Authors:
Christos Dimitroulis
Theophanes E. Raptis
Vasilios E. Raptis
Contact:
The POLYANA team
polyana.software@gmail.com
Version : 2.0.1
Release date : April 23rd, 2019
Web site : https://github.com/brapt2005/polyana
Contents:
- Introduction
- How to build and test POLYANA
- How to run POLYANA - the simple way
- How to work with directives
- How to work with groups of atoms
- How to process simulations on the fly (and why)
- How to use the accompanying utility
- Future goals
- References
- Legal stuff, etc.
1. Introduction
This file contains information about 'POLYANA', a program that reads output created by DL_POLY Molecular Dynamics suite ('Classic' version) [1] and returns radial distribution functions for centres of mass of groups of atoms or whole molecules. It has been designed with simplicity of use in mind: just press Enter and the program will read DL_POLY input and output files (CONTROL, FIELD and HISTORY) figure out what species are there in the simulation box and compute all radial distribution functions for pairs of like and unlike molecular species. Also, the advanced user will be happy to find that POLYANA's functions can be controlled and enhanced with the aid of simple directives placed at the end of DL_POLY's CONTROL file.
POLYANA is suitable for systems of 'small' molecules or groups of atoms, i.e. such that their size doesn't exceed half the shortest simulation cell dimension. However, POLYANA is expected to work correctly even for large branched species or star-like polymers and the like, provided the simulation cell is much larger than the molecules' or groups' dimensions - the only case one would be really interested in g(r) of such large species. Indeed, tests carried out with the aid of companion utility verify_unfold.f90 as described in the relevant README file, show that POLYANA can treat arbitrary topologies.
What's new in this version
In a nutshell:
-
Calculations not restricted to molecular centres of mass, but also extending to user-defined groups of atoms.
-
Radial distribution functions calculated over distances well beyond half the simulation cell length.
-
Stream processing or 'on the fly' mode.
-
OpenMP parallelism.
-
Minor bugfixes and improved input facility1.
POLYANA's last version [2] was mainly intended for radial distribution functions of molecular centres of mass. However, it was possible to 'hack' POLYANA by appropriately editing the atoms definitions in the DL_POLY's FIELD file to mask certain atom types and compute g(r)'s for groups of atoms rather than whole molecules. The current version [3] provides an explicit mechanism to let users define groups of atoms by inserting a definition with the appropriate syntax in FIELD and a novel directive (group) in CONTROL file; DL_POLY will simply ignore any such definition in FIELD. As regards the distance over which radial distribution functions extend, POLYANA relies on an observation by Theodorou and Suter [4] so as to extend the calculation beyond half the shortest simulation cell length by computing the correct differential volume with distance. As a means of tighter integration with DL_POLY, POLYANA can be combined with it in the style of Unix pipes to allow 'on the fly' processing of MD trajectories (to do this, DL_POLY has to be minimally modified and rebuilt so that it redirects trajectory data to standard output instead of writing a HISTORY file). Finally, POLYANA allows multithreaded (OpenMP) parallel execution. Users can compare time measurement displayed with the end of the calculations to check performance with number of threads.
Requirements
The below list (as well as most part of this document) is relevant to UNIX/Linux systems, but it should be fairly easy to port the project to other environments; to build and run POLYANA, one needs:
-
gfortran or other modern Fortran compiler (please, edit Makefile as needed). If your compiler does not comply with Fortran2003 standard, use alternative option indicated in the Makefile.
-
make; POLYANA is a small project and one can try and compile the source code manually. If make is available, it will just make your life a little easier.
-
Since this is a post-processing tool, DL_POLY itself is not needed to build POLYANA unless you want to run the tests - see Section 2. Of course, you need DL_POLY output files to process!
-
bash shell; the bash scripts in test directory have worked on various Linux platforms.The Fortran code itself should compile and run on any platform with an appropriate compiler.
-
Finally, the rdfplot companion script calls gnuplot to plot output files. This is not a strict requirement; POLYANA output is very simple so users can employ their favourite software to generate r.d.f. graphs.
2. How to build and test POLYANA
Compilation
This is straightforward. Just type
make
and press Enter. An executable called polyana will be generated in the bin subdirectory of the project folder; you can move it to any location specified in your $PATH environment variable. To build POLYANA and run the tests in test subfolder, type:
make test
This will copy the executable to the test directory and launch a script therein. It is assumed that DL_POLY's executable is DLPOLY.X, as defined in its own Makefile - otherwise, one has to edit run script in test directory. You can also run 'make', do whatever you want and run 'make test' later. Read more about the tests in Section 6 of this file.
Running the tests
NOTE: it is assumed that the name of DL_POLY's executable is DLPOLY.X as defined in the Makefile of its distribution.
As mentioned in Section 1, the simplest way to run the tests is by running 'make test'. Normally, POLYANA prints some messages on the screen. During the tests, POLYANA will run in the background and all its messages will be redirected to a file named 'polyana.out', in each test subdirectory. The g(r) output, of course, will be found in the corresponding RDF files (see next Section).
Alternatively, you can go to the test directory and launch the run script from there, assuming POLYANA executable is already therein (and DL_POLY is installed in your system!), so if you haven't yet, copy POLYANA to test now. To run the run script you must supply some arguments. Here is how:
./run [no arguments]
or
./run h
or
./run -h ........... will display a help screen and exit
./run md ........... will run DL_POLY from the beginning in each
test subdirectory, after deleting whatever
dl_poly output files already present.
./run polyana ....... will run polyana from the beginning in each
test subdirectory, after deleting whatever
polyana output already there. If no DL_POLY
output to process can be found in a certain
subdirectory, the script will print a messag
e and continue with the next subdirectory.
./run md polyana
or
./run polyana md .... will run DL_POLY and then, polyana in each
test subdirectory. This is the option invoke
d when running 'make test'.
The last -and most obvious- choice is to change to any test subdirectory and run DL_POLY and POLYANA 'manually'.
Finally, to 'clean' the test subdirs i.e. remove all DL_POLY and POLYANA output, just run the clean script (after chmod-ing to executable) from the test dir. This is also invoked when you run 'make clean' from the source directory.
3. How to run POLYANA - the simple way
To calculate molecular radial distribution functions, just run the executable in the directory of your MD run and the program will read FIELD to figure out what molecules are there in the system; CONFIG to retrieve the periodic boundary conditions key (if this is missing from the trajectory); and HISTORY to analyse the trajectory. With the end of processing, two files named RDF (not to confuse with DL_POLY's RDFDAT!) and POP, will be created.
In RDF, the centre-of-mass radial distribution functions are given for all types of molecules, numbered 1, 2, 3, ... according to the order they appear in FIELD. E.g, if water and ethanol molecules appear in FIELD in that order, then 1=water, 2=ethanol, and the columns 1-1, 2-2 and 1-2 for the respective g(r) functions will be printed in RDF. The default values of 0.1 Angstroem and 12.5 Angstroem will be used for the pair distance bin and maximum distance, respectively - see next Section on how to change these values.
In POP (standing for 'populations'), the number of type 'b' molecules around the average type 'a' molecule with distance, will be given in a similar arrangement as the columns in RDF. These numbers can also be obtained by integrating radial distribution functions - actually, rho*dV*g(r) - with distance. However, we don't have to carry out the integration; POLYANA will do it for us. Unlike RDF, columns ab and ba of POP are not equivalent. Therefore, in the case of a binary mixture, columns 1-1, 2-2, 1-2 and 2-1 can be found in the respective POP file.
Please, note that POLYANA will process the trajectory even if the simulation has not been completed - in that case a message will be emitted with the end of the computation letting us know that the trajectory file was found to be abnormally terminated - this would not prevent POLYANA from computing and printing results in RDF and POP. This is an attractive feature in that it allows users to look at the structure of their systems without waiting for the simulation to be over.
Another sign of POLYANA's robustness is the way it handles input files. To read periodic boundary conditions, POLYANA will look for HISTORY's appropriate header line. If that line is missing, POLYANA will not complaint; it will look for the PBC code in CONFIG. In the improbable case that CONFIG too is missing, POLYANA will set periodic conditions to parallelepiped, a quite common and generic type of simulated periodic systems, and will print a message letting the user know of the situation and how periodic conditions can be redefined as desired. But how can the user do that? Time to read the next section.
4. How to work with directives
POLYANA can read directives placed in CONTROL file, after the 'finish' DL_POLY directive, to control its execution and benefit from more of its capabilities. All POLYANA directives are listed below in alphabetical order:
Directive | Description
--- | ---
dr *d* | Distance bin for the histograms in g(r) calculations
end polyana | Marks the end of a section of POLYANA directives
every *n* | Calculate every n-th step (time saver for long trajectories)
group [total] | Compute g(r) for user-defined groups rather than molecules
omp *n* | Sets the number of OpenMP threads
pbc *n* | Sets periodic boundary conditions to one of the following:
0 | no pbc's
1 | cubic
2 | orthorhombic
3 | parallelepiped
6 | slab
polyana | Marks the beginning of section containing POLYANA directives
rmax *r* | Maximum distance for g(r) calculations
smooth | Smooth g(r) as in Allen & Tildesley, 1989, pp. 203-204 [5]
start *n* | Skip steps 1 to n-1 and process from n-th and beyond
stop *n* | Skip (don't process) configurations beyond the n-th
threads *n* | A synonym for 'omp'
total | Optional argument of *group* to include intramolecular pairs
width | A synonym for 'dr'
Launching the every n command will cause POLYANA to compute pair distances and update histograms for every n-th configuration only. This can be helpful when processing very long trajectories. The pbc directive, on the other hand, can be of use when both HISTORY's header and the CONFIG file are missing; otherwise it will be overriden by the pbc key therein - the key with higher precedence being the one in the HISTORY file.
POLYANA directives are case insensitive: start, START and Start are equivalent. Any number of spaces can be inserted before a directive or between a directive keyword and its numerical argument. The polyana and end polyana lines must exist and enclose the other lines if directives are to be used. If some or all directives are missing (see: 'run the simple way', Section 2) the default values will be used instead; same goes for missing directive arguments (all of them are optional). All default values are summarised below:
Directive | Default value
--- | ---
dr | 0.1 [Angstroems]
every | 1
group | .FALSE.
omp | system-dependent
pbc | NOTHING (a value that is unrelated to any PBC code number)
rmax | computed automatically based on cell dimensions
smooth | .FALSE.
start | 1
stop | HUGE(integer) (exceeding any reasonable nr of steps)
total | .FALSE.
Finally, directives can be 'commented out' using the hash (#) character.
The maximum distance, r_max, is not assigned a default value. Instead, it is calculated automatically based on the simulation cell size. In the general case of a parallelepiped cell, this is done as follows: If c1, c2 and c3 are the three cell vectors, then, three heights can be defined like so:
h_i = | c_i . (c_j x c_k) / || c_j x c_k || |
where indices i, j and k denote circular shifts of {1, 2, 3}. Then, the maximum distance is defined as
r_max = 0.5*min{h_1, h_2, h_3}
In the case of cubic simulation cells, the above expression reduces to half the cell size. However, in the particular case of cubic periodic conditions, POLYANA will extend by default the range of g(r) to L*sqrt(3)/2, L being the cell size; of course this can be overriden with the aid of the rmax directive. The user is referred to the previously cited paper of Theodorou and Suter for a thorough and in depth discussion of the topic.
POLYANA reads the first cell in the trajectory file, computes the number of bins by dividing the above computed rmax by the bin width and allocates memory to the histogram arrays used in RDF calculations. If the trajectory was computed in the NPT ensemble where the simulation varies with time POLYANA will keep reading all subsequent cell vectors and with each new step, r-max will be updated as the minimum of its current and new value ( thus discarding a few elements at the end of the histogram arrays).
Example of using directives
Suppose we ran a MD simulation and saved 6000 configurations. Of them, the first 1000 steps form the equilibration stage so we won't process them. Also, the last 1000 will not be processed, for whatever reason. Our g(r) will be computed for distances up to 10 Angstroems and the bin to be used will equal 0.25 Angs. Then, the POLYANA section in the CONTROL file should look like this:
...
[various DL_POLY directives]
...
finish [end of DL_POLY section]
polyana
start 1001
stop 5000
rmax 10.0
dr 0.25
end polyana
Indentation as above is not compulsory; it is used for the sake of readability.
5. How to work with groups of atoms
Explicit definition of groups
Often we are interested in looking at specific groups of atoms rather than whole molecules. Suppose, for instance, we have simulated a system of water mixed with n-butanol, using suitable united-atom models. Then, we would like to look at the way water molecules are arranged around the hydroxyl group and alkyl tail of the alcohol. To address problems of this kind, we have to do the following:
-
Add group directive in polyana ... end polyana section of CONTROL file.
-
Optionally, add total directive to take intramolecular pairs into account; otherwise, results will reflect only intermolecular group-group interactions.
-
Add group definitions in the ATOM directives of FIELD file that correspond to the molecules to be broken down into groups.
Group definitions obey the following general syntax:
(...(char int int) [...(char int int)] int ) [(...)]
where outter square brackets, [...], indicate optional arguments. In particular, a molecule is divided into groups, defined like so:
(grouptype nat nrep)
where grouptype is an 8-character string, nat is the number of atoms in the group and nrep is the number of times the group is repeated along the array of the atoms that comprise the molecule.
Groups of different types can be grouped themselves to form larger 'supergroups' which can be repeated many times, as for instance in the case of co-polymers. Then, definitions are enclosed in parentheses with the number each 'supergroup' is repeated, placed at the end, such as:
( (A 3 1) (B 2 1) 100)
This pattern can be applied recursively to define large structures of arbitrary complexity. Group definitions are placed in the ATOM directives of corresponding molecular types in FIELD file, after the number of atoms, like this:
ATOMS int group-definitions
If a molecule is to be divided into groups, these must be defined such that all atoms belong to one of the groups and the sum of atoms in all repeated groups be equal to the argument of the ATOM keyword.
It is reminded that group directive should also be inserted in CONTROL for the above definitions to take effect, otherwise they will be ignored so POLYANA will fall back to its default behaviour and calculate molecular functions. Lastly, it is noted that group admits an optional argument, namely total, to modify its function. Without it, intermolecular radial distribution functions are computed; otherwise, all group pairs, whether intra- or intermolecular, will be taken into account. In the latter case, bonded pairs will give rise to sharp peaks typical of bonds, bond angles and dihedral angles - if they exist. This is not the case with DL_POLY which excludes bonded atom-atom pairs from similar calculations in its RDFDAT output files.
Examples: single compounds
-
United-atom n-hexane as a trimer:
ATOMS 6 (terminal 2 1) (midsegm 2 1) (terminal 2 1)
-
United-atom n-hexane as a dimer:
ATOMS 6 (bead 3 1) (bead 3 1)
or
ATOMS 6 (bead 3 2)
-
United-atom n-dodecane as a tetramer:
ATOMS 12 (bead 3 4)
-
Copolymer A-(B2C3)100-A where consecutive Bs form a bead and Cs form another:
ATOMS 502 (A 1 1) ((B 2 1) (C 3 1) 100) (A 1 1)
Finally, we note that when nrep equals one, it can be omitted altogether; then the relevant above examples can be rewritten as follows:
1. ATOMS 6 (terminal 2) (midsegm 2) (terminal 2)
2. ATOMS 6 (bead 3) (bead 3)
4. ATOMS 502 (A 1) ((B 2) (C 3) 100) (A 1)
Example: mixtures
Let's take a real-life example and assume we are using the well-known TraPPE [6] and SPC/E [7] force fields to model a n-butanol-1/water system so the FIELD file looks more or less like this:
...
MOLECULES 2
Butanol
NUMMOLS ...
ATOMS 6
CH3H 15.0344 0.0000 1
CH2B 14.0336 0.0000 1
CH2B 14.0336 0.0000 1
CH2A 14.0336 0.2650 1
OC 15.9996 -0.7000 1
HC 1.0008 0.4350 1
...
...
FINISH
SPCE Water
NUMMOLS ...
ATOMS 3
OW 15.9996 -0.8476
HW 1.0080 0.4238
HW 1.0080 0.4238
CONSTRAINTS 3
1 2 1.0000
1 3 1.0000
2 3 1.63298
FINISH
Now, suppose we want to compute g(r) for water and butanol's hydroxyl group and alkyl tail. Then, the relevant ATOM records will be modified as follows:
Butanol
NUMMOLS ...
ATOMS 6 (alkyl 4) (hydroxyl 2)
...
...
FINISH
SPCE Water
NUMMOLS ...
ATOMS 3 (water 3)
...
...
FINISH
where we are allowed to ommit nrep because it equals 1 in all cases. Note also that since POLYANA computes molecular functions by default and water is taken as single entity, the corresponding group definition, (water 3), is redundant. Once again, it is reminded that the group directive should be present in CONTROL or the group definitions will be ignored.
Implicit definition of groups (or how to hack FIELD)
The above method works fine when atom types are arranged in FIELD such that user can readily group them into successive subunits of interest. However, some cases (e.g. complex molecular topologies or other restrictions) may require atom lines of the same subunit of interest to be placed far apart from each other in FIELD. Then, our explicit declaration scheme does not work and we have to resort to the the 'hacking' strategy employed with the previous POLYANA version. Let's outline the procedure using the last above presented example. To calculate the hydroxyl- water g(r) we rewrite the butanol lines as follows:
CH3H 0.0 0.0000 1
CH2B 0.0 0.0000 1
CH2B 0.0 0.0000 1
CH2A 0.0 0.2650 1
OC 15.9996 -0.7000 1
HC 1.0008 0.4350 1
Likewise, to calculate g(r) and density profile for the alkyl tail, we rewrite:
CH3H 15.0344 0.0000 1
CH2B 14.0336 0.0000 1
CH2B 14.0336 0.0000 1
CH2A 14.0336 0.2650 1
OC 0.0 -0.7000 1
HC 0.0 0.4350 1
Of note, this trick calculates inter-molecular radial distribution functions of user-defined groups while results obtained by group combined with total argument, include all such pairs in the system. For a thorough discussion on the topic, the reader is referred to our first publication introducing POLYANA (see references, Section 10). As another example, assuming that we look at geometric centres rather than centres of mass of the molecules, we simply set atom masses equal to one and the same value for all atom types.
6. How to process simulations on the fly (and why)
DL_POLY computes atomistic radial distribution functions during MD simulations. It is tempting to render POLYANA capable of exchanging information with DL_POLY 'on the fly' and computing molecular (or atom group) r.d.f.'s during simulations instead of waiting for them to be over. A solution in the form of Unix pipes has been implemented to this purpose; to make it work, a few minor modifications are required, namely:
-
DL_POLY: replace HISTORY file by standard output and rebuild.
-
POLYANA: edit Makefile to include the -DSTREAMS compiler option and rebuild.
In this way, DL_POLY will send all trajectory records to standard output while POLYANA will be reading from standard input and stream again to standard output; thus, the two applications can be combined as follows:
DL_POLY.X | polyana > HISTORY
Apart from obtaining post-processing results immediately, this solution can also be of great convenience when disk space restrictions are very tight, by allowing direct compression of the trajectory:
DL_POLY.X | polyana | gzip -c > HISTORY.gz
Of note, when in stream mode, all POLYANA messages otherwise appearing onscreen, are now redirected to a file named STDOUT.
The required modifications are very easy to implement:
DL_POLY Classic
In file setup_module.f we set parameter nrite from 6 to some other value not associated with another file unit, e.g.
C integer, parameter :: nrite = 6
integer, parameter :: nrite = 11
Then, we set parameter nhist to 6:
C integer, parameter :: nhist = 21
integer, parameter :: nhist = 6
In files traject.f and traject_u.f we comment out the statements that open and close the HISTORY file:
...
C open(nhist,file='HISTORY',position='append')
or
C open(nhist,file='HISTORY',form='unformatted',position='append')
...
C close (nhist)
...
Then, we rebuild DL_POLY. The new executable should be printing HISTORY records to the screen. If it doesn't work as expected, try make clean and rebuild.
POLYANA
The source code has been extended to be able to read HISTORY records in the form of incoming byte streams. All we have to do is edit the compiler options record in Makefile to include the appropriate preprocessor flag,
#options =-cpp -fopenmp -fbounds-check
options =-cpp -fopenmp -fbounds-check -DSTREAMS
and recompile. The new executable should be reading HISTORY records piped to it and print them to screen. If it doesn't, then try make clean and rebuild.
7. How to use the accompanying utility
RDF files are easy to plot. To facilitate this task even further, a bash script is provided, which generates a gnuplot script automatically and then, launches gnuplot to run that script and plot the RDF file. The 'rdfplot' script takes two command-line arguments: the number of RDF column pertaining to the species pair of interest, and an upper bound to the y-axis range. Thus:
./rdfplot 2 1.5
means that the second column of RDF (pertinent to the first pair of species) is to be plotted with respect to distance (first column) and the y-scale will range from 0 to 1.5. Of course, the generated gnuplot script, rdfplot.gp, can be modi- fied by the users as they see fit.
8. Future goals
Apart from the above presented functionality, many new features are coming with future versions. Some of them have already been implemented and are being tested for bugs, efficiency and so on, while others have been designed and soon will be added to POLYANA's quiver. The most important new functions include
-
Mean Square Displacement (MSD). Once molecular or group positions are known, it is trivial to use them in calculating MSD.
-
Reorientation dynamics of groups and molecules. When computing pair distances to determine the corresponding r.d.f.'s, we store group-group vectors at each time step. These can serve to compute time-average 1st and 2nd-order Legendre polynomials, P1(t; cos a), P2(t; cos a), where a denotes the angle formed by instances of such a vector at time steps t0 and t0+t. These results can be linked to data from spectroscopy.
-
In a similar vein, we can read atom velocities from HISTORY, calculate group or molecular velocities and compute their autocorrelation functions.
-
Potentials of Mean Force. Molecular radial distribution functions can be used to define free energy difference, A-A0=-kB*T*ln g(r), where kB and T denote Boltzmann's constant and temperature, respectively. Such an expression can be stored in the style of DL_POLY's TABLE files and serve as pair potential in coarse-grain simulations. This is currently tested for molecules; group-group interactions require also bonded potentials that are not in place yet.
-
Extend group syntax so it can handle system definitions in which records of atoms to group together in FIELD, are not consecutive. This feature is a work in progress.
9. References
- W. Smith, T. Forester J. Mol. Graph., 1996, 14, 136.
- C. Dimitroulis, T. Raptis, V. Raptis Comp. Phys. Commun., 2015, 197, 220-226.
- V. Raptis, C. Dimitroulis, T. Raptis Mol. Simul., 2019, DOI: 0.1080/08927022.2019.1603379
- D.N. Theodorou, U.W. Suter, J. Chem. Phys., 1985, 82, 955.
- M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford University Press, Oxford, 1989.
- B. Chen, J. Potoff, J. Siepmann J. Phys. Chem. B, 2001, 105, 3093.
- H. Berendsen, J. Grigera, T. Straatsma J. Phys. Chem. 1987, 91, 6269.
10. Legal stuff, etc.
Polyana is a program for computing molecular pair distribution functions.
How to cite
Please cite our most recent publication, number 3 in previous section.
License
Copyright (c) 2015-2019 Vasilios E. Raptis polyana.software@gmail.com
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Download
The source code for this program can also be downloaded from here:
http:
Contact
Having problems or questions about this program? You are welcome to contact us:
The POLYANA team
polyana.software@gmail.com
1 Bugfixes:
-
Unlike RDF, columns a-b and b-a in POP file are not equivalent; both of them are printed now.
-
Issue concerning occasional crashes when reading FIELD file, has been fixed; subsequent modifications ensured and tests verified robust performance when reading input files and resilience in cases of missing files or data.
-
With every n directives, n must be taken into account when averaging the histograms and cell volume.
