Open Access

Kara Katharina Maria Grotz

• This cumulative thesis discusses the development of optimized force field parameters for Magnesium and resulting improved simulations of Magnesium-RNA interactions, including the in silico exploration of binding sites. This thesis is based on four publications as well as unpublished data. A fifth publication that was written during the time of the Ph.D. is discussed in the Appendix. This publication analyzes monovalent ion-specific effects at mica surfaces. Nucleic acids in general and RNA in particular are fundamental to life itself. Especially in the folding and function of RNA, metal cations are crucial to screen the negatively charged nucleic acid backbones to allow for complex functional structures. They stabilize the tertiary structure of RNA and even drive its folding. Furthermore, similarly to proteins, RNAs can catalyze multiple reactions, rather than consisting of the 20 amino acids of a protein, RNA constitues of only four different building blocks. Metal cations play an important role here as additional cofactors. One essential ion is Magnesium (Mg2+), commonly referred to as the most important cofactor for nucleic acids. Mg2+ carries two positive charges. Its comparably small size and high charge result in a high charge density that has strong polarizing effects on its surroundings. Furthermore, Mg2+ forms a sharply defined first hydration shell with an integer number of coordinating water molecules. As a result, an exclusion zone exists around the ion within which no water molecules are observed. Moreover, Mg2+ displays a high solvation free energy and a low exchange rate of waters from its first hydration shell. Finally, it contains a strong preference towards oxygens . Together, this makes Mg2+ a particularly well suited interaction partner for the charged non-bridging phosphate oxygens on nucleic acid backbones and explains its crucial biological role. The immense number of physiological and technological functions and applications indicates the significant scientific attention Mg2+ received. In experimental studies, however, severe difficulties arise for multiple reasons: Mg2+ is spectroscopically silent and cannot be detected directly by resonance techniques like NMR or EPR. Indirect observation is possible, either by detecting changes in the overall RNA structure with and without bound Mg2+, or by replacing the Mg2+ ion with another spectroscopically visible ion. In the latter, however, it cannot be guaranteed that the altered ion does not also alter the interaction site or even the whole structure. Another detection method is X-ray crystallography, but here challenges arise from Mg2+ being almost indistinguish- able from other ions as well as from water if not for very high resolutions and precise stereochemical considerations. Alternatively, molecular dynamics (MD) simulations can be performed, with the power of adding atomistic insight to the interplay of metal cations and nucleic acids. MD simulations, however, are only as accurate as their underlying interaction models and the development of accurate models for the description of Mg2+ faces challenges especially in describing three properties: (i) Polarizability. Commonly used simple models like the 12-6 type Lennard-Jones model typically fail to reproduce simultaneously thermodynamic and structural properties of a single ion in water. Alternative strategies include the use of a 12-6-4 type Lennard-Jones potential as proposed by Li and Merz, where the additional r−4 term explicitly accounts for polarization effects. The resulting Lennard-Jones potential is thereby more attractive and more long-ranged than for typical models of the 12-6 type. (ii) Kinetics. Most Mg2+ models either fully ignore considerations about the timescales on which water exchanges from the first hydration shell of the ion or use inappropriate methodology to calculate the underlying kinetics. A realistic characterization of the involved timescales is imperative to be able to describe a seemingly simple process like the transition from inner-to-outer sphere binding and vice versa. This transition governs most biochemical reactions involving Mg2+ and therefore subsequent processes can only by as fast as the transition itself. However, already the previous step – the exchange of a water from the first hydration shell of the ion – is described my current Mg2+ models up to four orders of magnitude too slowly, which makes the observation of such events on the timescale of a typical simulation difficult or even impossible. Alln ́er et al. [48] as well as Lemkul and MacKerell explicitly considered the exchange rate into their parameter optimization procedure. To compute the rate, both studies applied Transition State Theory along a single reaction coordinate – the distance towards one of the exchanging waters. However, it could be shown that the water exchange from the first hydration shell requires at least the consideration of both exchanging water molecules in order to be able to realistically record the underlying rate using Transition State Theory. Furthermore, the model of Alln ́er et al. significantly underestimates the free energy of solvation of the ion. (iii) Interactions between Mg2+ and nucleic acids. Typically, ionic force field parame- terization concentrates on the optimization of solution properties. The trans- ferability of these solution optimized parameters towards interactions with biomolecules, however, often fails.
• Nukleinsäuren im Allgemeinen und RNA im Besonderen sind grundlegende Bausteine des Lebens. Für eine Vielzahl von integralen Funktionen der Nukleinsäuren ist die Interaktion mit Metalkation unabdingbar. Ein besonderes Ion ist dabei Magnesium (Mg2+), dass auch als wichtigster Cofaktor für Nukleinsäuren bezeichnet wird. Molekulardynamiksimulationen (MD-Simulationen) sind in der Lage atomistische Einblicke in das Zusammenspiel von Metallkationen und Nukleinsäuren zu geben. MD-Simulationen können jedoch nur so akkurat sein wie ihre zugrunde liegenden Wechselwirkungsmodelle und die Entwicklung genauer Modelle zur Beschreibung von Mg2+ steht vor Herausforderungen, insbesondere bei der Beschreibung von drei für Mg2+ wesentlichen Eigenschaften: (i) Polarisierbarkeit, verursacht durch die hohe Ladungsdichte von Mg2+. Sie führt dazu, dass häufig verwendete einfache Modelle wie das Lennard-Jones-Modell vom Typ 12-6 typischerweise nicht gleichzeitig thermodynamische und strukturelle Eigenschaften eines einzelnen Ions in Wasser reproduzieren können. (ii) Kinetik. Der Austausch von Wasser aus der ersten Hydrathülle findet auf der Mikrosekunden-Zeitskala statt. Die Assoziation und Dissoziation von Mg2+ an RNA und weitere Prozesse sind als nachfolgende Schritte dementsprechend langsamer, was deren Beobachtung auf der Zeitskala einer typischen Simulation erschwert bzw. unmöglich macht. Zusätzlich unterschätzen aktuelle Mg2+-Modelle die tatsächliche Austauschrate um bis zu vier Größenordnungen. (iii) Wechselwirkungen zwischen Mg2+ und Nukleinsäuren. Meistens konzentriert sich die Parametrisierung ionischer Kraftfelder auf die Optimierung der Wechselwirkungen zwischen dem Ion und seiner umgebenden Lösung, meist Wasser. Die Übertragbarkeit dieser lösungsmitteloptimierten Parameter auf Wechselwirkungen mit Biomolekülen ist jedoch oft nicht gegeben.