Water interaction with proteins

Bernardo Barbiellini, Northeastern University

Specific Aims

Water is crucial for the three-dimensional structure and activity of proteins. The aim of this work is to present cases where the conventional molecular dynamics approach fails and one need to introduce a quantum mechanical description of the hydrogen bond [1] in order to understand these processes. In solution, proteins possess a conformational flexibility that encompasses a wide range of hydration states not seen in the crystal. In addition, water acts as a lubricant, so easing the necessary hydrogen bonding changes. Water molecules can bridge between the carbonyl oxygen atoms and amide protons of different peptide links to catalyze the formation, and its reversal, of peptide hydrogen bonding. The internal molecular motions in proteins, necessary for biological activity, are very dependent on the level of hydration. We will use computer simulations to model the quantum behavior of electrons involved in hydrogen bonds of the water with the proteins. In particular we will focus on the behavior of ordered water with long range quantum coherence interacting with tubulin proteins. This research may be helpful to find new treatments for cancer.

Significance

The first hydration shell around proteins is ordered, with high proton transfer rates. It is also 10-20% denser than the bulk water [2]. Using X-ray analysis, this water shows a wide range of non-random hydrogen-bonding environments and energies. Proteins are formed from a mixture of polar and non-polar groups. Water is most well-ordered round the polar groups where residence times are longer than around non-polar groups. Both types of group create order in the water molecules surrounding them but their ability to do this and the type of ordering produced are very different. Polar groups are most capable of creating ordered hydration through hydrogen bonding

.

Figure 3. The water network links secondary structures within the protein and so determines not only the fine detail of the protein's structure but also how particular molecular vibrations may be preferred. The above chain of ten water molecules, linking the end of one a-helix (helix 9, 211-227) to the middle of another (helix 11, 272-285) is found from the X-ray diffraction data of glucoamylase-471, a natural proteolytic fragment of Aspergillus awamori glucoamylase [2].

Moreover, protein folding is driven by hydrophobic interactions, due to the unfavorable entropy decrease forming a large surface area of non-polar groups with water. Consider a water molecule next to a surface to which it cannot hydrogen bond. The incompatibility of this surface with the low-density water that forms over such a surface encourages the surface minimization that drives the proteins' tertiary structure formation [2].

 

Approach

(a) Quantum Methods

The Schrödinger equation is a wave equation given by

In principle, the Schrödinger equation allows us to calculate all of the properties of a chemical system. Unfortunately, an exact solution of the Schrödinger equation is possible only for very simple systems. Still, quantum calculations are of interest because they can deal with electronic effects, electron delocalization, charge-transfer, and other phenomena, which are otherwise difficult or impossible to treat at the level of classical mechanics.

Ab initio ("from scratch") calculations are an attempt to solve the Schrödinger equation, making assumptions and approximations as needed. The first approximation (the Born-Oppenheimer approximation) is that the nuclei do not move much, relative to the electrons. Thus, the nuclei are fixed in space, and the calculation is to determine the distribution of electrons around the nuclei, orbital by orbital. These calculations are numerically extremely intensive and are not practical for proteins (very small peptides are a practical limit at present).

(b) Molecular Mechanics/Force field Methods

A force field is composed of equations and parameters. Equations are chosen which will mathematically model interatomic forces, and parameters are empirically fit to these equations so that the system produces an appropriate model of the energies of interest.

The interactions to be modeled divide broadly into two groups: bonded interactions and non-bonded interactions. The bonded interactions include (a) bond length stretching/compression; (b) bond angle bending; (c) dihedral angle (torsional) rotation; (d) so-called "improper torsions," which keep planar groups planar and maintain the chirality of tetrahedral atoms. The non-bonded interactions are van der Waals attraction/repulsion and electrostatic attraction/repulsion.

In some cases, special treatment has been applied to the case of hydrogen bonds; in other cases, they are treated as a special case of electrostatics (for example when the bond distance is large).

An implicit assumption in force field calculations is that all of the energy terms for a given molecule are additive. However this hypothesis is not fulfilled in general by the hydrogen, bond because of its cooperative effect, which was discussed above.

(c) Mixed methods

We will develop and use a mixed mode quantum mechanical/ molecular mechanical (QM/MM) program for highly accurate energy calculations of protein-ligand interactions in the active site.

Part of this code is already commercially available [3]. The program will be specifically designed for proteins and allows a number of different QM/MM boundaries for residues in the active site. Traditional molecular mechanics calculations, although highly improved over the years, still have limited accuracy compared to the highest level quantum mechanic treatments, particularly in diverse and novel chemical environments, and are not able to describe correctly short hydrogen bond. In the quantum mechanical region, one can describe effects like electron transfer, charge transfer, and charge polarization, all properties that a regular molecular mechanics force field is incapable of capturing. Conversely, highly accurate quantum mechanical calculations are still limited to a few hundred atoms even with the fastest computers. The solution is to employ a mixed mode calculation where only the critical region is treated quantum mechanically. This treatment, however, requires not only good molecular mechanical and quantum mechanical treatments, but particular attention must also be paid to an accurate joining of the two regimes at the boundary region.

(d) Density Matrix

The density matrix is a fundamental property of quantum mechanical systems, because it determines the degree of locality of the bonding properties. Inelastic x-ray scattering data are particular important for determining the density matrix from the experiment. Our main goal is to develop powerful computational methods to extract the density matrix for the electrons involved in the hydrogen bonds directly from future scattering experiments. As a matter of fact the previous quantum methods can be extended to determine the density matrix from a given set of observed properties. This will involve the following steps:

(1) Choose an appropriate basis set for describing the relevant electron wave functions.

(2) Calculate the desired experimental properties from the corresponding

density matrix and evaluate the agreement between the calculated

and observed properties using the Chi square statistics.

(3) If the agreement is not acceptable, find other wave functions and occupation numbers, that will improve the result.

The method can systematically improved: if one is not satisfied with the agreement with the experiment after step 3, simply return to step 1 and choose a better representation for the wave functions.

Innovation

Microtubules are tiny sub-components of cells [4,5]. They are prominent aspects of the skeleton of all eukaryotic cells (being parts of a ubiquitous structure known as the cytoskeleton) - they are the structural and dynamical basis of the cells: for example they mediate cell division. They may participate in important quantum mechanical phenomena [6] involving water ordering in their interior. We therefore plan to study these systems with the methods described above in order to acquire a new insight on their nature.

Figure 6. Crystallographic structure of microtubules.

 

Microtubules are composed of internetworked tubulin proteins. Tubulins are internetworked and undergo "conformational state changes" as shown in Figure 7.

Figure 7. Left: Microtubule (MT) structure: a hollow tube of 25 nanometers diameter, consisting of 13 columns of tubulin dimers arranged in a skewed hexagonal lattice Right (top): Each tubulin molecule may switch between two (or more) conformations, coupled to London forces in a hydrophobic pocket. Right (bottom): Each tubulin can also exist (it is proposed) in quantum superposition of both conformational states.

 

Tubulin is a heterodimer [4], shown in Figure 6,consisting of alpha and beta-tubulin subunits. The alpha and beta-tubulins are 40% identical in amino acid structure, and their three-dimensional structures are basically.

Figure 7: Tubulin Structure.

 

Both alpha and beta forms have a molecular mass of approximately 50 kDa and a diameter of about 4 - 5 nm. Microtubules of mammalian cells disintegrate at temperatures below 10 C. On the other hand, they reconstitute from tubulin in vitro at physiological temperature in the presence of GTP (at equimolar concentrations to tubulin) and magnesium ions. On the basis of the reversibility of cold-induced microtubule disassembly, tubulin can be easily purified by so-called temperature-dependent disassembly/reassembly cycles. This procedure was introduced by Shelanski et al. (1973) to obtain microtubule protein from brain tissue, which is known to be rich in tubulin [5].

Microtubule-binding proteins, shortly called MAPs, are believed to stimulate the formation of microtubules and to stabilize them. For mammalian brain, two main groups of high molecular weight MAPs around 300 kDa

The microtubule also appears as a polar structure with a plus and a minus end [5]. Polarity is a very important feature for microtubule functioning. It is the basic property for interaction with water molecules and for direction dependent cellular events, e.g., vesicle transport.

The tube-shaped microtubules and the tubulins are likely candidates for quantum coherence because [6]:

(i) Microtubule individual subunit (tubulin) conformations may be coupled to quantum-level events (electron movement, dipole, phonon).

(ii) Microtubule paracrystalline lattice structure, symmetry, cylindrical configuration and parallel alignment promote long-range cooperativity and order. Moreover hollow microtubule interiors appear capable of water ordering.

In this project we will focus in the water-ordering inside the microtubules. Thus, we may have similar conditions as in crystal ice where the quantum nature of the hydrogen bond was found important [1]. We could also check our simulations by using X ray scattering techniques .

Finally the present project may have also some important pharmaceutical consequences. Because microtubules are essential for cells to grow and divide, they are the target of various drugs, including the widely used anti-cancer drug Taxol [7]. Taxol is a drug derived from the bark of yew trees. It stabilizes microtubules and causes most of the free tubulin to assemble into microtubules, effectively arresting mitosis.

 

Figure 8: A space-filling structure of tubulin. A Taxol-like molecule, shown in red, is bound to the structure [7].

 

We will determine the detailed, three-dimensional structure of tubulin, bound to a Taxol-like molecule in a solvent such as water. This structure not only will help researchers better understand microtubules and the cellular processes they facilitate, but may also aid efforts to design more effective Taxol-like drugs.

In conlcusion, microtubules take part in so many different cellular functions that the continued study of tubulin is sure to enhance our knowledge of these functions and will almost inevitably produce new treatments for cancer.

Bibliographic References

[1] http://www.bell-labs.com/news/1999/january/12/1.html

E. D. Isaacs, A. Shukla, P. M. Platzman, D. R. Hamann, B. Barbiellini and C.Tulk, Phys. Rev. Lett., 82, 600-603 (1999).

[2] http://www.sbu.ac.uk/water/protein.html

[3] http://www.schrodinger.com

[4] http://srv2.lycoming.edu/~newman/courses/bio43599/tubulin/index.html

[5] http://www.imb-jena.de/~kboehm/Tubulin.html

[6] http://www.consciousness.arizona.edu/hameroff/slideshow_2.htm

[7] http://www.nigms.nih.gov/news/releases/downing.html

E. Nogales, S.G. Wolf, K.H. Downing, Structure of the ab tubulin dimer by electron crystallography, Nature 391, 199-203 (1998).