Factors. 1989; 1: 271-281Crossref PubMed Scopus (76) Google Scholar, 5Seifert R.A. Hart C.E. Phillips P.E. Forstrom J.W. Ross R. Murray M.J. Bowen-Pope D.F. J. Biol. Chem. 1989; 264: 8771-8778Abstract Full Text PDF PubMed Google Scholar). More recently, PDGF-C and -D isoforms, which form homodimers, have also been identified; these too exhibit different affinities for PDGF α- and β-receptors (6Li X. Pontén A. Aase K. Karlsson L. Abramsson A. Uutela M. Bäckström G. Hellström M. Boström H. Li H. Soriano P. Betsholtz C. Heldin C. Alitalo K. Östman A. Eriksson U. Nat. Cell Biol. 2000; 2: 302-309Crossref PubMed Scopus (493) Google Scholar, 7Bergsten E. Uutela M. Li U. Pietras K. Östman A. Heldin C. Alitalo K. Eriksson U. Nat. Cell Biol. 2001; 3: 512-516Crossref PubMed Scopus (456) Google Scholar, 8LaRochelle W.J. Jeffers M. McDonald W.F. Chillakuru R.A. Giese N.A. Lokker N.A. Sullivan C. Boldog F.L. Yang M. Corine-Vernet C. Burgess C.E. Fernandes E. Deegler L.L. Rittman B. Shimkets J. Shimkets R.A. Rothberg J.M. Lichenstein H.S. Nat. Cell Biol. 2001; 3: 517-521Crossref PubMed Scopus (309) Google Scholar). PDGF receptors belong to the well studied class of signal transducers collectively known as receptor-tyrosine kinases (9van der Geer P. Hunter T. Lindberg R.A. Annu. Rev. Cell Biol. 1994; 10: 251-337Crossref PubMed Scopus (1233) Google Scholar, 10Schlessinger J. Cell. 2000; 103: 211-225Abstract Full Text Full Text PDF PubMed Scopus (3456) Google Scholar). As with other receptors of this class, ligand-induced dimerization of PDGF receptors activates their intrinsic kinase domains, which catalyze the autophosphorylation of the receptors on multiple intracellular tyrosine residues in trans (11Kelly J.D. Haldeman B.A. Grant F.J. Murray M.J. Seifert R.A. Bowen-Pope D.F. Cooper J.A. Kazlauskas A. J. Biol. Chem. 1991; 266: 8987-8992Abstract Full Text PDF PubMed Google Scholar, 12Heldin C. Östman A. Rönnstrand L. Biochim. Biophys. Acta. 1998; 1378: F79-F113PubMed Google Scholar, 13Emaduddin M. Ekman S. Ronnstrand L. Heldin C. Biochem. J. 1999; 341: 523-528Crossref PubMed Scopus (16) Google Scholar). The phosphorylated receptor may then act as a scaffold for specific binding interactions with cytosolic signal transduction enzymes and adaptor proteins (14Claesson-Welsh L. J. Biol. Chem. 1994; 269: 32023-32026Abstract Full Text PDF PubMed Google Scholar). Among the most important of these are isoforms of phosphoinositide (PI) 3-kinase, which phosphorylate phosphatidylinositol (PtdIns) lipids in cell membranes to produce the 3′-PI second messengers PtdIns(3)P, PtdIns(3,4)P2, and PtdIns(3,4,5)P3 (15Fruman D.A. Meyers R.E. Cantley L.C. Annu. Rev. Biochem. 1998; 67: 481-507Crossref PubMed Scopus (1297) Google Scholar, 16Vanhaesebroeck B. Leevers S.J. Ahmadi K. Timms J. Katso R. Driscoll P.C. Woscholski R. Parker P.J. Waterfield M.D. Annu. Rev. Biochem. 2001; 70: 535-602Crossref PubMed Scopus (1347) Google Scholar). The 110 kDa α and β isoforms of the PI 3-kinase catalytic subunit are involved in receptor-tyrosine kinase signaling, and they almost exclusively phosphorylate PtdIns(4,5)P2 to form PtdIns(3,4,5)P3, with PtdIns(3,4)P2 generated from the subsequent dephosphorylation of PtdIns(3,4,5)P3. The 85 kDa regulatory subunit coordinates binding of PI 3-kinase to PDGF receptors through dual SH2 domains, transmitting a conformational change that activates the catalytic subunit (17Escobedo J.A. Kaplan D.R. Kavanaugh W.M. Turck C.W. Williams L.T. Mol. Cell. Biol. 1991; 11: 1125-1132Crossref PubMed Scopus (180) Google Scholar, 18McGlade C.J. Ellis C. Reedijk M. Anderson D. Mbamalu G.A.D.R. Panayotou G. End P. Bernstein A. Kazlauskas A. Waterfield M.D. Pawson T. Mol. Cell. Biol. 1992; 12: 991-997Crossref PubMed Google Scholar, 19Cooper J.A. Kashishian A. Mol. Cell. Biol. 1993; 13: 1737-1745Crossref PubMed Scopus (48) Google Scholar, 20Shoelson S.E. Sivaraja M. Williams K.P. Hu P. Schlessinger J. Weiss M.A. EMBO J. 1993; 12: 795-802Crossref PubMed Scopus (140) Google Scholar). Equally if not more important is the induced localization of PI 3-kinase in proximity to its plasma membrane-associated substrate (21Klippel A. Reinhard C. Kavanaugh W.M. Apell G. Escobedo M. Williams L.T. Mol. Cell. Biol. 1996; 16: 4117-4127Crossref PubMed Scopus (415) Google Scholar). Cellular roles for 3′-PIs are now appreciated (22Toker A. Cantley L.C. Nature. 1997; 387: 673-676Crossref PubMed Scopus (1216) Google Scholar, 23Rameh L.E. Cantley L.C. J. Biol. Chem. 1999; 274: 8347-8350Abstract Full Text Full Text PDF PubMed Scopus (847) Google Scholar). Their general mechanism of action is the membrane recruitment and activation of signaling proteins containing pleckstrin homology (PH) domains, such as the serine-threonine kinase Akt. Akt isoforms are activated in response to PDGF and other factors in a strictly PI 3-kinase-dependent manner (24Franke T.F. Yang S. Chan T.O. Datta K. Kazlauskas A. Morrison D.K. Kaplan D.R. Tsichlis P.N. Cell. 1995; 81: 727-736Abstract Full Text PDF PubMed Scopus (1810) Google Scholar, 25Datta K. Bellacosa A. Chan T.O. Tsichlis P.N. J. Biol. Chem. 1996; 271: 30835-30839Abstract Full Text Full Text PDF PubMed Scopus (260) Google Scholar) and have been strongly implicated in multiple cell survival pathways (26Datta S.R. Dudek H. Tao X. Masters S. Fu H. Gotoh Y. Greenberg M.E. Cell. 1997; 91: 231-241Abstract Full Text Full Text PDF PubMed Scopus (4895) Google Scholar, 27Romashkova J.A. Makarov S.S. Nature. 1999; 401: 86-90Crossref PubMed Scopus (1654) Google Scholar). The recruitment of Akt to the plasma membrane, through transient interaction of its PH domain with PtdIns(3,4,5)P3 or PtdIns(3,4)P2, is a necessary first step in Akt activation; sequential phosphorylation of Thr308 and Ser473 (residue positions in human Akt-1) completes the process (28Kohn A.D. Takeuchi F. Roth R.A. J. Biol. Chem. 1996; 271: 21920-21926Abstract Full Text Full Text PDF PubMed Scopus (407) Google Scholar, 29Andjelkovic M. Alessi D.R. Meier R. Fernandez A. Lamb N.J.C. Frech M. Cron P. Cohen P. Lucocq J.M. Hemmings B.A. J. Biol. Chem. 1997; 272: 31515-31524Abstract Full Text Full Text PDF PubMed Scopus (893) Google Scholar, 30Stokoe D. Stephens L.R. Copeland T. Gaffney P.R.J. Reese C.B. Painter G.F. Holmes A.B. McCormick F. Hawkins P.T. Science. 1997; 277: 567-570Crossref PubMed Scopus (1043) Google Scholar, 31Bellacosa A. Chan T.O. Ahmed N.N. Datta K. Malstrom S. Stokoe D. McCormick F. Feng J. Tsichlis P. Oncogene. 1998; 17: 313-325Crossref PubMed Scopus (450) Google Scholar). 3-Phosphoinositide-dependent protein kinase-1 (PDK-1) is recruited by PtdIns(3,4,5)P3 and catalyzes phosphorylation of Akt on Thr308, and a second, yet to be identified 3′-PI-dependent kinase (dubbed PDK-2) phosphorylates the critical Ser473 residue (32Alessi D.R. James S.R. Downes C.P. Holmes A.B. Gaffney P.R.J. Reese C.B. Cohen P. Curr. Biol. 1997; 7: 261-269Abstract Full Text Full Text PDF PubMed Google Scholar, 33Stephens L. Anderson K. Stokoe D. Erdjument-Bromage H. Painter G.F. Holmes A.B. Gaffney P.R.J. Reese C.B. McCormick F. Tempst P. Coadwell J. Hawkins P.T. Science. 1998; 279: 710-714Crossref PubMed Scopus (907) Google Scholar, 34Anderson K.E. Coadwell J. Stephens L.R. Hawkins P.T. Curr. Biol. 1998; 8: 684-691Abstract Full Text Full Text PDF PubMed Scopus (302) Google Scholar, 35Scheid M.P. Huber M. Damen J.E. Hughes M. Kang V. Neilsen P. Prestwich G.D. Krystal G. Duronio V. J. Biol. Chem. 2002; 277: 9027-9035Abstract Full Text Full Text PDF PubMed Scopus (146) Google Scholar). A detailed molecular level understanding of intracellular signal transduction, including the PDGF receptor/PI 3-kinase/Akt pathway, has thus emerged, yet our knowledge base is largely qualitative. To examine complexities such as the timing and duration of signal activation, which have been implicated as important factors governing cell function (36Marshall C.J. Cell. 1995; 80: 179-185Abstract Full Text PDF PubMed Scopus (4213) Google Scholar, 37Jones S.M. Klinghoffer R. Prestwich G.D. Toker A. Kazlauskas A. Curr. Biol. 1999; 9: 512-521Abstract Full Text Full Text PDF PubMed Scopus (128) Google Scholar), a more quantitative approach is warranted. To this end, we have made reasonably precise measurements of PDGF-stimulated activation of the PDGF receptor/PI 3-kinase/Akt signaling pathway in NIH 3T3 fibroblasts, at various times and over a range of PDGF concentrations. We were thus able to assess the sensitivity of each step in the pathway, with respect to both the magnitude and kinetics of the response. Accompanying this analysis is a proposed model that describes the pathway in mathematical terms, with a minimum number of rate parameters. We find that activation of Akt is saturated with respect to PDGF receptor phosphorylation, apparently at the level of activating PI 3-kinases. Thus, at higher concentrations of PDGF the kinetics of 3′-PI production and activation of Akt are sustained and largely limited by the rate of 3′-PI turnover. Although we found that both p110α and p110β catalytic subunits of PI 3-kinase are recruited by PDGF receptors in our cells, our results suggest that p110α contributes most to 3′-PI production and Akt activation. Another primary result of our modeling and analysis concerns the mechanism of PDGF receptor dimerization. We report that a model in which dimeric PDGF ligand binds to one receptor molecule and then cross-links a second, unbound receptor is neither quantitatively nor qualitatively consistent with our data. On the other hand, our data is completely consistent with a model in which dimerization requires the association of two 1:1 ligand-receptor complexes as an initial step, perhaps with formation of a stable 1:2 complex thereafter. Reagents and Antibodies—All tissue culture reagents were purchased from Invitrogen. Human recombinant PDGF-BB was from Peprotech, and LY294002 was from Calbiochem. Antibodies against the extracellular domain of PDGF β-receptor were from Oncogene Research Products (PC-17, without bovine serum albumin), and horseradish peroxidase-conjugated Fab fragments recognizing phosphotyrosine (RC20) were from Transduction Laboratories. Antibodies against the Akt 1/2 N terminus and the peptide substrate for Akt were from Santa Cruz Biotechnology, and [γ-32P]ATP was from PerkinElmer Life Sciences. Phosphospecific antibodies against Akt (pSer473) and PDGF β-receptor (pTyr751) were from Cell Signaling Technologies, antibodies against PI 3-kinase p110α and p110β isoforms were from Upstate Biotechnology, and protein A-Sepharose was from Zymed Laboratories Inc. Unless otherwise noted, all other reagents were from Sigma. Cell Culture and Preparation of Detergent Lysates—NIH 3T3 fibroblasts (American Type Culture Collection) were subcultured in 10-cm tissue culture dishes with Dulbecco's modified Eagle medium (DMEM) containing 10% fetal bovine serum, 2 mml-glutamine, and the antibiotics penicillin and streptomycin. Dishes to be processed on the same day were plated with equal numbers of cells and allowed to reach at least 90% confluency. The cells were incubated for 4 h in DMEM containing 2 mml-glutamine, the antibiotics penicillin and streptomycin, and 1 mg/ml fatty acid-free bovine serum albumin (BSA). At various times, PDGF-BB and other treatments were added to each plate at the final concentration indicated and incubated for the time interval specified at 37 °C in 5% CO2. At the end point of the experiment, each plate was washed once with ice-cold Dulbecco's phosphate-buffered saline (PBS) and then lysed in 500 μl of ice-cold buffer containing 50 mm HEPES, pH 7.4, 100 mm NaCl, 10% v/v glycerol, 1% v/v Triton X-100, 1 mm sodium orthovanadate, 10 mm sodium pyrophosphate, 50 mm β-glycerophosphate, pH 7.3, 5 mm sodium fluoride, 1 mm EGTA, and 10 μg/ml each aprotinin, leupeptin, pepstatin A, and chymostatin. After scraping insoluble debris and transferring to an Eppendorf tube, the lysates were vortexed briefly, incubated on ice for 20 min, and clarified by centrifugation. The supernatants were collected and stored frozen at –80 °C until use. Protein assays (Micro BCA, Pierce) were used to confirm that lysates collected on the same day contained roughly equivalent total protein concentrations. Enzyme-linked Immunosorbent Assay (ELISA) of PDGF β Receptor Phosphorylation—Opaque, high protein binding microtiter plates (Corning) were coated overnight with at least 375 ng of capture antibody recognizing the PDGF β-receptor extracellular domain per well. The wells were then incubated with ELISA blocking buffer (10% v/v horse serum, 0.05% v/v Tween-20 in PBS) for 1 h at room temperature. After washing once with the same buffer, each well was incubated with 50 μl of ELISA blocking buffer plus 50 μl of cell lysate for 90 min with agitation at room temperature, followed by extensive washing with high salt buffer (10 mm Tris-HCl, pH 7.5, 500 mm NaCl, 0.1% Tween-20, and 0.1% SDS). Wells were then incubated with horseradish peroxidase-conjugated anti-phosphotyrosine Fab fragments at 0.2 μg/ml in ELISA blocking buffer for 1 h at room temperature, followed by more washes with high salt buffer. Finally, substrate solution (ELISA Femto, Pierce) was applied, and the relative light signals were acquired using a microplate luminometer (Wallac Microbeta). Akt Kinase Activity Assay—High protein binding microtiter plates (Corning) were incubated overnight with 500 ng/well protein G in carbonate buffer, followed by washes with carbonate buffer alone. The wells were then incubated with anti-Akt antibodies at 500 ng/well in carbonate buffer for 2 h with agitation at room temperature. This solution was removed, and BSA blocking buffer (10 mg/ml BSA, 0.05% Tween 20 in PBS) was added for 1 h at room temperature. After washing once with BSA blocking buffer, 25 μl of BSA blocking buffer and 50 μl of cell lysate were added to each well and incubated for 90 min with agitation at room temperature. After washing three times with BSA blocking buffer and twice with reaction buffer (20 mm Tris-HCl, pH 7.5, 5 mm β-glycerophosphate, pH 7.3, 1 mm EGTA, 0.2 mm dithiothreitol, and 0.1 mg/ml fatty acid-free BSA), each well was incubated with 80 μl of reaction buffer supplemented with 1 μg of peptide substrate, 1 μm ATP, 2 μCi [γ-32P]ATP, and 15 mm MgCl2 for 1 h with agitation at room temperature. The reaction was stopped by adding 80 μl of 100 mm H3PO4 to each well. From each well 100 μl was carefully transferred to the corresponding well in a phosphocellulose filter-bottom plate (Millipore), pre-equilibrated with 100 mm H3PO4. After extensive washing with 100 mm H3PO4 and then 75% ethanol, the filter plate was dried and counted with 40 μl of scintillation fluid per well in a microplate scintillation counter (Wallac Microbeta). Quantitative Immunoblotting—Pooled cell lysates were subjected to SDS-PAGE in 20 cm-wide gels using standard techniques. When immunoprecipitations were performed, each lysate was first incubated with 5 μg of capture antibodies and 25 μl of protein A-Sepharose for 2 h at 4 °C, followed by extensive washing with lysis buffer. After gel electrophoresis, proteins were transferred to PVDF membrane (Immobilon, Millipore) and probed with the indicated antibodies. The blots were incubated with chemiluminescence substrates (Pierce) and imaged using a high sensitivity CCD camera (BioRad Fluor S-Max). All pixel intensities were within the dynamic range. Total Internal Reflection Fluorescence (TIRF) Microscopy—This technique was performed essentially as described (38Haugh J.M. Codazzi F. Teruel M. Meyer T. J. Cell Biol. 2000; 151: 1269-1279Crossref PubMed Scopus (254) Google Scholar). Our microscope was equipped with a Melles Griot tunable wavelength laser (60 mW at 488 nm), Zeiss upright stand, Ludl emission filter wheel with Chroma filters, and Hamamatsu ORCA ER digital CCD. The Akt PH domain was cloned into pEGFP-C1 (Clontech) to express the GFP-AktPH construct in mammalian cells. Cells were plated onto glass cover slips coated with poly-d-lysine and later transfected with GFP-AktPH using LipofectAMINE Plus (Invitrogen). The following day, the cells were incubated in serum-free medium for 4 h and then visualized on the microscope. The stage was enclosed in a chamber maintained at 37 °C, and the imaging buffer was composed of 20 mm HEPES pH 7.4, 125 mm NaCl, 5 mm KCl, 1.5 mm MgCl2, 1.5 mm CaCl2, 10 mm glucose, and 2 mg/ml fatty acid-free BSA, to which PDGF-BB and other treatments were added at the times indicated. Images were acquired and analyzed using Metamorph software (Universal Imaging). Estimation of Integrated Responses—As an estimation of the integral of a measured variable with respect to time, the trapezoidal rule in Equation 1 was employed. ∫0tNy(t)dt≈12∑i=0N-1(yi+1+yi)(ti+1-ti)(Eq. 1) Dividing the time integral by the total duration of the time course tN yields the time-averaged value of the measurement. This was found to be a robust way of normalizing data from time course experiments collected on different days. Model Computation—The coupled ordinary differential equations were solved by numerical integration using Excel. Parameter optimization was performed using the Solver tool, minimizing the sum of absolute deviations (least-squares minimization showed bias toward agreement with data for higher PDGF concentrations). Numerical accuracy was confirmed by comparing model output with different time intervals. Model calculations using the stiff ODE solver in MATLAB gave essentially identical results. Quantitative Measurements of PDGF β Receptor Autophosphorylation Kinetics Reveal a Positively Cooperative Activation Mechanism—Tyrosine phosphorylation of the PDGF β receptor, the hallmark of receptor dimerization and kinase activation, was measured in detergent lysates of NIH 3T3 fibroblasts using a quantitative sandwich ELISA assay. In control experiments, it was confirmed that this measurement is linear with respect to the amount of lysate protein incubated in the wells under the conditions of our assay. Tissue culture plates containing equal numbers of cells were stimulated with PDGF-BB concentrations of 0.05, 0.1, 0.2, 0.5, 1, 3, or 10 nm for durations of 2, 5, 10, or 20 min on the same day. Lysates from two unstimulated plates were also prepared. Each lysate was assayed in duplicate, and the procedure was replicated on five different days. The phosphorylation signal at each condition was normalized by the time-averaged 10 nm phosphorylation signal, integrated numerically over the 20-min time course, obtained on the same day. The means of the five experiments are displayed in Fig. 1A, as a function of time for the various doses of PDGF. At low concentrations of PDGF-BB (below 0.5 nm), tyrosine phosphorylation of the PDGF β-receptor achieves a steady state, and the plateau value is sensitive to PDGF-BB concentration in this regime. At higher ligand concentrations (above 0.5 nm), receptor phosphorylation is clearly transient, exhibiting a maximum value at 2–5 min. As the concentration of PDGF-BB is increased, the peak phosphorylation level becomes less sensitive to ligand concentration, and the peak occurs at increasingly earlier times. Another feature observed in the data is the presence of positive cooperativity with respect to PDGF concentration. At low concentrations of PDGF, doubling the ligand concentration yielded gains in receptor phosphorylation of 3–4-fold. Consistent with this, the peak receptor phosphorylation levels over the entire range of PDGF doses exhibit an observed Hill coefficient of 1.6, as shown in Fig. 1B. Receptor activation from 10 to 90% maximum is achieved within roughly one log of PDGF concentration, rather than the two logs predicted from single-site ligand-receptor binding. The Activities of PI 3-Kinase and Akt Are Saturated with Respect to the Number of Phosphorylated PDGF Receptors, with No Apparent Cooperativity—From the same NIH 3T3 lysates used to measure PDGF β receptor phosphorylation at various PDGF concentrations and times, we assessed the activation of Akt by in vitro kinase assay. As in the PDGF receptor phosphorylation ELISA, great care was taken here to ensure that the measurement was sensitive to dilution of the lysate applied to the wells coated with anti-Akt antibodies, and all measurements were made in duplicate. The Akt activation time courses, displayed in Fig. 2A, are clearly distinct from the kinetics of PDGF β-receptor phosphorylation. In terms of the dose response, half-maximal Akt activation is observed between 0.1 and 0.2 nm PDGF, and at PDGF concentrations above 0.5 nm, the Akt activation kinetics are insensitive to PDGF dose and more sustained in relation to receptor phosphorylation. These observations suggest that the ability of the cell to activate Akt is saturated with respect to phosphorylated PDGF receptors. To further assess the relationship between receptor phosphorylation and Akt activity, the two responses were correlated. When a signal is integrated over time, the resulting quantity is sensitive to both the magnitude and kinetics of the response. In Fig. 2B, the time-integrated Akt activity is plotted as a function of the associated time-integral of PDGF receptor phosphorylation for each concentration of PDGF-BB to assess the sensitivity of this relationship, which we term the receptor-signal response curve. In terms of time integrals, Akt activation is 50% maximal when receptor phosphorylation is only ∼10% of its maximum value. In addition, the relationship does not exhibit apparent positive cooperativity; a Hill coefficient of 1 fit the data well, far better than values of 1.5 or higher. In previous work with the same cells, the PDGF dose response and kinetics of 3′-PI production were reported (38Haugh J.M. Codazzi F. Teruel M. Meyer T. J. Cell Biol. 2000; 151: 1269-1279Crossref PubMed Scopus (254) Google Scholar), showing the same essential features observed here for Akt activation. Half-maximal 3′-PI production was stimulated in the range of 0.1–0.3 nm PDGF-BB, and at PDGF-BB concentrations of 1 nm and above, the kinetics were sustained and insensitive to PDGF concentration. These observations indicate that the pathway is saturated upstream of Akt, at the level of PI 3-kinase activation. The lack of cooperativity in Fig. 2B further suggests a roughly linear relationship between the 3′-PI level and Akt activation. Akt Activation Correlates with Receptor-mediated Recruitment of PI 3-Kinase p110α; Higher Levels of PDGF Receptor Phosphorylation Are Required to Recruit PI 3-Kinase p110β— We sought to confirm the relationship between PDGF receptor phosphorylation and Akt activation using alternative assays, and to further explore the saturation of the pathway at the level of PI 3-kinase activation. Lysates of cells stimulated with PDGF-BB for 10 min were pooled from 3 days of experiments. As shown in Fig. 3A, anti-phosphotyrosine immunoblotting of cell lysate proteins yielded intense bands at just below 200 kDa, attributed to the phosphorylation of PDGF β-as well as α-receptors dimerized in the plasma membrane. The band intensity is half-maximal at roughly 0.5 nm PDGF-BB, in accord with the ELISA measurements (Fig. 1). A similar pattern was observed when the same lysate proteins were blotted with an antibody recognizing pTyr751 of PDGF β-receptor (residue in the human receptor), one of the PI 3-kinase p85 binding sites. Akt activities in the same lysates were assessed by immunoblotting with phospho-Akt-specific antibodies. Half-maximal activation was observed between 0.1–0.2 nm PDGF-BB, in agreement with our in vitro Akt kinase assays. In parallel, the same lysates were subjected to immunoprecipitation with antibodies against the p110α or p110β catalytic subunit of PI 3-kinase, and the recovered proteins were probed for phosphotyrosine (Fig. 3B). Bands corresponding to PDGF receptors were readily detected in both cases, presumably reflecting the PDGF receptor-mediated recruitment of p85-p110 complexes; however, recruitment of p110α and p110β followed markedly different patterns. Whereas p110α recruitment responded to low levels of receptor phosphorylation and reached saturation at 0.5 nm PDGF-BB and above, significant p110β recruitment required higher receptor phosphorylation levels. To the extent that formation of receptor-p85-p110 complexes is indicative of PI 3-kinase activation, these results suggest that Akt activation is more sensitive to recruitment of complexes containing p110α. The Kinetics of Akt Deactivation, in Relation to Changes in the 3′-PI Level, Reveal the Influences of 3′-PI Turnover and Akt Dephosphorylation—To address the relative rates of processes that influence the activation and deactivation of Akt, 3′-PI generation and Akt activity were measured in separate experiments designed to introduce rapid increases and decreases in PI 3-kinase activity. Total internal reflection fluorescence microscopy was used to monitor the kinetics of 3′-PI production in individual cells transfected with the fluorescent probe GFP-AktPH (38Haugh J.M. Codazzi F. Teruel M. Meyer T. J. Cell Biol. 2000; 151}, number={39}, journal={JOURNAL OF BIOLOGICAL CHEMISTRY}, publisher={American Society for Biochemistry & Molecular Biology (ASBMB)}, author={Park, CS and Schneider, IC and Haugh, JM}, year={2003}, month={Sep}, pages={37064–37072} }