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Mathematical Crystallography
Table of Contents

Time-resolved crystallography lets us see molecules in action, like watching a movie of chemical reactions. It's revolutionizing our understanding of how proteins and other molecules move and change during important processes.

This cutting-edge technique uses super-fast X-ray pulses to capture snapshots of molecules at different stages. By piecing these snapshots together, scientists can create a detailed picture of how molecules transform over time.

Experimental Techniques

Advanced X-ray Sources and Methods

  • Pump-probe experiments enable time-resolved studies by initiating reactions with a pump pulse and probing the sample with a subsequent X-ray pulse
  • Synchrotron radiation provides high-intensity X-ray beams for structural studies, allowing for faster data collection and higher resolution
  • X-ray free-electron lasers (XFELs) generate ultra-bright, femtosecond X-ray pulses, enabling studies of ultrafast processes and radiation-sensitive samples
    • XFELs produce pulses with peak brilliance billions of times higher than synchrotron sources
    • Femtosecond pulse duration allows for "diffraction before destruction" experiments
  • Serial femtosecond crystallography utilizes XFELs to collect diffraction data from a stream of microcrystals, overcoming radiation damage limitations
    • Requires millions of microcrystals in suspension
    • Each crystal is exposed to a single XFEL pulse, producing a partial diffraction pattern
    • Diffraction patterns from many crystals are combined to create a complete dataset

Specialized Diffraction Techniques

  • Laue diffraction uses polychromatic X-rays to collect multiple reflections simultaneously, reducing data collection time
    • Enables capture of structural changes on microsecond to nanosecond timescales
    • Particularly useful for studying enzyme reactions and protein folding
  • Time-resolved Laue crystallography combines Laue diffraction with rapid reaction initiation methods
    • Can capture structural snapshots of reaction intermediates
    • Provides insights into reaction mechanisms and conformational changes

Structural Dynamics

Ultrafast Processes and Intermediate States

  • Ultrafast structural dynamics studies investigate atomic and molecular motions on femtosecond to picosecond timescales
    • Reveals rapid structural changes during chemical reactions or protein function
    • Techniques include time-resolved spectroscopy and diffraction methods
  • Reaction intermediates represent transient structural states during chemical or biological processes
    • Capturing intermediates provides insights into reaction mechanisms and pathways
    • Time-resolved crystallography can identify and characterize these short-lived species

Experimental Approaches for Structural Dynamics

  • Time-resolved serial femtosecond crystallography (TR-SFX) combines XFEL technology with pump-probe techniques
    • Allows for studying structural changes with femtosecond time resolution
    • Can capture very early stages of light-activated processes (photosynthesis, vision)
  • Mixing-injector systems enable the study of solution-phase reactions in time-resolved experiments
    • Reactants are mixed just before injection into the X-ray beam
    • Allows for investigating diffusion-limited processes and enzyme catalysis
  • Temperature-jump experiments initiate structural changes through rapid heating
    • Can be used to study protein folding and unfolding processes
    • Often combined with time-resolved X-ray scattering or spectroscopy