28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX)
- 28-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- 28-01 Instructional exposition (textbooks, tutorial papers, etc.)
- 28-02 Research exposition (monographs, survey articles)
- 28-03 Historical (must also be assigned at least one classification number from Section 01)
- 28-04 Explicit machine computation and programs (not the theory of computation or programming)
- 28-06 Proceedings, conferences, collections, etc.
- 28Axx Classical measure theory
- 28Bxx Set functions, measures and integrals with values in abstract spaces
- 28Cxx Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]
- 28Dxx Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]
- 28Exx Miscellaneous topics in measure theory
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- Markov-Ketten-Monte-Carlo-Verfahren (1)
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Monte Carlo Simulation Methods for Studying the Thermodynamics of Ligand Binding & Transfer Processes in Biomolecules
(2012)
-
R. Thomas Ullmann
- The binding and transfer of ligands is of central
importance for the function of many biomolecular
systems. The main topic of this thesis is the
development and application of Monte Carlo (MC)
simulation methods for studying complex ligand
binding equilibria which can also involve
conformational changes. The simulated systems
were described by microstates within a continuum
electrostatics/molecular mechanics (CE/MM) model
of the receptor-ligand system. The CE/MM modeling
methodology was improved. The improvements led to
more detailed molecular models that enable a more
realistic reproduction of system properties and
environmental conditions. The developed simulation
methods were applied to biomolecular systems whose
function involves aspects that are important for
the understanding of bioenergetic energy
transduction. The results of this thesis are
presented in five articles that are published in
peer reviewed scientific journals.
Manuscript A presents the Monte Carlo simulation
software GMCT which was largely developed in this
thesis. The software offers a variety of different
simulation methods that allow the user to harness
the full potential of CE/MM models in the simulation
of complex receptor systems.
Manuscript B presents a novel theoretical framework
for free energy calculations with the free energy
perturbation method. The novel framework is more
broadly applicable and can lead to more efficient
simulations than previous formulations. The
derivation of the formalism also led to interesting
insights into general statistical mechanics. The
formalism was implemented in GMCT and could already
be used fruitfully for the free energy calculations
presented in Manuscripts C and D.
Manuscript C demonstrates the application of free
energy measures of cooperativity to study the
coupling of protonation, reduction and conformational
change in azurin from Pseudomonas aeruginosa (PaAz).
Such a coupling is prototypic for bioenergetic systems
because it forms the thermodynamic basis of their
energy transducing function. PaAz is an experimentally
well characterized, small electron transport protein.
For this reason, PaAz was used here as model system
to demonstrate the usefulness of cooperativity free
energies in detecting and quantifying thermodynamic
coupling between events in complex biomolecular
systems. The results of this study led to new insight
that could help to determine the still enigmatic
physiological role of PaAz.
In Manuscript D, free energy calculations were
applied to study the thermodynamics of transport
through the ammonium transporter Amt-1 from
Archaeoglobus fulgidus (AfAmt-1). Ammonium is the most
directly utilizable nitrogen source for plants and
microorganisms. AfAmt-1 and its homologues facilitate
the transport of ammonia/ammonium across biological
membranes in living beings from all domains of life.
It is intensely debated how these proteins perform
their function and whether ammonia or its protonated
form ammonium is actually transported. The study
extended upon previous theoretical studies by
including the effects of substrate concentration,
electrochemical transmembrane gradients,
proton-coupled binding equilibria and competitive
binding of different ligand species. It was found
that the transported species is most likely the
ammonium ion. An ammonia/proton symport mechanism
that involves a pair of coplanar histidine residues
at the center of the transmembrane pore as transient
proton acceptor is made plausible by the high
genetic conservation of these residues.
Manuscript E presents a first application of the
microstate description within a CE/MM model to the
simulation of the non-equilibrium dynamics of a
molecular system. We simulated the re-reduction
kinetics of the primary electron donor in the
photocycle of the bacterial photosynthetic reaction
center from Blastochloris viridis. The simulation
results are in very good agreement with
experimentally measured data.
