@Article{Donnini2016,
author = "Serena Donnini and R. Thomas Ullmann and Gerrit Groenhof and Helmut Grubm{\"{u}}ller",
title = "{Charge-neutral constant pH molecular dynamics simulations using a parsimonious proton buffer}",
journal = "J. Chem. Theory Comput.",
volume = "12",
pages = "1040-1051",
year = "2016",
doi = "10.1021/acs.jctc.5b01160",
abstract = "{In constant pH molecular dynamics simulations, the protonation states of titratable
sites can respond to changes of the pH and of their electrostatic environment.
Consequently, the number of protons bound to the biomolecule, and therefore the
overall charge of the system, fluctuates during the simulation. To avoid artifacts
associated with a non-neutral simulation system, we introduce an approach to maintain
neutrality of the simulation box in constant pH molecular dynamics simulations, while
maintaining an accurate description of all protonation fluctuations. Specifically,
we introduce a proton buffer that, like a buffer in experiment, can exchange protons
with the biomolecule enabling its charge to fluctuate. To keep the total charge of the
system constant, the uptake and release of protons by the buffer are coupled to the
titration of the biomolecule with a constraint. We find that, because the fluctuation
of the total charge (number of protons) of a typical biomolecule is much smaller than
the number of titratable sites of the biomolecule, the number of buffer sites required
to maintain overall charge neutrality without compromising the charge fluctuations of
the biomolecule, is typically much smaller than the number of titratable sites, implying
markedly enhanced simulation and sampling efficiency.}",
}
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| main paper 1 | |
| supporting information 1 |
@Article{Ullmann2012GMCT,
author = "R. Thomas Ullmann and G. Matthias Ullmann",
title = "{GMCT: A Monte Carlo simulation package for
macromolecular receptors}",
journal = "J. Comput. Chem.",
volume = "33",
pages = "887-900",
year = 2012,
doi = {10.1002/jcc.22919},
abstract = "{GMCT (generalized Monte Carlo titration) is a versatile
suite of computer programs for the efficient
simulation of complex macromolecular receptor systems as
for example proteins.
The computational model of the system is based on a
microstate description of the receptor and an average
description of its surroundings in terms of chemical
potentials.
The receptor can be modeled in great detail including
conformational flexibility and many binding sites with
multiple different forms that can bind multiple different
ligand types.
Membrane embedded systems can be modeled with
electrochemical potential gradients.
Overall properties of the receptor as well as properties
of individual sites can be studied with a variety of
different Monte Carlo (MC) simulation methods.
Metropolis MC, Wang-Landau MC and efficient free energy
calculation methods are included.
GMCT is distributed as free open source software at
www.bisb.uni-bayreuth.de under the terms of the
GNU Affero General Public License.
}",
}
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| main paper 1 |
@PhDthesis{Ullmann2012PhD,
author = "R. Thomas Ullmann",
title = "Monte Carlo simulation methods for studying the
thermodynamics of ligand binding & transfer processes
in biomolecules",
school = "Universit{\"{a}}t Bayreuth",
year = 2012,
abstract = "{
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 NH3}$/H$^{+}
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 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.}",
}
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| main paper 1 |
@Article{Ullmann2012Amt-1,
author = "R. Thomas Ullmann and Susana L. A. Andrade and G. Matthias Ullmann",
title = "{Thermodynamics of transport through the ammonium transporter Amt-1
investigated with free energy calculations}",
journal = jpcB,
volume = {116},
pages = {9690-9703},
year = 2012,
doi = {10.1021/jp305440f},
abstract = "{Amt-1 from Archaeoglobus fulgidus (AfAmt-1) belongs
to the Amt/Rh family of ammonium/ammonia transporting membrane
proteins.
The transport mode and the precise microscopic permeation
mechanism utilized by these proteins are intensely debated.
Open questions concern the identity of the transported
substrate (ammonia and/or ammonium) and whether the
transport is passive or active.
To address these questions, we studied the overall
thermodynamics of the different transport modes as
a function of the environmental conditions.
Then, we investigated the thermodynamics of the
underlying microscopic transport mechanisms with
free energy calculations within a continuum
electrostatics model.
The formalism developed for this purpose is
of general utility in the calculation of
binding free energies for ligands with multiple
protonation forms or other binding forms.
The results of our calculations are compared
to the available experimental and theoretical
data on Amt/Rh proteins and
discussed in light of the current knowledge
on the physiological conditions
experienced by microorganisms and plants.
We found that microscopic models of electroneutral
and electrogenic transport modes are in principle
thermodynamically viable.
However, only the electrogenic variants have a net
thermodynamic driving force under the physiological
conditions experienced by microorganisms and plants.
Thus, the transport mechanism of AfAmt-1 is most
likely electrogenic.}",
}
| file | filetype |
| main paper 1 | |
| supporting information 1 |
@Article{Ullmann2011PaAzCoop,
author = "R. Thomas Ullmann and G. Matthias Ullmann",
title = "{Coupling of protonation, reduction and conformational
change in azurin from Pseudomonas aeruginosa
investigated with free energy measures of cooperativity}",
journal = jpcB,
volume = "115",
pages = "10346-10359",
year = 2011,
doi = {10.1021/jp204644h},
abstract = "{We used free energy calculations within a continuum electrostatics
model to analyze the coupling of protonation, reduction and
conformational change in azurin from Pseudomonas aeruginosa (PaAz).
PaAz was characterized extensively with a
variety of experimental methods.
Experimentally determined $\mathrm{p}K_{\mathrm{a}}$
values and pH-dependent reduction potentials are
used to validate our computational model.
It is well known from experiment that the reduction of
the copper center is coupled to the protonation of at least two
titratable residues (His-35 and His-83) and to the flip
of the peptide bond between Pro-36 and Gly-37.
Free energy measures of cooperativity are used for a
detailed analysis of the coupling between protonation,
reduction and conformational change in PaAz.
The reduction of the copper center, the protonation
of His-35 and peptide flip are shown to be cooperative.
Our results show that cooperativity free energies are
useful in detecting and quantifying thermodynamic
coupling between events in biomolecular systems.
The protonation of His-35 and the peptide flip are
found to be so tightly coupled that
these events happen effectively concerted.
This concerted change results in a marked alteration
of the electrostatic surface potential of azurin
that might affect the
interaction of azurin with its binding partners.
}",
}
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| main paper 1 | |
| supporting information 1 |
@Article{Ullmann2010FEP,
author = "R. Thomas Ullmann and G. Matthias Ullmann",
title = "{A generalized free energy perturbation theory accounting for
end states with differing configuration space volume}",
journal = jpcb,
volume = "115",
pages = "507-521",
year = 2010,
doi = {10.1021/jp1093838},
abstract = "{We present a generalized free energy perturbation theory
that is inspired by Monte Carlo techniques and based
on a microstate description of a transformation between
two states of a physical system.
It is shown that the present free energy perturbation theory
stated by the Zwanzig equation follows as a special case of
our theory.
Our method uses a stochastic mapping of the end states
that associates a given microstate from one ensemble with a microstate
from the adjacent ensemble according to a probability distribution.
In contrast, previous free energy perturbation methods use a static,
deterministic mapping that associates fixed pairs of microstates from
the two ensembles.
The advantages of our approach are that end states of differing configuration
space volume can be treated easily also in case of discrete configuration spaces
and that the method does not require the potentially cumbersome search for an
optimal deterministic mapping.
The application of our theory is illustrated by some example problems.
We discuss practical applications for which our findings could
be relevant
and point out perspectives for further development
of the free energy perturbation theory.
}",
}
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| main paper 1 | |
| supporting information 1 |
@Article{Becker2007,
author = "Torsten Becker and R. Thomas Ullmann and G. Matthias Ullmann",
title = "{Simulation of the electron transfer between the tetraheme subunit
and the special pair of the photosynthetic reaction center using
a microstate description}",
journal = jpcb,
volume = "111",
pages = "2957-2968",
year = 2007,
doi = "10.1021/jp066264a",
abstract = "{Charge transfer through biological macromolecules is essential
for many biological processes such as, for instance, photosynthesis
and respiration. Protons or electrons are transferred between
titratable residues or redox-active cofactors, respectively.
Transfer rates between these sites depend on the current charge
configuration of neighboring sites. Here, we formulate the kinetics
of charge-transfer systems in a microstate formalism. A unique
transfer rate constant can be assigned to the interconversion
of microstates. Mutual interactions between sites participating
in the transfer reactions are naturally taken into account.
The formalism is applied to the kinetics of electron transfer
in the tetraheme subunit and the special pair of the reaction
center of Blastochloris viridis. It is shown that continuum
electrostatic calculations can be used in combination with an
existing empirical rate law to obtain electron-transfer rate
constants. The re-reduction kinetics of the photo-oxidized
special pair simulated in a microstate formalism is shown to
be in good agreement with experimental data. A flux analysis
is used to follow the individual electron-transfer steps.
}",
}
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| main paper 1 |
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