# Membrane Modeling for XylE-transporter

## Abstract

In order to choose the proper promotor for the XylE-transporter the membrane integrity is evaluated for Membrane-Transporter Systems. XylE-transporters are consecutively added to the system and membrane thickness is compared to literature references.
The aim is to provide an educated guess in silico for transporter promotor selection within BioBrick construction and simultaneously preserving membrane integrity despite maximizing transporter quantitiy.

## Introduction

### MD Simulations

Molecular Dynamics (MD) simulations is one of the most common tools in computational biology. They are used to predict the mechanical behavior of a protein. At first a 3D Model of the protein is needed. This model gets transferred into a 3D environment. A force field is chosen which simulates all occuring forces during the simulation. In MD Simulations, a force field is a collection of mathematical functions and parameters which describe the potential energy of particles (atoms and molecules) and link them to a specific system nomenclature. For illustration the potential derived from the Assisted Model Building with Energy Refinement (AMBER) can be divided in four terms:

$V(r_1...r_n)=\sum_{ij} \epsilon [(\frac{\sigma_{ij}}{r_{ij}})^{12}-(\frac{\eta_{ij}}{r_{ij}})^6] + \sum_{ij} \frac{1}{4\pi \epsilon_0} \frac{q_i q_j}{r_{ij}^2}$

$+ \sum_{dihedral} K_{\Phi} [1+\cos(n \Phi - \delta)] + \sum_{bonds} \frac{1}{2} K_d(d-d_0) +\sum_{angles} \frac{1}{2} K_{\theta}(\theta-\theta_0)$

These terms are the core components of a force field. Thus the sum of all these terms approximates the total energy of a given system. Since we have an approximation of the potential and trajectories in phase space, the force acting on the particles can be computed as the derivative of this potential with respect to the particle position.

The first equation represents the non bonded interactions within a system. It can be divided into the Lennard-Jones potential, which approximates the interaction between a pair of neutral atoms or molecules. It is a empirically derived potential for van der Waals interactions. The second part is a Coulomb potential. It approximates the electrostatics between a pair of atoms i and j with partial charges by Edwald summation. The next term describes the oszillation of a chemical bonds as an harmonic spring. The last term describes the binding angels as well as the dihedral angels which are also approximated by harmonic springs. Force field parameters are derived by quantum mechanical calculations and fitted to available experimental datasets. The quality of MD simulations is largely depending on the applied force field.

### Coarse graining and the Martini Forcefield

Large biomolecular assemblies, such as biomembranes, require tremendous computational time to compute significant time scales. To circumvent this obstacle a coarse-graining protocol can be implemented in the simulation routine.

Coarse graining speaks for itself: the system is scaled into a coarser environment, using pseudocoordinates and pseudoatoms. That leads to a smoother potential and accelerates optimization.
Additionally, two or more atoms are mapped into one pseudoatoms, which decreases the particle quantity and therefore coordinates and forces to compute.

Martini persectudes a 4 to 1 mapping strategy, resulting in acceleration of a magnitude of four or more. Considering dynamics an elastic-network (e.g. ElNeDyn) can be applied to improve the physical accurancy of the simulation.
Even though force fields are fitted to experimental and theoretical data, as Martini to the Gibbs-Energy of the Octanol-Water Partition Coefficient considering thermodynamics, every simulation needs its experimental interface to retain validity of the analysis and has to be choosen correspondingly to the problem.

## Membrane Modelling and Simulation

Membrane transport of the substrat Xylose could be a limiting factor in monomerproduction. To maximize Xylose-influx it is obvious, that the amount of membrane transporter proteins has to be maximized aswell. In this context it seems advisable to choose a highly active promoter for BioBrick construction.
In order to consider membrane integrity coarse-grained MD simulations of different system containing an increasing amount of membrane transporters were run. The membrane thickness was derived and compared to literature references to provide an educated guess for promotor selection in membrane transporter BioBrick construction.

### General workflow

1. The membrane compisition of the inner E. Coli membrane was estimated according to reference 1 and the available martini lipids resulting in an equimolar distribution of the lipids DPPC, DOPE, POPE and POPG.
2. A coarse-grained membrane patch was generated using the Insane script, consisting of 132 molecules per lipidtype.
3. The system was neutralized, solvated in water and 150mM NaCl and equibrilated to 323 K and 1 bar to match native conditions.
4. The XylE coordinates from 4GC0.pdb were coarse-grained according to the Martini forcefield and combined with the elastic network model ElNeDyn.
5. The protein model was energy minimized and equibrilated to 323 K and 1 bar to match native conditions.
6. The membrane proteins were oriented to the membrane according to their OPM-entry using VMD.
7. The membrane proteins were embedded using high lateral pressure of 1000 bar.
8. After embedding the membrane proteins a 2us NPT-simulation was computed to relax membrane and evaluate membrane integrity.

## Results

The computed system containing a quantity of two transporters exhibits stable behaviour and consistency with the literature references. The derived average membrane thickness of 34.7 A (Fig. 2) deviates marginally from the literature reference of 37.5 A, although the standart deviation is increased.

A look at membrane top in Figure 3 exhibits an uneven distribution of different lipid residues, which can cause such irregularities. A longer membrane simulation pre-run to let the lipids diffuse evenly can be a possible solution.

Both proteins show a minor deviation to their reference structure shown in Figure 4, but with a maximum of 0.35 nm is the RMSD still within considerable ranges.

Within this simulation both transporters get in contact from the bottomside as seen in Figure 5. In the RMSF in Figure 6 are no additional fluctuations visible; both proteins tend to fluctuate less than in solution, if they are embedded in a membrane. Explicit possible interactions between both proteins are not considered, hence a contact side shows no effect on the kinetic behaviour of the proteins.

Conclusive a cloning series start with a konstituive promotor is a good choice. All protein and lipid characterization values differ marginally, but noticeable from the references.

#### References

1. Oursel D, et al. Lipid composition of membranes of Escherichia coli by liquid chromatography/tandem mass spectrometry using negative electrospray ionization. Rapid Communications in Mass Spectrometry (2007)
2. Mitra K, et al. Modulation of the bilayer thickness of exocytic pathway membranes by membrane proteins rather than cholesterol. Proceedings of the National Academy of Sciences (2004)
3. Frenkel D, Smit B. Understanding Molecular Dynamics Simulations. 2nd Edition, Academic Press (2001)
4. Gromacs Manual Version 5.0.6
5. Marrink S, et al. The MARTINI Force Field:  Coarse Grained Model for Biomolecular Simulations. Journal of Physical Chemistry (2007)
6. Wassenaar T, et al. Computational Lipidomics with insane: A Versatile Tool for Generating Custom Membranes for Molecular Simulations. Journal of Chemical Theory and Computation (2015)
7. Periole X, et al. Combining an Elastic Network With a Coarse-Grained Molecular Force Field: Structure, Dynamics, and Intermolecular Recognition. Journal of Chemical Theory and Computation (2009)
8. Javanainen M. Universal Method for Embedding Proteins into Complex Lipid Bilayers for Molecular Dynamics Simulations. Journal of Chemical Theory and Computation (2014)