Cellular environment effects

Proteins and nucleic acids operate inside cells, where the concentration of macromolecules can be > 300 mg/mL. In addition, they function in a very heterogeneous medium, from cell membrane to the cytoplasm, which is a highly saline environment.

Fluorescence (Giepmans et al. Science 2006, 312, 217-224) and NMR spectroscopy (Sakakibara et al., Nature 2009, 458, 102-105) are among the very few techniques that allow the observation of a particular protein in the ‘sea of macromolecules’ present in the cytoplasm. Whilst for NMR is starting to provide already high-resolution structural information, only qualitative or semi-quantitative structural determinants can be obtained by fluorescence spectroscopy. In fact, the lack of our understanding of the physical origin of spectral features greatly hampers interpretation. Computational spectroscopy could be of great help in this respect.

Computational spectroscopy in vitro and in cell conditions

Optical properties of chromophores embody a key facet of cell biology, allowing for a precise interrogation of a variety of biochemical events, including signaling, metabolism, and aberrant processes. These range from probing transient interactions between biomolecules (proteins and nucleic acids), to protein dynamics and fibrillation and plaque formation in neurodegenerative diseases. Understanding how the environment tunes such optical properties is therefore is therefore crucial, yet this information is so far mostly lacking. A powerful tool to address this issue is given by the so-called quantum mechanics/molecular mechanics (QM/MM) methods. In this approach, the chromophore may be treated at the quantum mechanical level, while the environment is described with an effective potential: the influence of the MM (presumably very complex and very large) environment is basically included as an external potential and, in case the chromophore is covalently bound to MM region, by a mechanical coupling with the environment. Most often the QM approach is solved within density functional theory (DFT) to study ground state properties, and time-dependent DFT (TDDFT) when excited states are involved, as in the case of the optical properties TDDFT is computationally very efficient, yet its predictive power depends dramatically on the system and on the functional used to reproduce the exchange and correlation interactions. Several approaches, including post-Hartree-Fock ones (configuration interaction and similar methods), have been already used to predict optical properties of biomolecules. Many-body perturbation theory (MBPT is an attractive alternative, although of course it comes with higher computational cost than TDDFT. However, biophysical applications of one of the most widely used schemes of MBPT, the combination of the GW method with the Bethe-Salpeter equation (BSE) are, so far, lacking. The GW method is used for the evaluation of the single quasiparticle energies, and the BSE to introduce excitonic effects. We are collaborating with O. Pulci (University Tor Vergata, Rome) and A. Rubio to establish protocols to provide accurate and transferable calculations of optical properties.

We are currently calculating the optical properties of rhodamine-based probes attached to the phosphate binding protein, which are used as inorganic phosphate (Pi) sensors. Binding of Pi to the protein provokes structural rearrangements of the protein. This is associated with a drastic change in the absorption and emission spectra of the rhodamines, along with an enhancement in the emission intensity of about 18 folds. The structural facets on which this process is based are not clear. Our calculations will be validated against experiments performed by the experimental collaborators in the Martin Webb's group at the MRC in London. This work might establish the molecular basis of fluorescence and absorption spectral shifts upon ligand-used conformational changes and may be used as a general protocol in a variety of biophysical applications.

Ions and protons in highly saline conditions

Several popular used ion models for molecular simulations have been parametrized at zero ionic strength. However, concentrations of ions are much higher in cell, and in particular inside biological ion channel or near DNA and RNA. We are testing the commonly used ion models in term of the non-ideal properties of single ions in electrolyte solutions by free energy calculations (collaboration with Bob Eisenberg and Simone Raugei).

We are also testing the domain of applicability of alkali ions’ force fields in describing ion permeation along the NanC porin (collaboration with Bob Eisenberg group) in a project funded by DFG.

The classical ion force field ion models selected from the test calculations on electrolytes will allow us to determine the best guess for the free energy associated with Na⁺ and K⁺ using force field based descriptions, under physiological salt conditions. Technically demanding, but well-established techniques like metadynamics (A. Laio and M. Parinello, Proc. Natl. Soc. Sci. USA, 99, 20 (2002)) will be used for this purpose. As an obvious first choice, the projection of the cation’s position onto the NanC channel axis may serve as reaction coordinate, see figure below. Comparison of the free energy profiles for Na+ and K+ will reveal the role of each channel amino acid residue along the paths, respectively, and the role of ion-ion correlations.

From studies on model compounds it has been known that polarization and charge-transfer effects play an important role in ion permeation (T. W. Whitfield et al., J. Chem. Theory Comput 3, 2068 (2007) and D. Bucher et al., Biophys. Chem. 124, 292 (2006)). Since this is expected to be very true for a highly-charged ion channel NanC as well, we will create free energy profiles using QM/MM methods, i.e. calculations where the most important chain residues and permeating ions are treated at the quantum level, and the remainder of the system by a force field. The partial charges from the force-field region will polarize the QM region in a specific manner allowing to elucidate the electrostatic and steric interactions of individual amino acids with the QM zone, respectively.

Our calculations will be complemented by special (non-atomistic) Monte Carlo simulations using reduced structural models (D. Bonda et al, J. Gen. Physiol. 133, 497 (2009)) – these calculations yield current profiles for the ion permeation, (i) help to explain how ion channels exert selectivity and (ii) provide estimates of the free energy of permeation. The latter feature allows to compare the results to the atomistic simulations, and so enhances the understanding of the methodologies’ strengths and weaknesses and of the NanC functional mechanism.

First principle-based statistical thermodynamics calculations are addressed issues about protein transfer events in biological systems.

Proton transfer at water/hydrophobic liquid interface

Recently, both experimental and computational studies suggested that protons are preferably located on water/hydrophobic surfaces (S. Iuchi, H. Chen, F. Paesani, G. Voth, J. Phys. Chem B 113, 4017 (2009)). Therefore, a fully understanding of this phenomenon is highly desirable and will impact significantly on how we look at biological interfaces, as present in protein folding, protein/protein interaction and lipid membrane.

We are investigating the structure and the energetics of an excess proton at the water/hydrophobic surface with ab initio molecular dynamics for a system size ~1800 atoms. In our model, both proton transfer processes and electronic polarization effects are included, compared to former studies.

The free energy profile of the proton to the surface, constructed by using the metadynamics method, will give a state of the art answer to this fundamental question.

In addition, we are interested to investigate the effect of coupling between physiological anions (Cl^-) and protons in highly saline conditions for this phenomenon, collaborating with Peter Pohl's group (University of Linz, Austria).

This project is supported by PRACE early access call and running on JUGENE supercomputer.

Ab initio molecular dynamics simulation of proton transport in biological ion channel

Ion channels are crucial for a normal functioning of cells as they are involved in signaling and sensing pathways. Dysfunction of ion channels are thus at the basis of several diseases called channelopathies, including, for instance, cystic fribrosis, renal disorders or osteoporosis. The pentadecapeptide dimer Gramicidin A is a monovalent ion selective transmembrane channel, which effectively conducts monovalent ions such as H⁺, K⁺ or Na⁺, but blocks divalent ions as well as anions (D. A. Kelkar, A. Chattopadhyay, Biochimica et Biophysica Acta 1768, 2011 (2007) and Z. Qin, H. L. Tepper, G. A. Voth J. Phys. Chem. B 111, 9931 (2007)).

The transport of excess protons along the 1-dimensional wire of water molecules inside the Gramicidin channel is faster (a single conduction event takes about 500 ps) than in any other narrow-pore biological channel conducting H⁺ or other monovalent ions (T. E. DeCoursey J. Physiol. 22, 5305 (2008)). The inside of the pore is characterized by carbonyl groups interacting with the water molecules and the excess proton. Empirical quantum-mechanical methods have lead to several insights on the mechanism of proton permeation, yet the conductance calculated with such approaches is much smaller than the experimental value.

A key to an in-depth understanding of the unique features of this presumably Grotthuss-type proton transport process is an appropriate treatment of bond breaking and making processes, hydrogen bonding, nuclear tunneling effects, mutual electronic polarization effects of the hydronium ion H₃O⁺ and its environment as well as an adequate inclusion of a transmembrane potential, which acts as a driving force for the ions.

These requirements clearly call for the use of first-principle methods. We are currently studying proton transport along the Gramicidin channel in a full ab initio Car-Parrinello molecular dynamics approach. The entire system consists of the Gramicidin A dimer surrounded by 8 phospholipids (DMPC) and about 140 water molecules (about 1900 atoms). We will calculate the free energy profile of the process applying the metadynamics approach. Among others the results will be used to derive a kinetic model for proton conductance or to simulate ¹⁷O-NMR chemical shifts of the carbonyl groups, which can be compared to experimental data.

This project adds a new dimension in the simulation of biological ion channels as it allows to predict quantitatively and fully from first principles, energetics and spectroscopic properties of fundamental biological systems in laboratory-feasible conditions by making use of the immense computational resources of the JUGENE supercomputer through the support of the PRACE 1st regular call.