Single-molecule force measurement via optical tweezers reveals different kinetic features of two BRaf mutants responsible for cardio-facial-cutaneous (CFC) syndrome

Cheng Wen; Chae-Seok Lim; Anpei Ye; J. Julius Zhu

doi:10.1364/BOE.4.002835

Single-molecule force measurement via optical tweezers reveals different kinetic features of two BRaf mutants responsible for cardio-facial-cutaneous (CFC) syndrome

Cheng Wen, Chae-Seok Lim, Anpei Ye, and J. Julius Zhu

Biomedical Optics Express
Vol. 4,
Issue 12,
pp. 2835-2845
(2013)
•https://doi.org/10.1364/BOE.4.002835

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Cheng Wen, Chae-Seok Lim, Anpei Ye, and J. Julius Zhu, "Single-molecule force measurement via optical tweezers reveals different kinetic features of two BRaf mutants responsible for cardio-facial-cutaneous (CFC) syndrome," Biomed. Opt. Express 4, 2835-2845 (2013)

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Related Topics
Table of Contents Category
- Optical Traps, Manipulation, and Tracking
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Medical optics and biotechnology (170.0170)
- Biology (170.1420)
- Optical confinement and manipulation (170.4520)
- Optical tweezers or optical manipulation (350.4855)

About this Article
History
- Original Manuscript: September 3, 2013
- Revised Manuscript: October 9, 2013
- Manuscript Accepted: October 23, 2013
- Published: November 14, 2013

Accessible

Open Access

Abstract

BRaf (B- Rapid Accelerated Fibrosarcoma) protein is an important serine/threonine-protein kinase. Two domains on BRaf can independently bind its upstream kinase, Ras (Rat Sarcoma) protein. These are the Ras binding domain (RBD) and cysteine-rich-domain (CRD). Herein we use customized optical tweezers to compare the Ras binding process in two pathological mutants of BRaf responsible for CFC syndrome, abbreviated BRaf (A246P) and BRaf (Q257R). The two mutants differ in their kinetics of Ras-binding, though both bind Ras with similar increased overall affinity. BRaf (A246P) exhibits a slightly higher Ras/CRD unbinding force and a significantly higher Ras/RBD unbinding force versus the wild type. The contrary phenomenon is observed in the Q257R mutation. Simulations of the unstressed-off rate, k_off(0), yield results in accordance with the changes revealed by the mean unbinding force. Our approach can be applied to rapidly assess other mutated proteins to deduce the effects of mutation on their kinetics compared to wild type proteins and to each other.

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Corrections

Cheng Wen, Chae-Seok Lim, Anpei Ye, and J. Julius Zhu, "Single-molecule force measurement via optical tweezers reveals different kinetic features of two BRaf mutants responsible for cardio-facial-cutaneous (CFC) syndrome: errata," Biomed. Opt. Express 6, 244-244 (2015)
https://www.osapublishing.org/boe/abstract.cfm?uri=boe-6-1-244

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References

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Publication

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[Crossref] [PubMed]
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[Crossref] [PubMed]
A. B. Vojtek, S. M. Hollenberg, and J. A. Cooper, “Mammalian RAS interacts directly with the serine/threonine kinase raf,” Cell 74(1), 205–214 (1993).
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[Crossref] [PubMed]
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[Crossref] [PubMed]
M. L. Bennink, S. H. Leuba, G. H. Leno, J. Zlatanova, B. G. de Grooth, and J. Greve, “Unfolding individual nucleosomes by stretching single chromatin fibers with optical tweezers,” Nat. Struct. Biol. 8(7), 606–610 (2001).
[Crossref] [PubMed]
M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]
M. Salomo, U. F. Keyser, M. Struhalla, and F. Kremer, “Optical tweezers to study single Protein A/Immunoglobulin G interactions at varying conditions,” Eur. Biophys. J. 37(6), 927–934 (2008).
[Crossref] [PubMed]
M. Carrion-Vazquez, A. F. Oberhauser, T. E. Fisher, P. E. Marszalek, H. Li, and J. M. Fernandez, “Mechanical design of proteins studied by single-molecule force spectroscopy and protein engineering,” Prog. Biophys. Mol. Biol. 74(1-2), 63–91 (2000).
[Crossref] [PubMed]
Q. Song, C. Wen, Y. Zhang, G. Wang, and A. Ye, “Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array,” Chin. Opt. Lett. 6, 1671–7694 (2008).
G. I. Bell, “Models for the specific adhesion of cells to cells,” Science 200(4342), 618–627 (1978).
[Crossref] [PubMed]
T. Erdmann, S. Pierrat, P. Nassoy, and U. S. Schwarz, “Dynamic force spectroscopy on multiple bonds: Experiments and model,” Europhys. Lett. 81(4), 48001 (2008).
[Crossref]

2011 (1)

F. Bordeleau, J. Bessard, N. Marceau, and Y. Sheng, “Measuring integrated cellular mechanical stress response at focal adhesions by optical tweezers,” J. Biomed. Opt. 16(9), 095005 (2011).
[Crossref] [PubMed]

2010 (1)

G. Hatzivassiliou, K. Song, I. Yen, B. J. Brandhuber, D. J. Anderson, R. Alvarado, M. J. C. Ludlam, D. Stokoe, S. L. Gloor, G. Vigers, T. Morales, I. Aliagas, B. Liu, S. Sideris, K. P. Hoeflich, B. S. Jaiswal, S. Seshagiri, H. Koeppen, M. Belvin, L. S. Friedman, and S. Malek, “RAF inhibitors prime wild-type RAF to activate the MAPK pathway and enhance growth,” Nature 464(7287), 431–435 (2010).
[Crossref] [PubMed]

2008 (4)

K. C. Neuman and A. Nagy, “Single-molecular force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nature Meth. 5, 1218 (2008).

M. Salomo, U. F. Keyser, M. Struhalla, and F. Kremer, “Optical tweezers to study single Protein A/Immunoglobulin G interactions at varying conditions,” Eur. Biophys. J. 37(6), 927–934 (2008).
[Crossref] [PubMed]

Q. Song, C. Wen, Y. Zhang, G. Wang, and A. Ye, “Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array,” Chin. Opt. Lett. 6, 1671–7694 (2008).

T. Erdmann, S. Pierrat, P. Nassoy, and U. S. Schwarz, “Dynamic force spectroscopy on multiple bonds: Experiments and model,” Europhys. Lett. 81(4), 48001 (2008).
[Crossref]

2006 (1)

T. Niihori, Y. Aoki, Y. Narumi, G. Neri, H. Cavé, A. Verloes, N. Okamoto, R. C. M. Hennekam, G. Gillessen-Kaesbach, D. Wieczorek, M. I. Kavamura, K. Kurosawa, H. Ohashi, L. Wilson, D. Heron, D. Bonneau, G. Corona, T. Kaname, K. Naritomi, C. Baumann, N. Matsumoto, K. Kato, S. Kure, and Y. Matsubara, “Germline KRAS and BRAF mutations in cardio-facio-cutaneous syndrome,” Nat. Genet. 38(3), 294–296 (2006).
[Crossref] [PubMed]

2003 (1)

C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421(6921), 423–427 (2003).
[Crossref] [PubMed]

2002 (1)

H. Davies, G. R. Bignell, C. Cox, P. Stephens, S. Edkins, S. Clegg, J. Teague, H. Woffendin, M. J. Garnett, W. Bottomley, N. Davis, E. Dicks, R. Ewing, Y. Floyd, K. Gray, S. Hall, R. Hawes, J. Hughes, V. Kosmidou, A. Menzies, C. Mould, A. Parker, C. Stevens, S. Watt, S. Hooper, R. Wilson, H. Jayatilake, B. A. Gusterson, C. Cooper, J. Shipley, D. Hargrave, K. Pritchard-Jones, N. Maitland, G. Chenevix-Trench, G. J. Riggins, D. D. Bigner, G. Palmieri, A. Cossu, A. Flanagan, A. Nicholson, J. W. C. Ho, S. Y. Leung, S. T. Yuen, B. L. Weber, H. F. Seigler, T. L. Darrow, H. Paterson, R. Marais, C. J. Marshall, R. Wooster, M. R. Stratton, and P. A. Futreal, “Mutations of the BRAF gene in human cancer,” Nature 417(6892), 949–954 (2002).
[Crossref] [PubMed]

2001 (3)

C. Peyssonnaux and A. Eychène, “The Raf/MEK/ERK pathway: new concepts of activation,” Biol. Cell 93(1-2), 53–62 (2001).
[Crossref] [PubMed]

J. A. Avruch, A. Khokhlatchev, J. M. Kyriakis, Z. Luo, G. Tzivion, D. Vavvas, and X. F. Zhang, “Ras activation of the Raf kinase: tyrosine kinase recruitment of the MAP kinase cascade,” Recent Prog. Horm. Res. 56(1), 127–156 (2001).
[Crossref] [PubMed]

M. L. Bennink, S. H. Leuba, G. H. Leno, J. Zlatanova, B. G. de Grooth, and J. Greve, “Unfolding individual nucleosomes by stretching single chromatin fibers with optical tweezers,” Nat. Struct. Biol. 8(7), 606–610 (2001).
[Crossref] [PubMed]

2000 (2)

M. Carrion-Vazquez, A. F. Oberhauser, T. E. Fisher, P. E. Marszalek, H. Li, and J. M. Fernandez, “Mechanical design of proteins studied by single-molecule force spectroscopy and protein engineering,” Prog. Biophys. Mol. Biol. 74(1-2), 63–91 (2000).
[Crossref] [PubMed]

W. Kolch, “Meaningful relationships: the regulation of the Ras/Raf/MEK/ERK pathway by protein interactions,” Biochem. J. 351(2), 289–305 (2000).
[Crossref] [PubMed]

1998 (1)

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Force and velocity measured for single molecules of RNA polymerase,” Science 282(5390), 902–907 (1998).
[Crossref] [PubMed]

1995 (1)

T. R. Brtva, J. K. Drugan, S. Ghosh, R. S. Terrell, S. Campbell-Burk, R. M. Bell, and C. J. Der, “Two Distinct Raf Domains Mediate Interaction with Ras,” J. Biol. Chem. 270(17), 9809–9812 (1995).
[Crossref] [PubMed]

1994 (2)

E. Chuang, D. Barnard, L. Hettich, X. F. Zhang, J. Avruch, and M. S. Marshall, “Critical binding and regulatory interactions between Ras and Raf occur through a small, stable N-terminal domain of Raf and specific Ras effector residues,” Mol. Cel. Biol. 8, 359091 (1994).

S. Ghosh, W. Q. Xie, A. F. Quest, G. M. Mabrouk, J. C. Strum, and R. M. Bell, “The cysteine-rich region of raf-1 kinase contain zinc, translocates to liposomes, and is adjacent to a segment that binds GTP-ras,” J. Biol. Chem. 4, 8144497 (1994).

1993 (1)

A. B. Vojtek, S. M. Hollenberg, and J. A. Cooper, “Mammalian RAS interacts directly with the serine/threonine kinase raf,” Cell 74(1), 205–214 (1993).
[Crossref] [PubMed]

1978 (1)

G. I. Bell, “Models for the specific adhesion of cells to cells,” Science 200(4342), 618–627 (1978).
[Crossref] [PubMed]

Aliagas, I.

Alvarado, R.

Anderson, D. J.

Aoki, Y.

Avruch, J.

Avruch, J. A.

Barnard, D.

Baumann, C.

Bell, G. I.

G. I. Bell, “Models for the specific adhesion of cells to cells,” Science 200(4342), 618–627 (1978).
[Crossref] [PubMed]

Bell, R. M.

Belvin, M.

Bennink, M. L.

Bessard, J.

Bignell, G. R.

Bigner, D. D.

Block, S. M.

Bonneau, D.

Bordeleau, F.

Bottomley, W.

Brandhuber, B. J.

Brtva, T. R.

Bryant, Z.

C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421(6921), 423–427 (2003).
[Crossref] [PubMed]

Bustamante, C.

C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421(6921), 423–427 (2003).
[Crossref] [PubMed]

Campbell-Burk, S.

Carrion-Vazquez, M.

Cavé, H.

Chenevix-Trench, G.

Chuang, E.

Clegg, S.

Cooper, C.

Cooper, J. A.

A. B. Vojtek, S. M. Hollenberg, and J. A. Cooper, “Mammalian RAS interacts directly with the serine/threonine kinase raf,” Cell 74(1), 205–214 (1993).
[Crossref] [PubMed]

Corona, G.

Cossu, A.

Cox, C.

Darrow, T. L.

Davies, H.

Davis, N.

de Grooth, B. G.

Der, C. J.

Dicks, E.

Drugan, J. K.

Edkins, S.

Erdmann, T.

T. Erdmann, S. Pierrat, P. Nassoy, and U. S. Schwarz, “Dynamic force spectroscopy on multiple bonds: Experiments and model,” Europhys. Lett. 81(4), 48001 (2008).
[Crossref]

Ewing, R.

Eychène, A.

C. Peyssonnaux and A. Eychène, “The Raf/MEK/ERK pathway: new concepts of activation,” Biol. Cell 93(1-2), 53–62 (2001).
[Crossref] [PubMed]

Fernandez, J. M.

Fisher, T. E.

Flanagan, A.

Floyd, Y.

Friedman, L. S.

Futreal, P. A.

Garnett, M. J.

Gelles, J.

Ghosh, S.

Gillessen-Kaesbach, G.

Gloor, S. L.

Gray, K.

Greve, J.

Gusterson, B. A.

Hall, S.

Hargrave, D.

Hatzivassiliou, G.

Hawes, R.

Hennekam, R. C. M.

Heron, D.

Hettich, L.

Ho, J. W. C.

Hoeflich, K. P.

Hollenberg, S. M.

A. B. Vojtek, S. M. Hollenberg, and J. A. Cooper, “Mammalian RAS interacts directly with the serine/threonine kinase raf,” Cell 74(1), 205–214 (1993).
[Crossref] [PubMed]

Hooper, S.

Hughes, J.

Jaiswal, B. S.

Jayatilake, H.

Kaname, T.

Kato, K.

Kavamura, M. I.

Keyser, U. F.

Khokhlatchev, A.

Koeppen, H.

Kolch, W.

W. Kolch, “Meaningful relationships: the regulation of the Ras/Raf/MEK/ERK pathway by protein interactions,” Biochem. J. 351(2), 289–305 (2000).
[Crossref] [PubMed]

Kosmidou, V.

Kremer, F.

Kure, S.

Kurosawa, K.

Kyriakis, J. M.

Landick, R.

Leno, G. H.

Leuba, S. H.

Leung, S. Y.

Li, H.

Liu, B.

Ludlam, M. J. C.

Luo, Z.

Mabrouk, G. M.

Maitland, N.

Malek, S.

Marais, R.

Marceau, N.

Marshall, C. J.

Marshall, M. S.

Marszalek, P. E.

Matsubara, Y.

Matsumoto, N.

Menzies, A.

Morales, T.

Mould, C.

Nagy, A.

K. C. Neuman and A. Nagy, “Single-molecular force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nature Meth. 5, 1218 (2008).

Naritomi, K.

Narumi, Y.

Nassoy, P.

T. Erdmann, S. Pierrat, P. Nassoy, and U. S. Schwarz, “Dynamic force spectroscopy on multiple bonds: Experiments and model,” Europhys. Lett. 81(4), 48001 (2008).
[Crossref]

Neri, G.

Neuman, K. C.

K. C. Neuman and A. Nagy, “Single-molecular force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nature Meth. 5, 1218 (2008).

Nicholson, A.

Niihori, T.

Oberhauser, A. F.

Ohashi, H.

Okamoto, N.

Palmieri, G.

Parker, A.

Paterson, H.

Peyssonnaux, C.

C. Peyssonnaux and A. Eychène, “The Raf/MEK/ERK pathway: new concepts of activation,” Biol. Cell 93(1-2), 53–62 (2001).
[Crossref] [PubMed]

Pierrat, S.

T. Erdmann, S. Pierrat, P. Nassoy, and U. S. Schwarz, “Dynamic force spectroscopy on multiple bonds: Experiments and model,” Europhys. Lett. 81(4), 48001 (2008).
[Crossref]

Pritchard-Jones, K.

Quest, A. F.

Riggins, G. J.

Salomo, M.

Schnitzer, M. J.

Schwarz, U. S.

T. Erdmann, S. Pierrat, P. Nassoy, and U. S. Schwarz, “Dynamic force spectroscopy on multiple bonds: Experiments and model,” Europhys. Lett. 81(4), 48001 (2008).
[Crossref]

Seigler, H. F.

Seshagiri, S.

Sheng, Y.

Shipley, J.

Sideris, S.

Smith, S. B.

C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421(6921), 423–427 (2003).
[Crossref] [PubMed]

Song, K.

Song, Q.

Q. Song, C. Wen, Y. Zhang, G. Wang, and A. Ye, “Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array,” Chin. Opt. Lett. 6, 1671–7694 (2008).

Stephens, P.

Stevens, C.

Stokoe, D.

Stratton, M. R.

Struhalla, M.

Strum, J. C.

Teague, J.

Terrell, R. S.

Tzivion, G.

Vavvas, D.

Verloes, A.

Vigers, G.

Vojtek, A. B.

A. B. Vojtek, S. M. Hollenberg, and J. A. Cooper, “Mammalian RAS interacts directly with the serine/threonine kinase raf,” Cell 74(1), 205–214 (1993).
[Crossref] [PubMed]

Wang, G.

Q. Song, C. Wen, Y. Zhang, G. Wang, and A. Ye, “Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array,” Chin. Opt. Lett. 6, 1671–7694 (2008).

Wang, M. D.

Watt, S.

Weber, B. L.

Wen, C.

Q. Song, C. Wen, Y. Zhang, G. Wang, and A. Ye, “Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array,” Chin. Opt. Lett. 6, 1671–7694 (2008).

Wieczorek, D.

Wilson, L.

Wilson, R.

Woffendin, H.

Wooster, R.

Xie, W. Q.

Ye, A.

Q. Song, C. Wen, Y. Zhang, G. Wang, and A. Ye, “Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array,” Chin. Opt. Lett. 6, 1671–7694 (2008).

Yen, I.

Yin, H.

Yuen, S. T.

Zhang, X. F.

Zhang, Y.

Q. Song, C. Wen, Y. Zhang, G. Wang, and A. Ye, “Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array,” Chin. Opt. Lett. 6, 1671–7694 (2008).

Zlatanova, J.

Biochem. J. (1)

W. Kolch, “Meaningful relationships: the regulation of the Ras/Raf/MEK/ERK pathway by protein interactions,” Biochem. J. 351(2), 289–305 (2000).
[Crossref] [PubMed]

Biol. Cell (1)

C. Peyssonnaux and A. Eychène, “The Raf/MEK/ERK pathway: new concepts of activation,” Biol. Cell 93(1-2), 53–62 (2001).
[Crossref] [PubMed]

Cell (1)

A. B. Vojtek, S. M. Hollenberg, and J. A. Cooper, “Mammalian RAS interacts directly with the serine/threonine kinase raf,” Cell 74(1), 205–214 (1993).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

Q. Song, C. Wen, Y. Zhang, G. Wang, and A. Ye, “Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array,” Chin. Opt. Lett. 6, 1671–7694 (2008).

Eur. Biophys. J. (1)

Europhys. Lett. (1)

T. Erdmann, S. Pierrat, P. Nassoy, and U. S. Schwarz, “Dynamic force spectroscopy on multiple bonds: Experiments and model,” Europhys. Lett. 81(4), 48001 (2008).
[Crossref]

J. Biol. Chem. (2)

J. Biomed. Opt. (1)

Mol. Cel. Biol. (1)

Nat. Genet. (1)

Nat. Struct. Biol. (1)

Nature (3)

C. Bustamante, Z. Bryant, and S. B. Smith, “Ten years of tension: single-molecule DNA mechanics,” Nature 421(6921), 423–427 (2003).
[Crossref] [PubMed]

Nature Meth. (1)

K. C. Neuman and A. Nagy, “Single-molecular force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nature Meth. 5, 1218 (2008).

Prog. Biophys. Mol. Biol. (1)

Recent Prog. Horm. Res. (1)

Science (2)

G. I. Bell, “Models for the specific adhesion of cells to cells,” Science 200(4342), 618–627 (1978).
[Crossref] [PubMed]

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Fig. 1 Schematic representation of the Ras-Raf-MEK–ERK pathway. Activated Ras-GTP binds to Raf via two domains, RBD and CRD, which are marked by dashed circles on the figure.

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Fig. 2 Diagram of the experimental setup. The beam expander comprises L1 and L2. L3 is a coupling mirror, which focuses the collimated laser beam at the conjugate point of the tube mirror (L4) and the objective of the microscope. The image of the bead is projected to the quadrant photodiode detector (QD) by L5. An acousto-optic deflector (AOD) is employed to manipulate the beam during calibration. The AOD is controlled by a field programmable gate array (FPGA), which is driven by a direct digital synthesizer (DDS).

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Fig. 3 (a) Image of beads acquired by CCD (left: a trapped Ras-bead; right: a fixed BRaf-bead. Bead diameter: 5 μm). (b) Diagram of the optical tweezers setup for measuring the unbinding force between trapped Ras-beads and fixed BRaf-beads. The fixed BRaf-bead is brought in contact with the trapped bead by the PZT. (c) If binding between the beads occurs, the trapped bead deviates from the equilibrium position as the fixed bead is pulled back. (d) When the gradient force on the trapped bead is strong enough to break the association, unbinding occurs.

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Fig. 4 A typical unbinding trace acquired by the QD for measurement (The voltage output of the QD has been converted to force using Eq. (6).). I: Corresponding to the process illustrated in Fig. 3(c). II: Corresponding to the process illustrated in Fig. 3(d).

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Fig. 5 Histogram of unbinding force for Ras/BRaf and Ras-GTP/BRaf (A470) interactions and the fitting curve of the experimental data. Insert: Adhesion ratios for Ras-GTP/BRaf, Ras-GTP/BRaf (A246P), Ras-GTP/BRaf (Q257R), Ras/BRaf and Ras-GTP/BRaf (A470) interactions. The adhesion ratios of three specific interaction groups all exceeded 20%, while those of control groups were all around 10%. “n” referred to the number of contact cases measured in each group.

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Fig. 6 (a) Unbinding force histograms and simulated curves for the Ras-GTP/BRaf interaction, which include 585 binding-unbinding events among 1800 attachment events. (b) Ras-GTP/BRaf (A246P) interactions, which include 596 binding-unbinding events among 2536 attachment events. (c) Ras-GTP/BRaf (Q257R) interactions, which include751 binding-unbinding events in 2269 attachment events. The arrow indicates the position of each specific binding peak. The fitting of nonspecific interactions is according to Eq. (7). The fitting of binding peak is according to Eq. (11)-(13).

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Tables (2)

Table 1 Mean unbinding force for peaks no. 2–4 in the histograms of unbinding force for Ras-GTP/BRaf, Ras-GTP/BRaf (A246P), and Ras-GTP/BRaf (Q257R) interactions.

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Table 2 The k_off(0) and x_b values for Ras-GTP/BRaf, Ras-GTP/BRaf (A246P), and Ras-GTP/BRaf (Q257R) bonds.

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Equations (13)

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x_{b} (t) = c \exp (- 2 π f_{0} t) + A_{0} {[(f / f_{0}) + 1]}^{(- 1 / 2)} \sin (2 π f t + φ)

f_{0} = k / (2 π γ)

A = A_{0} {[{(f / f_{0})}^{2} + 1]}^{(- 1 / 2)}

k = 2 π γ f_{0} = 2 π γ f {[{(A_{0} / A)}^{2} - 1]}^{(- 1 / 2)}

k = 0.415 \cdot m W^{- 1} \cdot p N \cdot μ m^{- 1} .

F_{u} = k \cdot K_{Q} \cdot v

f (x, μ, σ, K) = K \cdot [1 / (x σ)] \cdot \exp [- {(\ln x - μ)}^{2} / (2 σ^{2})]

f (x, μ_{i = 1, 2, 3}, σ, K_{i = 1, 2, 3}) = \sum_{i = 1}^{3} K_{i} \cdot \exp [- {(x - μ_{i})}^{2} / (2 σ^{2})]

d p_{i} / d t = r_{i + 1} p_{i} - r_{i} p_{i}

r_{i} = i k_{o f f} = i k_{o f f} (0) \cdot e x p [m t / (i F_{0})]

\begin{array}{l} D (F_{u}) = \sum_{N_{t} = 1}^{N_{t m}} p_{α} (N_{t}) \cdot D_{N_{t}} (F_{u}) \\ = \sum_{N_{t} = 1}^{N_{t m}} p_{α} (N_{t}) \cdot (k_{o f f} (0) / m) \cdot \exp [F_{u} \cdot x_{b} / (K_{B} T)] \cdot \\ \exp {(k_{o f f} (0) / m) \cdot (K_{B} T / x_{b}) \cdot [1 - \exp (F_{u} x_{b} / K_{B} T)]} \end{array}

p_{α} (N_{t}) = α_{N_{t}} / (α_{1} + α_{2} + ... + α_{N_{t m}})

\begin{array}{l} D (F_{u}) = D_{n o n s p e c i f i c} + p_{α C R D} (1) D_{1 C R D} (F_{u}) + p_{α R B D} (1) D_{1 R B D} (F_{u}) + \\ p_{α C R D + R B D} (1) D_{1 C R D + R B D} (F_{u}) + ε (F_{u}) \end{array}

BRaf species	μ ₁	μ ₂	μ ₃	μ₁ + μ₂	R ^2†	p^†
	(pN)	(pN)	(pN)	(pN)
BRaf (WT)	40 $\pm$ 8	95 $\pm$ 11	136 $\pm$ 12	135	0.75	< 0.01
BRaf (A246P)	46 $\pm$ 5	114 $\pm$ 12	156 $\pm$ 18	160	0.78	< 0.01
BRaf (Q257R)	60 $\pm$ 5	102 $\pm$ 12	155 $\pm$ 15	162	0.70	< 0.01

BRafspecies	CRD		RBD				R ^2*	p*
BRafspecies	k_off(0)	x_b _(nm)	k_off(0)	x_b _(nm)	k_off(0)	x_b _(nm)	R ^2*	p*
BRaf (WT)	7.7 × 10⁻³	0.51	2.1 × 10⁻³	0.37	3.7 × 10⁻⁵	0.31	0.89	<0.01
BRaf (A246P)	1.0 × 10⁻⁴	0.77	6.3 × 10⁻⁶	0.45	1.2 × 10⁻⁵	0.32	0.87	<0.01
BRaf (Q257R)	5.4 × 10⁻⁶	0.84	9.6 × 10⁻⁶	0.43	1.2 × 10⁻⁵	0.32	0.85	<0.01

BRaf species	μ ₁	μ ₂	μ ₃	μ₁ + μ₂	R ^2†	p^†
	(pN)	(pN)	(pN)	(pN)
BRaf (WT)	40 $\pm$ 8	95 $\pm$ 11	136 $\pm$ 12	135	0.75	< 0.01
BRaf (A246P)	46 $\pm$ 5	114 $\pm$ 12	156 $\pm$ 18	160	0.78	< 0.01
BRaf (Q257R)	60 $\pm$ 5	102 $\pm$ 12	155 $\pm$ 15	162	0.70	< 0.01

BRafspecies	CRD		RBD				R ^2*	p*
BRafspecies	k_off(0)	x_b _(nm)	k_off(0)	x_b _(nm)	k_off(0)	x_b _(nm)	R ^2*	p*
BRaf (WT)	7.7 × 10⁻³	0.51	2.1 × 10⁻³	0.37	3.7 × 10⁻⁵	0.31	0.89	<0.01
BRaf (A246P)	1.0 × 10⁻⁴	0.77	6.3 × 10⁻⁶	0.45	1.2 × 10⁻⁵	0.32	0.87	<0.01
BRaf (Q257R)	5.4 × 10⁻⁶	0.84	9.6 × 10⁻⁶	0.43	1.2 × 10⁻⁵	0.32	0.85	<0.01