Biology Monte Carlo method
Encyclopedia
Biology Monte Carlo methods (BioMOCA) have been developed at the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...

 to simulate ion transport in an electrolyte environment through ion channels or nano-pores embedded in membranes. It is a 3-D particle-based Monte Carlo
Monte Carlo
Monte Carlo is an administrative area of the Principality of Monaco....

 simulator for analyzing and studying the ion transport problem in ion channel systems or similar nanopores in wet/biological environments. The system simulated consists of a protein forming an ion channel (or an artificial nanopores like a Carbon Nano Tube, CNT), with a membrane (i.e. lipid bilayer) that separates two ion baths on either side. BioMOCA is based on two methodologies, namely the Boltzmann transport
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...

 Monte Carlo (BTMC) and particle-particle-particle-mesh (P3M). The first one uses Monte Carlo method to solve the Boltzmann equation, while the later splits the electrostatic forces into short-range and long-range components.

Backgrounds

In full-atomic molecular dynamics
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...

 simulations of ion channel
Ion channel
Ion channels are pore-forming proteins that help establish and control the small voltage gradient across the plasma membrane of cells by allowing the flow of ions down their electrochemical gradient. They are present in the membranes that surround all biological cells...

s, most of the computational cost is for following the trajectory of water molecules in the system. However, in BioMOCA the water is treated as a continuum dielectric background media. In addition to that, the protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

 atoms of the ion channel are also modeled as static point charges embedded in a finite volume with a given dielectric coefficient. So is the lipid membrane, which is treated as a static dielectric region inaccessible to ions. In fact the only non-static particles in the system are ions. Their motion is assumed classical, interacting with other ions through electrostatic interactions and pairwise Lennard-Jones potential
Lennard-Jones potential
The Lennard-Jones potential is a mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules. A form of the potential was first proposed in 1924 by John Lennard-Jones...

. They also interact with the water background media, which is modeled using a scattering mechanism.

The ensemble of ions in the simulation region, are propagated synchronously in time and 3-D space by integrating the equations of motion using the second-order accurate leap-frog scheme. Ion positions r and forces F are defined at time steps t, and t + dt. The ion velocities are defined at t – dt/2, t + dt/2. The governing finite difference equations of motion are



where F is the sum of electrostatic and pairwise ion-ion interaction forces.

Electrostatic field solution

The electrostatic potential is computed at regular time intervals by solving the Poisson’s equation


where and are the charge density of ions and permanent charges on the protein, respectively. is the local dielectric constant
Dielectric constant
The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum...

 or permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

, and is the local electrostatic potential. Solving this equation provides a self-consistent way to include applied bias and the effects of image charges induced at dielectric boundaries.

The ion and partial charges on protein residues are assigned to a finite rectangular grid using the cloud-in-cell (CIC) scheme. Solving the Poisson equation on the grid counts for the particlemesh component of the P3M scheme. However, this discretization leads to an unavoidable truncation of the short-range component of electrostatic force, which can be corrected by computing the short-range charge-charge Coulombic interactions
Coulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

.

Dielectric coefficient

Assigning the appropriate values for dielectric permittivity of the protein, membrane, and aqueous regions is of great importance. The dielectric coefficient determines the strength of the interactions between charged particles and also the dielectric boundary forces
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...

 (DBF) on ions approaching a boundary between two regions of different permittivity. However, in nano scales the task of assigning specific permittivity is problematic and not straightforward.

The protein or membrane environment could respond to an external field in a number of different ways. Field induced dipoles, reorientation of permanent dipoles, protonation and deprotonation of protein residues, larger scale reorganization of ionized side-chains and water molecules, both within the interior and on the surface of the protein, are all examples of how complicated the assignment of permittivity is. In MD simulations, where all the charges, dipoles, and field induced atomic dipoles are treated explicitly then it is suggested that a dielectric value of 1 is appropriate. However, in reduced-particle ion simulation programs, such as ours, where the protein, membrane, and water are continuum backgrounds and treated implicitly, and on top of that, the ion motion takes place on the same time-scale as the protein’s response to its presence, it is very difficult to assign the dielectric coefficients. In fact, changing the dielectric coefficients could easily alter the channel characteristics, such as ion permeation and selectivity The assignment of dielectric coefficient for water is another key issue. The water molecules inside ion channels could be very ordered due to tapered size of the pore, which is often lined with highly charged residues, or hydrogen bond formation between water molecules and protein. As a result, the dielectric constant of water inside an ion channel could be quite different from the value under bulk conditions. To make the matter even more complicated, the dielectric coefficients of water inside nanopore
Nanopore
A nanopore is a small hole. It may, for example, be created by a pore-forming protein or as a hole in synthetic materials such as silicon or graphene....

s is not necessarily an isotropic scalar value, but an anisotropic tensor having different values in different directions.

Anisotropic permittivity

It has become evident that the macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...

 properties of a system do not necessarily extend to the molecular length scales. In a recent research study carried by R. Jay Mashl, and Eric Jakobsson at the University of Illinois, Urbana-Champaign [personal communications], they used Molecular Dynamics simulations to study the properties of water in featureless hydrophobic cylinders with diameters ranging from 1 to 12 nm. This study showed that water undergoes distinct transitions in structure, dielectric properties, and mobility
Mobility
Mobility may refer to:* Mobility * "Mobiliy" , a song by Moby* Mobility * Mobility , the ability of military units or weapon systems to move to an objective-See also:* Academic mobility* Apprentices mobility...

 as the tube diameter is varied. In particular they found that the dielectric properties in the range of 1 to 10 nm is quite different from bulk water and is in fact anisotropic in nature.
Though, such featureless hydrophobic channels do not represent actual ion channels and more research has to be done in this area before one could use such data for ion channels, it is evident that water properties like permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

 inside an ion channel or nano-pore could be much more
complicated that it has been thought before. While a high axial dielectric constant shields ion’s electrostatic charges in the axial direction (along the channel), low radial dielectric constant increases the interaction between the mobile ion and the partial charges, or the dielectric charge images on the channel, conveying stronger selectivity in ion channels.

Solving the Poisson equation based on an anisotropic permittivity has been incorporated into BioMOCA using the box integration discretization method, which has been briefly described below.

Box integration discretization

In order to use box integration for discretizing a D-dimensional Poisson equation
with being a diagonal D × D tensor, this differential equation is reformulated as an integral equation. Integration the above equation over a D-dimensional region , and using Gauss theorem, then the integral formulation is obtained

In this appendix it is assumed to be a two-dimensional case. Upgrading to a three-dimensional system would be straightforward and legitimate as the Gauss theorem is also valid for the one and three dimensions. is assumed to be given on the rectangular regions between nodes, while is defined on the grid nodes (as illustrated on figure at the right).
The integration regions are then chosen as rectangles centered around node and extending to the 4 nearest neighbor nodes. The gradient is then approximated using centered difference normal to the boundary of the integration region , and average over the integration surface . This approach allows us to approximate the left hand side of the Poisson equation above in first order as




where and are the two components of the diagonal of the tensor .
Discretizing the right-hand side of the Poisson equation is fairly simple. is discretized on the same grid nodes, as it's been done for .

Ion size

The finite size of ions is accounted for in BioMOCA using pairwise repulsive forces
Coulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

 derived from the 6–12 Lennard-Jones potential
Lennard-Jones potential
The Lennard-Jones potential is a mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules. A form of the potential was first proposed in 1924 by John Lennard-Jones...

. A truncated-shifted form of the Lennard-Jones potential is used in the simulator to mimic ionic core repulsion. The modified form of the Lennard-Jones pairwise potential that retains only the repulsive component is given by


Here, is the Lennard-Jones energy parameter and is the average of the individual Lennard-Jones distance parameters for particles i and j. Using a truncated form of the potential is computationally efficient while preventing the ions from overlapping or coalescing, something that would be clearly unphysical.

Ion-protein interaction

Availability of high-resolution X-ray crystallographic measurements of complete molecular structures provides information about the type and location of all atoms that forms the protein. In BioMOCA the protein atoms are modeled as static point charges embedded in a finite volume inaccessible to the ions and associated with a user-defined dielectric coefficient. Moreover, a number of force-field parameters are available that provide information about the charge and radii of atoms in different amino-acid groups. The conjunction of the molecular structure and force fields provide the coordinates, radii, and charge of each atom in the protein channel. BioMOCA uses such information in the standard PQR (Position-Charge-Radius) format to map the protein system onto a rectangular grid.

Ideally, the steric interactions between protein atoms and the ions in the aqueous medium are to use a repulsive potential like Lennard-Jones to prevent ions from penetrating the protein. As this approach could add a significant load to the amount of calculations, a simpler approach is chosen that treats the protein surfaces as predetermined hard wall boundaries. Many recent open source molecular biology packages have built-in facilities that determine the volume accessible to ions in a protein system. The Adaptive Poisson Boltzmann Solver (APBS) scheme has been incorporated to BioMOCA to obtain the accessible volume region and therefore partition the simulation domain into continuous regions.

Ions are deemed to have access to protein and lipid regions and if any point within the finite-size of ionic sphere crosses the protein or membrane boundary, a collision is assumed and the ion is reflected diffusively.

Ion-water interactions

As a reduced particle approach, BioMOCA replaces the explicit water molecules with continuum background and handles the ion-water interactions using BTMC method, in which, appropriate scattering rates should be chosen. In other words, ion trajectories are randomly interrupted by scattering events that account for the ions’ diffusive motion in water. In between these scattering events, ions follow the Newtonian forces. The free flight times, Tf, are generated statistically from the total scattering rate according to


where r is a random number uniformly distributed on the unit interval. , a function of momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

, is the total scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

 rate for all collision
Collision
A collision is an isolated event which two or more moving bodies exert forces on each other for a relatively short time.Although the most common colloquial use of the word "collision" refers to accidents in which two or more objects collide, the scientific use of the word "collision" implies...

 mechanisms. At the end of each free flight, the ion’s velocity is reselected randomly from a Maxwellian distribution. As the correct scattering mechanism for ion-water interactions in nonbulk electrolyte solutions has yet to be developed, a position dependent scattering rate linked to the local diffusivity is used in our model. This dependency on position comes from the fact that water molecules can have different order of organization in different regions, which will affect the scattering rate
Scattering rate
-The interaction picture:Define the unperturbed Hamiltonian by H_0, the time dependent perturbing Hamiltonian by H_1 and total Hamiltonian by H.The eigenstates of the unperturbed Hamiltonian are assumed to be H=H_0+H_1\ H_0 |k\rang = E|k\rang...

.

Position-dependent diffusivity

It is widely accepted that the ions and water molecules do not have the same mobility or diffusivity in confined regions as in bulk. In fact, it is more likely to have a lessening in the effective mobility
Electron mobility
In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor, when pulled by an electric field. In semiconductors, there is an analogous quantity for holes, called hole mobility...

 of ions in ion channels. In reduced particle methods where the channel water is assumed as implicit continuum background, a mean ion mobility is needed to reveal how ions could diffuse due to local electrostatic forces and random events. In Transport Monte Carlo simulations, the total scattering rate (), is assumed to only result from ion-water interactions; it is related to ion diffusivity with the expression


where m is the mass of the ion and D is its diffusion constant. As the equation indicates, reduced diffusivity of ions inside the lumen of the channel renders to increased incidence of scattering events.

Hydration shells

In addition to having a diffusive effect on ion transport, water molecules also form hydration shells around individual ions due to their polar nature. The hydration shell not only shields the charge on ions from other ions but also modulates the ion radial distribution function causing the formation of peaks and troughs. The average minimum distance between two ions is increased as there is always at least one layer of water molecules present between them, acting as a physical deterrent preventing two ions from getting too close to each other, in a manner that is similar to the short-range repulsive component of the Lennard-Jones potential.

The theory of hydration shells is well developed in the physical chemistry literature however a simple model is required that captures the essential effects with as little computational overhead as possible. For this purpose the same pairwise potential discussed by Im and Roux is implemented to include the effect of hydration shells.


The coefficients ci were determined empirically for a 1 M KCl
KCL
KCL or KCl may stand for:*KCl, the chemical symbol for potassium chloride*Kirchhoff's current law*King's College London, constituent college of the University of London*Kyoto Common Lisp...

 solution, using MD simulations to benchmark the ion radial distribution functions against Equilibrium Monte Carlo simulations. The effect of hydration shells was found to be important in simulations at higher salt concentrations where the conductance of many ion channels, porin among them, is observed to saturate as the salt concentration in the electrolyte baths is further increased. Earlier simulations that did not include a model of hydration shells did not reproduce the conductance saturation behavior. This suggests an additional repulsive potential acting to prevent ion crowding, and hence limiting the concentration of ions and current density in the confined space of the pore even at high bath salt concentration. When the repulsive potential was included moderate channel conductance
Conductance
Conductance may refer to:* Electrical conductance, the ability for electricity to flow a certain path* Fluid conductance, the ability for fluid to transmit through materials* Thermal conductivity, the ability for temperatures to transmit through materials...

 was observed.

Boundary conditions

The electrical and physiological properties of ion channels are experimentally measured by inserting the channel into a lipid membrane separating two baths containing solutions of specific concentrations. A constant electrostatic bias is applied across the channel by immersing the electrodes in the two baths. Formulating boundary conditions that accurately represent these contact regions may require enormously large bath regions and is a challenging task. Beyond a Debye length from the membrane the electrostatic potential and ion densities do not vary appreciably. This assumption has been supported by the results of continuum results presented earlier. For typical salt concentrations used in ion channel simulations, the Debye length
Debye length
In plasma physics, the Debye length , named after the Dutch physicist and physical chemist Peter Debye, is the scale over which mobile charge carriers screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge...

 is of the order of 10 Å. Using the assumption, Dirichlet boundary conditions are imposed on the potential at the two domain boundary planes that are transverse to the channel, taking care that these planes are sufficiently far from the membrane.

The other problem in duplicating the experimental conditions is the problem of maintaining fixed charge density in the two baths. This problem is treated by maintaining the specified density in two buffer regions extending from the boundary plane toward the membrane. The number of ions needed to maintain the density in the two buffer regions is calculated at the start of the simulations. The count of the ions in these buffers is sampled throughout the simulation and an ion is injected whenever a deficit is observed. The initial velocity of the injected particle is decided according to Maxwellian distribution. It should be noted that the ions can leave the system only by exiting through the two Dirichlet boundary planes and an ion is not removed artificially from these buffer regions. The reflections from the Neumann boundary planes
Neumann boundary condition
In mathematics, the Neumann boundary condition is a type of boundary condition, named after Carl Neumann.When imposed on an ordinary or a partial differential equation, it specifies the values that the derivative of a solution is to take on the boundary of the domain.* For an ordinary...

 are treated as elastic reflections
Reflection seismology
Reflection seismology is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite/Tovex, a specialized air gun or a...

.

Multi-grids and grid focusing method

In all most any of the methods in simulation of ion channels, the major computational cost comes from the calculation of electrostatic forces acting on the ions. In continuum models, for instance, where ionic density
Charge density
The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume, respectively. It is measured in coulombs per meter , square meter , or cubic meter , respectively, and represented by the lowercase Greek letter Rho . Since there are positive as well as...

 exist rather than explicit ions, the electrostatic potential is calculated in a self-consistent manner by solving the Poisson equation. In MD simulations, on the other hand, the electrostatic forces acting on the particles are calculated by explicit evaluation of the Coulombic force term, often splitting the short-range and long-range electrostatic forces so they could be computed with different methods. In our model as a reduced particle method, the longrange electrostatic forces are evaluated by solving the Poisson equation and augmenting the forces so obtained wit a short-range component. By solving the Poisson equation it is possible to self-consistently include the forces arising from the bias to the system, while this is a difficult issue to be addressed in MD simulations.

Currently there are two Poisson solvers implemented in BioMOCA based on the finite difference method
Finite difference method
In mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.- Derivation from Taylor's polynomial :...

. One uses the pre-conditioned Conjugate Gradient scheme
Conjugate gradient method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too...

 (pCG) and is used by default. The later is borrowed from an APBS solver, which uses a V-multi-grid scheme. Other than the numerical approach to solve the Poisson equation, the main difference between the two solvers is on how they address the permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

 in the system. In the first solver, a dielectric value is assigned to each cell in the grid, while in the APBS solver the dielectric coefficients are defined on the grid nodes. As discussed earlier box integration method is used in the pCG solver, which allows us to treat the Poisson equation in the most accurate way. Even though a full multigrid solver based on box-integration method has been under development, there is a neat way to reuse the already exiting code and treat the ion channel systems.

Ion channel simulations require the presence of large bath regions for accurate treatment of screening. There being of such bath regions make the mesh domain of Poisson equation large and leads to either a large number of grid points with fine mesh resolution or a small number of grid points with very coarse discretization. From bulk simulations a coarse mesh is sufficient for describing the baths using the P3M scheme. However, a fine resolution is required in the channel domain because of the highly charged nature of these regions and the presence of spatially varying dielectric regions. Besides we are ultimately interested to study the channel behavior in terms of ion permeability
Semipermeable membrane
A semipermeable membrane, also termed a selectively permeable membrane, a partially permeable membrane or a differentially permeable membrane, is a membrane that will allow certain molecules or ions to pass through it by diffusion and occasionally specialized "facilitated diffusion".The rate of...

, selectivity, gating, density, etc… In other words, we are better off putting more computational resources in the channel region, and bare minimum in the baths to reduce the overall computational cost and speed up our simulations from weeks to perhaps days instead.
A scheme based on the grid focusing method has been developed that makes it possible to satisfy the requirement of large bath region and a fine grid resolution in channel at the same time in a computationally effective way. This methodology also allows us to have multiple fine mesh domains, which may be needed to describe multiple pore channels like OmpF porin, or an array of ion channels sharing the same bath regions or even having yet finer meshes inside a fine mesh for relatively large channels with narrow ion passages like Nicotine receptor channel
Nicotinic acetylcholine receptor
Nicotinic acetylcholine receptors, or nAChRs, are cholinergic receptors that form ligand-gated ion channels in the plasma membranes of certain neurons and on the postsynaptic side of the neuromuscular junction...

.

The first grid is coarse mesh spanning the entire problem domain including the bath regions and the channel region. The second grid (and so on for any other grids, 3rd, 4th, etc) is a relatively much finer mesh that spans a sub-domain of the system containing the region that requires fine resolution like the channel pore. The Poisson equation is first solved on the coarse mesh with all the Dirichlet and Neumann boundary conditions, taking into account the applied bias. Next the boundary conditions for the secondary meshes are obtained by interpolating from the first or previous solutions of the Poisson equation. The Poisson equation is solved again for the finer meshes using the new boundary conditions. In this way, electrostatic fields with different mesh discretization for different regions can be generated.

EMF and DBF

The electro-motive-force
Electromotive force
In physics, electromotive force, emf , or electromotance refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.It is important to note that the electromotive "force" is not a...

 (EMF) is the measurement of the energy needed for a charged particle like ion to cross the ion channel embedded in a membrane. Part of this potential energy barrier is due the interaction between the crossing ion and the permanent/partial charges on the protein residues. The other part comes from the induced dipoles in the protein/membrane dielectric medium, and is referred as dielectric-boundary-force (DBF). To compute the DBF alone, one may turn off all the static charges on the protein residues and drag the ion through the pore and compute the energy barrier using

It is important to note that EMF or DBF measurements are just qualitative measurements, as an ion does not necessarily cross the channel through the center of its lumen in a straight line and it is often accompanied by other ions moving in the same or opposite directions, which dramatically changes the dynamics of the system. Moreover, unlike steered MD calculations where the protein residues dynamically reposition themselves as an ion or ions are bouncing across the channel, in our EMF or DBF calculations protein is modeled as a static continuum, which further affects the energy calculations in a more quantitative way. Another issue that additionally impacts the measurements is absence of water hydration molecules, which move with the ion and shield part of its charge. Having said all of above, still computing EMF or DBF is valuable to address channel selectivity or gating. Computing either of these two energy barriers is available as an option in BioMOCA.

Visualization using VMD

VMD
Visual Molecular Dynamics
- External links :* * *...

 was equipped with the option of loading BioMOCA structures. This is a very useful feature as one could load both the protein structure (i.e. PDB or PQR file) along with the structures generated by BioMOCA to make comparisons. Figure at the right shows how BioMOCA has generated a structure for Gramicidin channel
Gramicidin
Gramicidin is a heterogeneous mixture of six antibiotic compounds, gramicidins A, B and C, making up 80%, 6%,and 14% respectively, all of which are obtained from the soil bacterial species Bacillus brevis and called collectively gramicidin D. Gramicidin D are linear pentadecapeptides; that is...

 with a membrane wrapped around it. Furthermore, BioMOCA also dumps the ion trajectories in standard formats so they could be later loaded to molecular visualization tools such as VMD and watched frame by frame in a movie format.

Recording trajectories in binary

Other than counting the number of ions crossing the channel, sometimes it is desirable to study their behavior at different regions of the channel. Such examples would be the average occupancy of ions or their average moving velocity inside the channel or a nanopore. BioMOCA has been equipped with the option of dumping every ions position, average and instantaneous velocities, potential
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

 and kinetic energies
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

, average and instantaneous displacements and other info at every step (or few steps) of the simulations in ASCII format, so such trajectory information could be studied later on to gather further statistics. From a technical point of view however, dumping such information for tens of ions, even at every few hundreds of time steps, could slow down the simulations and end up with huge files accumulating to tens of gigabytes. Loading such files later on from disk storage is also a very time consuming and computationally inefficient procedure. Over and above that, recoding the numerical information in ASCII
ASCII
The American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text...

 format does not hold its machine precision and has loss of accuracy.

Solving such problems is actually an easy task and it is simply to avoid using ASCII
ASCII
The American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text...

 format and use binary format instead. Not only it preserves the machine accuracy but also writing and reading to file system is a lot faster. The computational overhead to dump the trajectories becomes negligible and the trajectory files become about two orders of magnitude smaller in size. The downside might be that programming and decoding the data could become very tricky, but once it’s done correctly and with care, the advantages of using binary format are well worth the extra effort. BioMOCA is now equipped with the tools to record the trajectory information in binary format.

BioMOCA Suite

BioMOCA has been wrapped in a GUI, and it is available at nanoHUB.org
Nanohub
nanoHUB.org is science cyberinfrastructure comprising community-contributed resources and geared toward educational applications, professional networking, and interactive simulation tools for nanotechnology...

 as the BioMOCA Suite. The BioMOCA Suite can perform ion channel flow simulations on any user-supplied channel. The suite includes: a map generator subtool, which produces protein maps for BioMOCA from the supplied PQR file; a lipid wrapper subtool, which allows the user to embed their channel in a membrane; and the boundary force potential calculator, which determines the potential energy barrier presented by the channel. The user can also download the acc and charge files produced by the map generator and lipid wrapper.

Finally, the suite contains the biology Monte Carlo simulator, which simulates ion channel flow through the user provided channel. The user has the ability to change a number of parameters, including the transmembrane voltage, intra- and extra-cellular concentrations of Na+, Cl, K+, Ca2+, and Mg2+, and the run time.


External links

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