5 Naturwissenschaften und Mathematik
Monte Carlo Simulation Methods for Studying the Thermodynamics of Ligand Binding & Transfer Processes in Biomolecules
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.
Crystalline-core micelles based on triblock terpolymers with polyethylene middle blocks
- This thesis is focused on the crystallization-induced structure formation of polyethylene containing triblock terpolymers in organic solvents to surface-compartmentalized worm-like crystalline-core micelles (wCCMs). Obtaining profound knowledge of the parameters controlling the self-assembly process allowed the production of a variety of complex one-dimensional micellar architectures with many potential applications, such as adaptive surfactants.
At first, the basic parameters that control the crystallization-induced self-assembly were explored using symmetric polystyrene-block-polyethylene-block-poly(methyl methacrylate) (PS-b-PE-b-PMMA) triblock terpolymers and a PS-b-PE-b-PS triblock copolymer. In good solvents for the PE block, e.g. THF and toluene, the selective formation of wCCMs was observed over a wide range of concentration, applied crystallization temperature and polymer composition. Whereas wCCMs produced by PS-b-PE-b-PS showed a homogeneous PS corona, a patch-like compartmentalization of the corona was observed if the micelles were formed by PS-b-PE-b-PMMA. As THF shows equal solvent quality for both corona blocks, wCCMs with almost alternating PS and PMMA compartments of about 15 nm were observed in this solvent. However, if structure formation was conducted in bad solvents for PE, such as dioxane or dimethylacetamide, spherical micelles with amorphous PE cores were formed already before crystallization. Hence, the subsequent crystallization of PE resulted in spherical CCMs with a patchy or a homogeneous corona depending on the used triblock. These findings allow the highly selective production of stable spherical or worm-like CCMs from the same polymer.
As the corona structure of the patchy micelles self-assembled from triblock terpolymers was mainly deduced from transmission electron microscopy (TEM) performed on dried samples, a small-angle neutron scattering (SANS) study was performed in order to elucidate the morphology in solution. Therefore a partly deuterated triblock terpolymer was synthesized and measured at different contrasts to allow the selective detection of the different corona compartments. The resulting SANS curves could be interpreted using a form factor model for core-shell cylinders with alternating PS and PMMA hemishells including interparticle interactions, thus validating the TEM observations. Notably, Janus-type and patchy cylinders can be clearly distinguished using the applied form factor model.
Moreover, the controlled formation of wCCMs with tunable corona composition and structure was achieved using the cocrystallization of different triblock copolymers. Via random cocrystallization of PS-b-PE-b-PMMA and PS-b-PE-b-PS the corona morphology could be tuned continuously from a mixed corona at low PMMA content over spherical PMMA patches of increasing number and size to alternating PS and PMMA patches. This approach allows to manufacture wCCMs with predefined corona structure omitting the need to synthesize a new tailor-made triblock terpolymer for every desired morphology.
By establishing the controlled crystallization-driven self-assembly of triblock terpolymers with PE middle blocks, it was further possible to prepare wCCMs with predefined average lengths up to 500 nm and length polydispersities as low as Lw/Ln = 1.1. Here, self-assembled spherical CCMs of PS-b-PE-b-PS were used as seeds for the controlled growth of PS-b-PE-b-PS unimers. Upon further addition of PS-b-PE-b-PMMA unimers these grew epitaxially onto the preexisting wCCMs, resulting in triblock co-micelles that consisted of middle blocks with a homogeneous PS corona and outer blocks with alternating PS/PMMA compartments. These structures represent not only the first block co-micelles including blocks with a patchy corona, but also the first ones produced from purely organic block copolymers.
In view of application, the ability of patchy wCCMs formed by PS-b-PE-b-PMMA to stabilize interfaces was investigated using pendant-drop tensiometry. The observed reduction of the interfacial tension at the toluene/water interface was significantly higher than that of comparable triblock terpolymer single chains and that of wCCMs with a homogeneous PS corona. Interestingly, the obtained equilibrium interfacial tension equaled that of Janus cylinders with similar dimensions. To explain this unexpected finding the corona chains were proposed to adapt to the interface via selective collapse and shielding of the incompatible part of the corona chains. Studying wCCMs formed by several triblock terpolymers with different compositions, the interfacial activity was found to increase with increasing overall length of the corona chains, and to a certain extent with the molar fraction of PS units in the corona.