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Protein energy landscapes determined by five-dimensional crystallography.

Schmidt M, Srajer V, Henning R, Ihee H, Purwar N, Tenboer J, Tripathi S - Acta Crystallogr. D Biol. Crystallogr. (2013)

Bottom Line: Directly linking molecular structures with barriers of activation between them allows insight into the structural nature of the barrier to be gained.Comprehensive time series of crystallographic data at 14 different temperature settings were analyzed and the entropy and enthalpy contributions to the barriers of activation were determined.One hundred years after the discovery of X-ray scattering, these results advance X-ray structure determination to a new frontier: the determination of energy landscapes.

View Article: PubMed Central - HTML - PubMed

Affiliation: Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA.

ABSTRACT
Free-energy landscapes decisively determine the progress of enzymatically catalyzed reactions [Cornish-Bowden (2012), Fundamentals of Enzyme Kinetics, 4th ed.]. Time-resolved macromolecular crystallography unifies transient-state kinetics with structure determination [Moffat (2001), Chem. Rev. 101, 1569-1581; Schmidt et al. (2005), Methods Mol. Biol. 305, 115-154; Schmidt (2008), Ultrashort Laser Pulses in Medicine and Biology] because both can be determined from the same set of X-ray data. Here, it is demonstrated how barriers of activation can be determined solely from five-dimensional crystallography, where in addition to space and time, temperature is a variable as well [Schmidt et al. (2010), Acta Cryst. A66, 198-206]. Directly linking molecular structures with barriers of activation between them allows insight into the structural nature of the barrier to be gained. Comprehensive time series of crystallographic data at 14 different temperature settings were analyzed and the entropy and enthalpy contributions to the barriers of activation were determined. One hundred years after the discovery of X-ray scattering, these results advance X-ray structure determination to a new frontier: the determination of energy landscapes.

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Chemical kinetic mechanisms and rate coefficients of the PYP photocycle. At temperatures up to 313 K, eight rate coefficients (k1 to k8) and five intermediate states plus the dark state contribute. The occupancy of pB2 is very low and cannot be observed. Above 313 K the early intermediates are not detected because the time series start around 100 ns. pB2 accumulates to a detectable extent and the rate coefficients k9 and k10 contribute in addition. The main reaction pathway in PYP is indicated by bold arrows. The direct path from ICT to pG is irrelevant (dashed arrow).
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fig3: Chemical kinetic mechanisms and rate coefficients of the PYP photocycle. At temperatures up to 313 K, eight rate coefficients (k1 to k8) and five intermediate states plus the dark state contribute. The occupancy of pB2 is very low and cannot be observed. Above 313 K the early intermediates are not detected because the time series start around 100 ns. pB2 accumulates to a detectable extent and the rate coefficients k9 and k10 contribute in addition. The main reaction pathway in PYP is indicated by bold arrows. The direct path from ICT to pG is irrelevant (dashed arrow).

Mentions: Since the 1890s, the Van’t Hoff–Arrhenius equation, νexp(−βEa), has been used to describe the temperature dependence of chemical reaction rates. Ea is the energy of activation and the factor β = 1/(kBT) containing the Boltzmann factor kB accounts for the inverse temperature behavior. The pre-factor ν accounts for the dynamic behavior of the members of the ensemble. Eyring (1935 ▶) tied this equation to a transition state at the top of the barrier of activation, where R is the gas constant, NA is Avogadro’s number, h is Planck’s constant and ΔS# and ΔH# are the entropy and enthalpy differences from the initial state to the transition state, respectively. A reaction can be followed with time-resolved methods, from which conclusions on the underlying mechanism are drawn by kinetic modeling. In early approaches (Gibson, 1952 ▶; Austin et al., 1975 ▶), the structures of the reaction intermediates were inferred from static crystallography. Time-resolved crystallography (TRX; Moffat, 1989 ▶) finally unified kinetics with structure determination (Šrajer et al., 1996 ▶; Schmidt et al., 2003 ▶; Schmidt, 2008 ▶). Once the structures of intermediates are known, kinetic mechanisms can be tested by post-refinement against the TRX data (Schmidt, 2008 ▶; Schmidt et al., 2004 ▶). If the temperature is varied, the previously four-dimensional crystallographic data become five-dimensional (Schmidt et al., 2010 ▶). The photocycle of photoactive yellow protein (PYP) is used here as a model system from which five-dimensional crystallographic data were collected. The photocycle features distinct intermediate states, structures of which were determined earlier by picosecond and nanosecond TRX at only one temperature (Schotte et al., 2012 ▶; Jung et al., 2013 ▶; Ihee et al., 2005 ▶; Schmidt et al., 2004 ▶). Absorption of a blue photon at 485 nm provides 245 kJ mol−1 of energy to excite the central p-­coumaric acid (pCA) chromophore (Fig. 1 ▶). Part of the energy is rapidly dissipated (Martin et al., 1983 ▶; Fitzpatrick et al., 2012 ▶). The remaining energy is stored in an energy-rich atomic configuration (Groenhof et al., 2004 ▶) labeled IT. The chromophore is not yet fully isomerized from trans to cis (Schotte et al., 2012 ▶; van Stokkum et al., 2004 ▶; Jung et al., 2013 ▶). The IT state is followed by two states: ICT and pR1. ICT and pR1 are fully cis and branch away from IT in a volume-conserving bicycle-pedal and hula-twist reaction, respectively (Jung et al., 2013 ▶). The dominant species is ICT. In ICT the carbonyl O atom is flipped to the other side but the chromophore head is still fixed by two hydrogen bonds to amino acids Tyr42 and Glu46. In pR1 the chromophore head hydroxyl has lost one hydrogen bond. The entire chromophore has rotated about the chromophore axis. ICT relaxes to pR2. This relaxation causes the Cys69 S atom to which the chromophore is bound to move significantly. The strongest difference electron-density features are found near this S atom (Fig. 2 ▶b). The pR1 and pR2 states are occupied for many orders of magnitude in time. Finally, they relax to the pB state (Ihee et al., 2005 ▶; Schmidt et al., 2004 ▶). The pB state most likely resembles the signaling state of PYP. The chromophore head forms new hydrogen bonds to the displaced Asp52 and to an additional water that appears near the entrance to the chromophore pocket (Tripathi et al., 2012 ▶). Finally, pB relaxes to the dark state (pG). Microscopic rate coefficients k between the intermediates plus the extent of reaction initiation specify a mechanism. The mechanism proposed by two previous TR crystallographic studies of PYP (Jung et al., 2013 ▶; Ihee et al., 2005 ▶) is depicted in Fig. 3 ▶. The rate coefficients of this mechanism depend on the temperature. This dependence can be described by the transition-state equation (TSE; equation 1). Other equations such as Kramer’s equation (Hanggi et al., 1990 ▶), which parameterizes the pre-factors of the rate coefficients in terms of friction, are also frequently used. With this, our results would not be comparable with earlier results on PYP (Van Brederode et al., 1995 ▶, 1996 ▶; Ng et al., 1995 ▶), which were based on the TSE. Accordingly, we also use the TSE and express the barrier height in terms of enthalpy and entropy differences from the transition state. We demonstrate here how these thermodynamic parameters can be extracted solely from five-dimensional crystallography.


Protein energy landscapes determined by five-dimensional crystallography.

Schmidt M, Srajer V, Henning R, Ihee H, Purwar N, Tenboer J, Tripathi S - Acta Crystallogr. D Biol. Crystallogr. (2013)

Chemical kinetic mechanisms and rate coefficients of the PYP photocycle. At temperatures up to 313 K, eight rate coefficients (k1 to k8) and five intermediate states plus the dark state contribute. The occupancy of pB2 is very low and cannot be observed. Above 313 K the early intermediates are not detected because the time series start around 100 ns. pB2 accumulates to a detectable extent and the rate coefficients k9 and k10 contribute in addition. The main reaction pathway in PYP is indicated by bold arrows. The direct path from ICT to pG is irrelevant (dashed arrow).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3852658&req=5

fig3: Chemical kinetic mechanisms and rate coefficients of the PYP photocycle. At temperatures up to 313 K, eight rate coefficients (k1 to k8) and five intermediate states plus the dark state contribute. The occupancy of pB2 is very low and cannot be observed. Above 313 K the early intermediates are not detected because the time series start around 100 ns. pB2 accumulates to a detectable extent and the rate coefficients k9 and k10 contribute in addition. The main reaction pathway in PYP is indicated by bold arrows. The direct path from ICT to pG is irrelevant (dashed arrow).
Mentions: Since the 1890s, the Van’t Hoff–Arrhenius equation, νexp(−βEa), has been used to describe the temperature dependence of chemical reaction rates. Ea is the energy of activation and the factor β = 1/(kBT) containing the Boltzmann factor kB accounts for the inverse temperature behavior. The pre-factor ν accounts for the dynamic behavior of the members of the ensemble. Eyring (1935 ▶) tied this equation to a transition state at the top of the barrier of activation, where R is the gas constant, NA is Avogadro’s number, h is Planck’s constant and ΔS# and ΔH# are the entropy and enthalpy differences from the initial state to the transition state, respectively. A reaction can be followed with time-resolved methods, from which conclusions on the underlying mechanism are drawn by kinetic modeling. In early approaches (Gibson, 1952 ▶; Austin et al., 1975 ▶), the structures of the reaction intermediates were inferred from static crystallography. Time-resolved crystallography (TRX; Moffat, 1989 ▶) finally unified kinetics with structure determination (Šrajer et al., 1996 ▶; Schmidt et al., 2003 ▶; Schmidt, 2008 ▶). Once the structures of intermediates are known, kinetic mechanisms can be tested by post-refinement against the TRX data (Schmidt, 2008 ▶; Schmidt et al., 2004 ▶). If the temperature is varied, the previously four-dimensional crystallographic data become five-dimensional (Schmidt et al., 2010 ▶). The photocycle of photoactive yellow protein (PYP) is used here as a model system from which five-dimensional crystallographic data were collected. The photocycle features distinct intermediate states, structures of which were determined earlier by picosecond and nanosecond TRX at only one temperature (Schotte et al., 2012 ▶; Jung et al., 2013 ▶; Ihee et al., 2005 ▶; Schmidt et al., 2004 ▶). Absorption of a blue photon at 485 nm provides 245 kJ mol−1 of energy to excite the central p-­coumaric acid (pCA) chromophore (Fig. 1 ▶). Part of the energy is rapidly dissipated (Martin et al., 1983 ▶; Fitzpatrick et al., 2012 ▶). The remaining energy is stored in an energy-rich atomic configuration (Groenhof et al., 2004 ▶) labeled IT. The chromophore is not yet fully isomerized from trans to cis (Schotte et al., 2012 ▶; van Stokkum et al., 2004 ▶; Jung et al., 2013 ▶). The IT state is followed by two states: ICT and pR1. ICT and pR1 are fully cis and branch away from IT in a volume-conserving bicycle-pedal and hula-twist reaction, respectively (Jung et al., 2013 ▶). The dominant species is ICT. In ICT the carbonyl O atom is flipped to the other side but the chromophore head is still fixed by two hydrogen bonds to amino acids Tyr42 and Glu46. In pR1 the chromophore head hydroxyl has lost one hydrogen bond. The entire chromophore has rotated about the chromophore axis. ICT relaxes to pR2. This relaxation causes the Cys69 S atom to which the chromophore is bound to move significantly. The strongest difference electron-density features are found near this S atom (Fig. 2 ▶b). The pR1 and pR2 states are occupied for many orders of magnitude in time. Finally, they relax to the pB state (Ihee et al., 2005 ▶; Schmidt et al., 2004 ▶). The pB state most likely resembles the signaling state of PYP. The chromophore head forms new hydrogen bonds to the displaced Asp52 and to an additional water that appears near the entrance to the chromophore pocket (Tripathi et al., 2012 ▶). Finally, pB relaxes to the dark state (pG). Microscopic rate coefficients k between the intermediates plus the extent of reaction initiation specify a mechanism. The mechanism proposed by two previous TR crystallographic studies of PYP (Jung et al., 2013 ▶; Ihee et al., 2005 ▶) is depicted in Fig. 3 ▶. The rate coefficients of this mechanism depend on the temperature. This dependence can be described by the transition-state equation (TSE; equation 1). Other equations such as Kramer’s equation (Hanggi et al., 1990 ▶), which parameterizes the pre-factors of the rate coefficients in terms of friction, are also frequently used. With this, our results would not be comparable with earlier results on PYP (Van Brederode et al., 1995 ▶, 1996 ▶; Ng et al., 1995 ▶), which were based on the TSE. Accordingly, we also use the TSE and express the barrier height in terms of enthalpy and entropy differences from the transition state. We demonstrate here how these thermodynamic parameters can be extracted solely from five-dimensional crystallography.

Bottom Line: Directly linking molecular structures with barriers of activation between them allows insight into the structural nature of the barrier to be gained.Comprehensive time series of crystallographic data at 14 different temperature settings were analyzed and the entropy and enthalpy contributions to the barriers of activation were determined.One hundred years after the discovery of X-ray scattering, these results advance X-ray structure determination to a new frontier: the determination of energy landscapes.

View Article: PubMed Central - HTML - PubMed

Affiliation: Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA.

ABSTRACT
Free-energy landscapes decisively determine the progress of enzymatically catalyzed reactions [Cornish-Bowden (2012), Fundamentals of Enzyme Kinetics, 4th ed.]. Time-resolved macromolecular crystallography unifies transient-state kinetics with structure determination [Moffat (2001), Chem. Rev. 101, 1569-1581; Schmidt et al. (2005), Methods Mol. Biol. 305, 115-154; Schmidt (2008), Ultrashort Laser Pulses in Medicine and Biology] because both can be determined from the same set of X-ray data. Here, it is demonstrated how barriers of activation can be determined solely from five-dimensional crystallography, where in addition to space and time, temperature is a variable as well [Schmidt et al. (2010), Acta Cryst. A66, 198-206]. Directly linking molecular structures with barriers of activation between them allows insight into the structural nature of the barrier to be gained. Comprehensive time series of crystallographic data at 14 different temperature settings were analyzed and the entropy and enthalpy contributions to the barriers of activation were determined. One hundred years after the discovery of X-ray scattering, these results advance X-ray structure determination to a new frontier: the determination of energy landscapes.

Show MeSH