PROBLEMS
7.1 What are the units for the rate of a chemical reaction?
7.2 For a reaction A ↔ B that has an equilibrium constant of 10, what can be said about the rates?
7.3 For the irreversible reaction A → B, what effect will doubling the concentration of B have
on the rate of change of A?
7.4 The time dependence of the conversion of a substrate by an enzymatic reaction is characterized by a half-life of 150 s. How long is required for the concentration of the substrate
to decrease from 16 to 1 nM?
7.5 The time dependence of the conversion of a substrate by an enzymatic reaction is characterized by a rate of 0.0046 s
−1
. How long is required for the concentration of the substrate
to decrease from 16 to 1 nM?
7.6 Initially a system has species A at a concentration of 0.1 M. If a process proceeds from A
to both B and C in parallel first-order reactions, and the two forward rates are identical,
what are the final amounts of species B and C?
7.7 Initially a system has only species A at a concentration of 0.1 M. If a process proceeds from
A to both B and C in parallel first-order reactions, and the forward rate to produce B is ten
times larger than the rate to produce C, what are the final amounts of species B and C?
CHAPTER 7
KINETICS AND ENZYMES
161
REFERENCES
Boehr, D.D., McElheny, D., Dyson, H.J., and Wright, P.E.
(2006) The dynamic energy landscape of dihydrofolate reductase catalysis. Science 313, 1638–42.
Doudna, J.A. and Cech, T.R. (2002) The chemical repertoire of natural ribozymes. Nature 418, 222–8.
Eisenmesser, E.Z., Millet, O., Labeikovsky, W. et al.
(2005) Intrinsic dynamics of an enzyme underlies
catalysis. Nature 438, 117–21.
Frauenfelder, H., Sligar, S., and Wolynes, P.G. (1991)
The energy landscapes and motions of proteins.
Science 254, 1598–1603.
Giese, B. (2002) Electron transfer in DNA. Current
Opinion in Chemical Biology 6, 612–18.
Gilbert, W. (1986) The RNA world. Nature 319, 618.
Gray, H.B. and Winkler, J.R. (2005) Long-range
electron transfer. Proceedings of the National Academy
of Sciences USA 102, 3534–9.
Guerrier-Takada, C. and Altman, S. (1984) Catalytic
activity of an RNA molecule prepared by transcription in vitro. Science 223, 285–6.
Hüttenhofer, A. and Schattner, P. (2006) The principles of guiding by RNA: chimeric RNA-protein
enzymes. Nature Re9iews Genetics 7, 475–82.
Joyce, G.F. (2002) The antiquity of RNA-based evolution. Nature 418, 214–21.
Lantham, J.A. and Cech, T.R. (1989) Defining the
inside and outside of a catalytic RNA molecule.
Science 245, 276–82.
Lin, J., Balabin, I.A., and Beratan, D.N. (2005) The
nature of aqueous tunneling pathways between
electron-transfer proteins. Science 310, 1311–13.
Marcus, R.A. and Sutin, N. (1985) Electron transfers
in chemistry and biology. Biochimica Biophysica
Acta 811, 265–322.
Miyashita, O., Okamura, M.Y., and Onuchic, J.N.
(2005) Interprotein elctron transfer from cytochrome c 2 to photosynthetic reaction center: tunneling across an aqueous interface. Proceedings of the
National Academy of Sciences USA 102, 3558–63.
Murphy, C.J., Arkin, M.R., Jenkins, Y. et al. (1993)
Long-range photoinduced electron transfer through
a DNA helix. Science 262, 1025–9.
Orgel, L.E. (1998) The origin of life-a review of facts and
speculations. Trends in Biochemical Sciences 23, 491–5.
Page, C.C., Moser, C.C., and Dutton, P.L. (2003)
Mechanism for electron transfer within and between proteins. Current Opinion in Chemical Biology
7, 551–6.
Vendruscolo, M. and Dobson, C.M. (2006) Dynamic
visions of enzymatic reactions. Science 313, 1586–7.
9781405124362_4_007.qxd 4/29/08 10:41 Page 161
7.1 What are the units for the rate of a chemical reaction?
7.2 For a reaction A ↔ B that has an equilibrium constant of 10, what can be said about the rates?
7.3 For the irreversible reaction A → B, what effect will doubling the concentration of B have
on the rate of change of A?
7.4 The time dependence of the conversion of a substrate by an enzymatic reaction is characterized by a half-life of 150 s. How long is required for the concentration of the substrate
to decrease from 16 to 1 nM?
7.5 The time dependence of the conversion of a substrate by an enzymatic reaction is characterized by a rate of 0.0046 s
−1
. How long is required for the concentration of the substrate
to decrease from 16 to 1 nM?
7.6 Initially a system has species A at a concentration of 0.1 M. If a process proceeds from A
to both B and C in parallel first-order reactions, and the two forward rates are identical,
what are the final amounts of species B and C?
7.7 Initially a system has only species A at a concentration of 0.1 M. If a process proceeds from
A to both B and C in parallel first-order reactions, and the forward rate to produce B is ten
times larger than the rate to produce C, what are the final amounts of species B and C?
CHAPTER 7
KINETICS AND ENZYMES
161
REFERENCES
Boehr, D.D., McElheny, D., Dyson, H.J., and Wright, P.E.
(2006) The dynamic energy landscape of dihydrofolate reductase catalysis. Science 313, 1638–42.
Doudna, J.A. and Cech, T.R. (2002) The chemical repertoire of natural ribozymes. Nature 418, 222–8.
Eisenmesser, E.Z., Millet, O., Labeikovsky, W. et al.
(2005) Intrinsic dynamics of an enzyme underlies
catalysis. Nature 438, 117–21.
Frauenfelder, H., Sligar, S., and Wolynes, P.G. (1991)
The energy landscapes and motions of proteins.
Science 254, 1598–1603.
Giese, B. (2002) Electron transfer in DNA. Current
Opinion in Chemical Biology 6, 612–18.
Gilbert, W. (1986) The RNA world. Nature 319, 618.
Gray, H.B. and Winkler, J.R. (2005) Long-range
electron transfer. Proceedings of the National Academy
of Sciences USA 102, 3534–9.
Guerrier-Takada, C. and Altman, S. (1984) Catalytic
activity of an RNA molecule prepared by transcription in vitro. Science 223, 285–6.
Hüttenhofer, A. and Schattner, P. (2006) The principles of guiding by RNA: chimeric RNA-protein
enzymes. Nature Re9iews Genetics 7, 475–82.
Joyce, G.F. (2002) The antiquity of RNA-based evolution. Nature 418, 214–21.
Lantham, J.A. and Cech, T.R. (1989) Defining the
inside and outside of a catalytic RNA molecule.
Science 245, 276–82.
Lin, J., Balabin, I.A., and Beratan, D.N. (2005) The
nature of aqueous tunneling pathways between
electron-transfer proteins. Science 310, 1311–13.
Marcus, R.A. and Sutin, N. (1985) Electron transfers
in chemistry and biology. Biochimica Biophysica
Acta 811, 265–322.
Miyashita, O., Okamura, M.Y., and Onuchic, J.N.
(2005) Interprotein elctron transfer from cytochrome c 2 to photosynthetic reaction center: tunneling across an aqueous interface. Proceedings of the
National Academy of Sciences USA 102, 3558–63.
Murphy, C.J., Arkin, M.R., Jenkins, Y. et al. (1993)
Long-range photoinduced electron transfer through
a DNA helix. Science 262, 1025–9.
Orgel, L.E. (1998) The origin of life-a review of facts and
speculations. Trends in Biochemical Sciences 23, 491–5.
Page, C.C., Moser, C.C., and Dutton, P.L. (2003)
Mechanism for electron transfer within and between proteins. Current Opinion in Chemical Biology
7, 551–6.
Vendruscolo, M. and Dobson, C.M. (2006) Dynamic
visions of enzymatic reactions. Science 313, 1586–7.
9781405124362_4_007.qxd 4/29/08 10:41 Page 161