PySCeS: the Python Simulator for Cellular Systems is an extendable toolkit for the analysis and investigation of cellular systems. PySCeS is available for download at http://pysces.github.io and on GitHub where the source code is maintained: https://github.com/PySCeS/pysces

# Introduction¶

Welcome! This user guide will get you started with the basics of modelling cellular systems with PySCeS. It is meant to be read in conjunction with the chapter on The PySCeS Model Description Language, which specifies the syntax of the input file read by the program. If you already have PySCeS installed continue straight on; if not, Installing and configuring contains instructions on building and installing PySCeS.

PySCeS is distributed under the PySCeS (BSD style) licence and is made freely available as Open Source software. See LICENCE.txt for details.

The continued development of PySCeS depends, to a large degree, on support and feedback from Systems Biology community. If you use PySCeS in your work please cite it using the following reference:

Brett G. Olivier, Johann M. Rohwer and Jan-Hendrik S. Hofmeyr Modelling cellular systems with PySCeS, Bioinformatics, 21, 560-561, DOI 10.1093/bioinformatics/bti046.

We hope that you will enjoy using our software. If, however, you find any unexpected features (i.e. bugs) or have any suggestions on how we can improve PySCeS please let us know by opening an issue on Github.

The PySCeS development team.

# Getting started¶

In this section we assume you have PySCeS installed and configured (see Installing and configuring for details) and a correctly formatted PySCeS input file that describes a cellular system in terms of its reactions, species and parameters (refer to The PySCeS Model Description Language). Note that on all platforms PySCeS model files have the extension .psc.

To begin modelling we need to start up an interactive Python shell (we suggest IPython) and load PySCeS with import pysces:

Python 3.9.6 (default, Jun 30 2021, 10:22:16)
IPython 7.26.0 -- An enhanced Interactive Python. Type '?' for help.

In [1]: import pysces
Matplotlib backend set to: "TkAgg"
Pitcon routines available
NLEQ2 routines available
SBML support available
You are using NumPy (1.20.3) with SciPy (1.7.1)
Assimulo CVode available
RateChar is available
Parallel scanner is available

PySCeS environment
******************
pysces.model_dir = /home/jr/Pysces/psc
pysces.output_dir = /home/jr/Pysces

***********************************************************************
* Welcome to PySCeS (1.0.0) - Python Simulator for Cellular Systems   *
*                http://pysces.sourceforge.net                        *
* Copyright(C) B.G. Olivier, J.M. Rohwer, J.-H.S. Hofmeyr, 2004-2021  *
* Triple-J Group for Molecular Cell Physiology                        *
* Stellenbosch University, ZA and VU University Amsterdam, NL         *
* PySCeS is distributed under the PySCeS (BSD style) licence, see     *
* LICENCE.txt (supplied with this release) for details                *
* Please cite PySCeS with: doi:10.1093/bioinformatics/bti046          *
***********************************************************************


PySCeS is now ready to use. If you would like to test your installation try running the test suite:

pysces.test()


This also copies the test models supplied with PySCeS into your model directory.

## Creating a PySCeS model object¶

This guide uses the test models supplied with PySCeS as examples; if you would like to use them and have not already done so, run the PySCeS tests (described in the previous section).

Before modelling, a PySCeS model object needs to be instantiated. As a convention we use mod as the instantiated model instance. The following code creates such an instance using the test input file, pysces_test_linear1.psc:

>>> mod = pysces.model('pysces_test_linear1')
Assuming extension is .psc
Using model directory: /home/jr/Pysces/psc
Parsing file: /home/jr/Pysces/psc/pysces_test_linear1.psc

Calculating L matrix . . . . . . .  done.
Calculating K matrix . . . . . . .  done.


When instantiating a new model object, PySCeS input files are assumed to have a .psc extension. If the specified input file does not exist in the input file directory (e.g. misspelled filename), a list of existing input files is shown and the user is given an opportunity to enter the correct filename.

The model constructor can also be used to specify a model directory other than the default model path:

>>> mod = pysces.model('pysces_test_linear1', dir='/my/own/directory/for/psc')


Alternatively, input files can also be loaded from a string:

>>> F = open('/home/jr/Pysces/psc/pysces_test_linear1.psc', 'r')
>>> F.close()
>>> mod = pysces.model('test_lin1s', loader='string', fString=pscS)
Assuming extension is .psc
Using model directory: /home/jr/Pysces/psc
Using file: test_lin1s.psc
Parsing file: /home/jr/Pysces/psc/orca/test_lin1s.psc

Calculating L matrix . . . . . . .  done.
Calculating K matrix . . . . . . .  done.


Note that now the input file is saved and loaded as model_dir/orca/test_lin1s.psc.

Once a new model object has been created it needs to be loaded. During the load process the input file is parsed, the model description is translated into Python data structures and a stoichiometric structural analysis is performed.

Note

In PySCeS 0.7.1+ model loading is now automatically performed when the model object is instantiated. This behaviour is controlled by the autoload argument (default = True). To keep backwards compatibility with older modelling scripts, whenever doLoad() is called a warning is generated.

To force re-loading of a model from the input file, use mod.reLoad().

Once loaded, all the model elements contained in the input file are made available as model (mod) attributes so that in the input file where you might find initialisations such as s1 = 1.0 and k1 = 10.0, these are now available as mod.s1 and mod.k1. For variable species and compartments an additional attribute is created, which contains the element’s initial (as opposed to current) value. These are constructed as <name>_init

>>> mod.s1
1.0
>>> mod.s1_init
1.0
>>> mod.k1
10.0


Any errors generated during the loading process (almost always) occur as a result of syntax errors in the input file. These error messages may not be intuitive; for example, 'list out of range' exception usually indicates a missing multiplication operator(3( instead of 3*() or unbalanced parentheses.

## Basic model attributes¶

Some basic model properties are accessible once the model is loaded:

• mod.ModelFile, the name of the model file that was used.

• mod.ModelDir, the input file directory.

• mod.ModelOutput, the PySCeS work/output directory.

• Parameters are available as attributes directly as specified in the input file, e.g. k1 is mod.k1.

• External (fixed) species are made available in the same way.

• Internal (variable) species are treated in a similar way except that an additional attribute (parameter) is created to hold the species’ initial value (as specified in the input file), e.g., from s1, mod.s1 and mod.s1_init are instantiated as model object attributes.

• Compartments are also are assigned an initial value.

• Rate equations are translated into objects that return their current value when called, e.g. mod.R1().

All basic model attributes that are described here can be changed interactively. However, if the model rate equations need to be changed, this should be done in the input file after which the model should be re-instantiated and reloaded.

### Groups of model properties (either tuples, lists or dictionaries)¶

• mod.species the model’s variable species names (ordered relative to the stoichiometric matrix rows).

• mod.reactions reaction names ordered to the stoichiometric matrices columns.

• mod.parameters all parameters (including fixed species)

• mod.fixed_species only the fixed species names

• mod.__rate_rules__ a list of rate rules defined in the model

The following attributes are used by PySCeS to store additional information about the basic model components; generally they are supplied by the parser and should almost never be changed directly.

• mod.__events__ a list of event object references which can be interrogated for event information. For example, if you want a list of event names try [ev.name for ev in mod.__events__]

• mod.__rules__ a dictionary containing information about all rules defined for this model

• mod.__sDict__ a dictionary of species information

• mod.__compartments__ a dictionary containing compartment information

# Modelling¶

## Structural Analysis¶

As part of the model loading procedure, doLoad() automatically performs a stoichiometric (structural) analysis of the model. The structural properties of the model are captured in the stoichiometric matrix (N), kernel matrix (K) and link matrix (L). These matrices can either be displayed with a mod.showX() method or used in further calculations as NumPy arrays. The formal definition of these matrices, as they are used in PySCeS, is described in 1.

The structural properties of a model are available in two forms, as new-style objects which have all the array properties neatly encapsulated, or as legacy attributes. Although both exist it is highly recommended to use the new objects.

### Structural Analysis - new objects¶

For alternate descriptions of these model properties see the next (legacy) section.

• mod.Nmatrix view with mod.showN()

• mod.Nrmatrix view with mod.showNr()

• mod.Lmatrix view with mod.showL()

• mod.L0matrix

• mod.Kmatrix view with mod.showK()

• mod.K0matrix

• mod.showConserved() displays any moiety conserved relationships (if present).

• mod.showFluxRelationships() shows the relationships between dependent and independent fluxes at steady state.

All new structural objects have an array attribute which holds the actual NumPy array data, as well as ridx and cidx which hold the row and column indices (relative to the stoichiometric matrix) as well as the following methods:

• .getLabels() return the matrix labels as tuple([rows], [columns])

• .getColsByName() extract column(s) with label

• .getRowsByName() extract row(s) with label

• .getIndexes() return the matrix indices (relative to the Stoichiometric matrix) as tuple((rows), (columns))

• .getColsByIdx() extract column(s) referenced by index

• .getRowsByIdx() extract row(s) referenced by index

### Structural Analysis - legacy¶

• mod.nmatrix, N: displayed with mod.showN()

• mod.kmatrix, K: displayed with mod.showK()

• mod.lmatrix, L: displayed with mod.showL() (an identity matrix means that no conservation relationships exist, i.e. there is no linear dependence between species).

• If there are linear dependencies in the differential equations then the reduced stoichiometric matrix of linearly independent, differential equations Nr is available as mod.nrmatrix and is displayed with mod.showNr(). If there is no dependence Nr = N.

• In the case where there is linear dependence the moiety conservation sums can be displayed by using mod.showConserved(). The conservation totals are calculated from the initial values of the variable species as defined in the model file.

• When the K and L matrices exist, their dependent parts (K0, L0) are available as mod.kzeromatrix and mod.lzeromatrix.

• mod.showFluxRelationships() shows the relationships between dependent and independent fluxes at steady state.

If the mod.showX() methods are used, the row and column titles of the various matrices are displayed with the matrix. Additionally, all of the mod.showX() methods accept an open file object as an argument. If this file argument is present, the method’s results are output to a file and not printed to the screen. Alternatively, the order of each matrix dimension, relative to the stoichiometric matrix, is available as either a row or column array (e.g. mod.krow, mod.lrow, mod.kzerocol).

## Time simulation¶

PySCeS has interfaces to two ODE solvers, either LSODA from ODEPACK (part of SciPy) or SUNDIALS CVODE (using Assimulo). If Assimulo is installed, PySCeS will automatically select CVODE if compartments, events or rate rules are detected during model load as LSODA is not able capable of event handling or changing compartment sizes. If, however, you would like to select the solver manually this is also possible:

>>> mod.mode_integrator = 'LSODA'
>>> mod.mode_integrator = 'CVODE'


There are three ways of running a simulation:

1. Defining the start, end time and number of points and using the mod.Simulate() method directly:

>>> mod.sim_start = 0.0
>>> mod.sim_end = 20
>>> mod.sim_points = 50
>>> mod.Simulate()

2. Using the mod.doSim() method where only the end time and points need to be specified. For example, running a 20-point simulation from time 0 to 10:

>>> mod.doSim(end=10.0, points=20)

3. Or using mod.doSimPlot() which runs the simulation and graphically displays the results. In addition to doSim()’s arguments the following arguments may be used:

>>> mod.doSimPlot(end=10.0, points=21, plot='species', fmt='lines', filename=None)


where:

• plot can be one of 'species', 'rates' or 'all'.

• fmt is the plot format, UPI backend dependent (default= '' ) or the CommonStyle 'lines' or 'points'.

• filename if not None (default), then the plot is exported as filename.png

Another way of quickly visualising the results of a simulation is to use the mod.SimPlot() method.

>>> mod.SimPlot(plot='species', filename=None, title=None, log=None, format='lines')


where:

• plot: output to plot (default= 'species' ) + 'all' rates and species + 'species' species + 'rates' reaction rates + ['S1', 'R1', ] a list of model attributes (species, rates)

• filename (optional) if not None file is exported to filename (default=None)

• title the plot title (default=None)

• log use log axis for 'x', 'y', 'xy' (default=None)

• fmt plot format, UPI backend dependent (default= '' ) or the CommonStyle 'lines' or 'points'.

Called without arguments, mod.SimPlot() plots all the species concentrations against time.

### Simulation results¶

Starting with PySCeS versions 0.7.x the simulation results have been consolidated into a new mod.data_sim object. By default species concentrations/amounts, reaction rates and rate rules are automatically added to the data_sim object. If extra information (parameters, compartments, assignment rules) is required this can easily be added using mod.CVODE_extra_output, a list containing any model attribute which is not added by default.

The mod.data_sim object has many methods for extracting simulation data including:

• data_sim.getTime() returns a vector of time points

• data_sim.getSpecies() returns array([[time], [species]])

• data_sim.getRates() returns array([[time], [rates]])

• data_sim.getRules() returns array([[time], [rate rules]])

• data_sim.getXData returns array([[time], [CVODE_extra_output]])

• data_sim.getSimData(*args) return an array consisting of time plus any available data series:

>>> mod.data_sim.getSimdata('s1', 'R1', 'Rule1', 'xData2')

• data_sim.getAllSimData() return an array of all simulation data

• data_sim.getDataAtTime(time) return the results of the simulation at time.

• data_sim.getDataInTimeInterval(time, bound) return the simulation data in the interval [time-bound, time+bound], if bound is not specified it is assumed to be the step size.

All the data_sim.get* methods by default only return a NumPy array containing the requested data, however if the argument lbls is set to True then both the array as well as a list of column labels is returned:

>>> data, Slabels = mod.data_sim.getSpecies(lbls=True)


This is very useful when using the PySCeS plotting interface (see Plotting) to plot simulation results.

For quick reference, simulation results are also available as a Numpy record array (mod.sim). This allows the user to directly reference a particular model attribute, e.g. mod.sim.Time, mod.sim.R1, or mod.sim.s1. Each of these calls returns a vector of values of the particular model attribute over the entire simulation (length of mod.sim_time).

PySCeS sets integrator options that attempt to configure the integration algorithms to suit a particular model. However, almost every integrator option can be overridden by the user. Simulator settings are stored in the PySCeS mod.__settings__ dictionary. For LSODA some useful keys (default values indicated) are (mod.__settings__[*key*]):

'lsoda_atol': 1.0e-12
'lsoda_rtol': 1.0e-7
'lsoda_mxordn': 12
'lsoda_mxords': 5
'lsoda_mxstep': 0


where atol and rtol are the absolute and relative tolerances, while mxstep=0 means that LSODA chooses the number of steps (up to 500). If this is still not enough, PySCeS automatically increases the number of steps necessary to find a solution.

The following options can be set for CVODE, with their defaults indicated:

'cvode_abstol': 1.0e-15
'cvode_mxstep': 1000
'cvode_reltol': 1.0e-9
'cvode_stats': False
'cvode_return_event_timepoints': True


where atol, rtol and mxstep are as above. If CVODE cannot find a solution in the given number of steps it automatically increases cvode_mxstep and tries again, however, it also keeps track of the number of times that this adjustment is required and if a specific threshold is passed it will begin to increase cvode_reltol by 1.0e3 (to a maximal value of 1.0e-3). If cvode_stats is enabled CVODE will display a report of its internal parameters after the simulation is complete. Finally, CVODE will by default also output the time points when events are triggered, even if these were not originally specified in mod.sim_time. To disable this behaviour and strictly report only the times in mod.sim_time, set cvode_return_event_timepoints to False.

PySCeS solves for a steady state using either the non-linear solvers HYBRD, NLEQ2 or forward integration. By default PySCeS has solver fallback enabled which means that if a solver fails or returns an invalid result (e.g., contains negative concentrations) it switches to the next available solver. The solver chain is as follows:

1. HYBRD (can handle ‘rough’ initial conditions, converges quickly).

2. NLEQ2 (highly optimised for extremely non-linear systems, more sensitive to bad conditioning and slightly slower convergence).

3. FINTSLV (finds a result when the change in max([species]) is less than 0.1%; slow convergence).

Solver fallback can be disabled by setting mod.mode_solver_fallback = 0. Each of the three solvers is highly configurable and although the default settings should work for most models, configurable options can be set by way of the mod.__settings__ dictionary.

To calculate a steady state use the mod.doState() method:

>>> mod.doState()
(hybrd) The solution converged.


The results of a steady-state evaluation are stored as arrays as well as individual attributes and can be easily displayed using the mod.showState() method:

• mod.showState() displays the current steady-state values of both the species and fluxes.

• For each reaction (e.g. R2) a new attribute mod.J_R2, which represents its steady-state value, is created.

• Similarly, each species (e.g. mod.s2) has a steady-state attribute mod.s2_ss.

• mod.state_species is an array of steady-state species values in mod.species order.

• mod.state_flux is an array of steady-state fluxes in mod.reactions order.

There are various ways of initialising the steady-state solvers although, in general, the default values should be sufficient.

• mod.mode_state_init initialises the solver using either the initial values specified in the input file (0), or a value close to zero (1). The default behaviour is to use the initial values.

Since PySCeS version 0.7 the mod.data_sstate object by default stores steady-state data (species, fluxes, rate rules) in a manner similar to mod.data_sim. One notable exception is that the current steady-state values are also made available as attributes to this object (e.g. species S1’s steady-state value is stored as mod.data_sstate.S1). Using the mod.STATE_extra_output list it is possible to store user-defined data in the data_sstate object. Steady-state data can be easily retrieved using the by now familiar .get* methods.

• data_sstate.getSpecies() returns a species array

• data_sstate.getFluxes() returns a flux array

• data_sstate.getRules() returns a rate rule array

• data_sstate.getXData() returns an array defined in STATE_extra_output

• data_sstate.getStateData(*args) return user defined array of data ('S1','R2')

• data_sstate.getAllStateData() return all steady-state data as an array

All these methods also accept the lbls=True argument in which case they return both array data and a label list:

>>> ssdat, sslbl = mod.data_sstate.getSpecies(lbls=True)


### Stability analysis¶

PySCeS can analyse the stability of systems that can attain a steady state. It does this by calculating the eigenvalues of the Jacobian matrix for the reduced system of independent ODEs.

• mod.doEigen() calculates a steady-state and performs the stability analysis

• mod.showEigen prints out a stability report

• mod.doEigenShow() combines both of the above

The eigenvalues are also available as attributes mod.lambda1 etc. By default the eigenvalues are stored as mod.eigen_values but if mod.__settings__['mode_eigen_output'] = 1 is set, in addition to the eigenvalues the left and right eigenvectors are stored as mod.eigen_vecleft and mod.eigen_vecright, respectively. Please note that there is currently no guarantee that the order of the eigenvalue array corresponds to the species order.

## Metabolic Control Analysis¶

For ease of use the following methods are collected into a set of meta-routines that all first solve for a steady state and then perform the required Metabolic Control Analysis (MCA) 2, 3 evaluation methods.

### Elasticities¶

The elasticities towards both the variable species and parameters can be calculated using mod.doElas() which generates as output:

• Scaled elasticities referenced as mod.ecRate_Species, e.g. mod.ecR4_s2.

• mod.showEvar() displays the non-zero elasticities calculated with respect to the variable species.

• mod.showEpar() displays the non-zero parameter elasticities.

As a prototype we also store the elasticities in an object, mod.ec.*; this may become the default way of accessing elasticity data in future releases but has not been fully stabilised yet.

### Control coefficients¶

Both control coefficients and elasticities can be calculated using a single method, mod.doMca().

• mod.showCC() displays the complete set of flux and concentration control coefficients.

• Individual concentration-control coefficients are referenced as mod.ccSpecies_Rate, e.g. mod.ccs1_R4.

• Similarly, mod.ccJFlux_Rate is a flux-control coefficient, e.g. mod.ccJR1_R4.

As it is generally common practice to use scaled elasticities and control coefficients, PySCeS calculated these by default. However, it is possible to calculate unscaled elasticities and control coefficients by setting the attribute mod.__settings__['mode_mca_scaled'] = 0, in which case the model attributes are attached as mod.uec and mod.ucc respectively.

As a prototype we also store the control coefficients in an object, mod.cc.*; this may become the default way of accessing control coefficient data in future releases but has not been fully stabilised yet.

### Response coefficients¶

PySCeS can calculate the parameter response coefficients for a model with the mod.doMcaRC() method. Unlike the elasticities and control coefficients, the response coefficients are made available as a single attribute mod.rc. This attribute is a data object, containing the response coefficients as attributes and has the following methods:

• rc.var_par individual response coefficients can be accessed as attributes made up of variable_parameter e.g. mod.rc.R1_k1

• rc.get('var', 'par') return a response coefficient

• rc.list() returns all response coefficients as a dictionary of {key: value} pairs

• rc.select('attr', search='a') select all response coefficients that refer to 'attr' e.g. select('R1') or select('k2')

• rc.matrix: the matrix of response coefficients

• rc.row: row labels

• rc.col: column labels

### Response coefficients with respect to moiety-conserved sums¶

The mod.doMcaRC() method only calculates response coefficients with respect to explicit model parameters. However, in models with moiety-conservation the total concentration of all the species that form part of a particular moiety-conserved cycle is also a parameter of the model. PySCeS infers such moiety-conserved sums from the initial species concentrations specified by the user. In some cases it might be interesting to consider the effects that a change in the total concentration of a moiety will have on the steady-state. This analysis may be done with the method mod.doMcaRCT().

Since moiety-conserved sums are not explicitly named in PySCeS model files, 'T_' is prepended to all the species names listed in mod.Consmatrix.row. For instance, if the dependent species in a moiety-conserved cycle is 'A', then 'T_A' designates the moiety-conserved sum.

The object mod.rc is augmented with the results of mod.doMcaRCT(). Response coefficients may thus be accessed with mod.rc.get('var', 'T_par').

# Parameter scanning¶

## Single dimension parameter scans¶

PySCeS has the ability to quickly generate and plot single dimension parameter scans. Scanning a parameter typically involves changing a parameter through a range of values and recalculating the steady state at each step. Two methods are provided which simplify this task, mod.Scan1() is provided to generate the scan data while mod.Scan1Plot() is used to visualise the results. The first step is to define the scan parameters:

• mod.scan_in is a string defining the parameter to be scanned e.g. 'k0'

• mod.scan_out is a list of strings representing the attribute names to be tracked in the output, e.g. ['J_R1','J_R2','s1_ss','s2_ss']

• You also need to define the range of points that you would like to scan over. For a linear range NumPy has a useful function numpy.linspace(start, end, points) (NumPy can be accessed by importing it in your Python shell via import numpy). If you need to generate a log range use numpy.logspace(start, end, points).

Both numpy.linspace and numpy.logspace use the number of points (including the start and end points) in the interval as an input. Additionally, the start and end values of numpy.logspace must be entered as indices, e.g. to start the range at 0.1 and end it at 100 you would write numpy.logspace(-1, 2, steps). Setting up a PySCeS scan session might look something like:

>>> import numpy
>>> mod.scan_in = 'x0'
>>> mod.scan_out = ['J_R1','J_R6','s2_ss','s7_ss']
>>> scan_range = numpy.linspace(0,100,11)


Before starting the parameter scan, it is important to check that all the model attributes involved in the scan do actually exist. For example, mod.J_R1 is created when mod.doState() is executed, likewise all the elasticities (mod.ecR_S) and control coefficients (mod.ccJ_R) are only created when the mod.doMca() method is called. If all the attributes exist you can perform a parameter scan using the mod.Scan1(scan_range) method which takes your predefined scan range as an argument:

>>> mod.Scan1(scan_range)

Scanning ...
11 (hybrd) The solution converged.
(hybrd) The solution converged ...

done.


When the scan has been successfully completed, the results are stored in the array (mod.scan_res) that has mod.scan_in as its first column followed by columns that represent the data defined in mod.scan_out (if invalid steady states are generated during the scan they are replaced by NaN). Scan1 also reports the scan parameter values which generated the invalid states. If one or more of the specified input or output parameters are not valid model attributes, they will be ignored. Once the parameter scan data has been generated, the next step is to visualise it using the mod.Scan1Plot() method:

>>> mod.Scan1Plot(plot=[], title=None, log=None, format='lines', filename=None)

• plot if empty, mod.scan_out is used, otherwise any subset of mod.scan_out (default= [])

• filename the filename of the PNG file to save (default= None, no export)

• title the plot title (default= None)

• log if None a linear axis is assumed, otherwise one of ['x', 'y', 'xy'] (default= None)

• format the backend dependent line format (default= 'lines') or the CommonStyle 'lines' or 'points'.

Called without any arguments, Scan1Plot() plots all of mod.scan_out against mod.scan_in.

In a similar way that simulation results are captured in the mod.sim array, 1D-scan results are also available as a Numpy record array (mod.scan) for quick reference and easy access by the user. All the model attributes defined in mod.scan_in and mod.scan_out can be accessed in this way, e.g. mod.scan.x0, mod.scan.J_R1, mod.scan.s2_ss, etc.

## Two-dimensional parameter scans¶

Two-dimensional parameter scans can also easily be generated using the mod.Scan2D method:

>>> mod.Scan2D(p1, p2, output, log=False)

• p1 is a list of [model parameter 1, start value, end value, points]

• p2 is a list of [model parameter 2, start value, end value, points]

• output the steady-state variable e.g. 'J_R1' or 'A_ss'

• log if True scan using log ranges for both axes

To plot the results of two dimensional scan use the mod.Scan2DPlot method. Note: the GnuPlot interface must be active for this to work (see the section on Plotting later on in this guide).

>>> mod.Scan2DPlot(title=None, log=None, format='lines', filename=None)

• filename the filename of the PNG file (default= None, no export)

• title the plot title (default= None)

• log if None a linear axis is assumed, otherwise one of ['x', 'xy', 'xyz'] (default= None)

• format the backend dependent line format (default= 'lines') or the CommonStyle 'lines' or 'points'.

## Multi-dimensional parameter scans¶

This PySCeS feature allows multi-dimensional parameter scanning. Any combination of parameters is possible and can be added as leader parameters that change independently or follower parameters whose change is coordinated with the previously defined parameter. Unlike mod.Scan1() this function is accessed via the pysces.Scanner class that is separately instantiated with a loaded PySCeS model object:

>>> sc1 = pysces.Scanner(mod)
>>> sc1.addScanParameter('k2', 0.1, 1000, 5, log=True)
>>> sc1.addScanParameter('k4', 0.1, 1000, 5, log=True, follower=True)
>>> sc1.Run()

... scan: 55 states analysed

>>> sc1_res = sc1.getResultMatrix()
>>> print sc1_res[0]
array([1., 0.1, 0.1, 97.94286647, 49.1380999])

>>> print sc1_res[-1]
array([1.0e+01, 1.0e+03, 1.0e+03, -3.32564878e+00, 3.84227702e-03])


In this scan we define two independent (x3, k2) and one dependent (k3) scan parameters and track the changes in the steady-state variables J_R1 and s1_ss. Note that k2 and k4 use a logarithmic scale. Once run the input parameters cannot be altered, however, the output can be changed and the scan rerun.

• sc1.addScanParameter(name, start, end, points, log, follower) where name is the input parameter (as a string), start and end define the range with the required number of points, While log and follower are boolean arguments indicating the point distribution and whether the axis is independent or not.

• sc1.addUserOutput(*args) an arbitrary number of model attributes to be output can be added (this method automatically tries to determine the level of analysis necessary), e.g. addUserOutput('J_R1', 'ecR1_k2')

• sc1.Run() run the scan, if subsequent runs are required after changing output attributes, use sc1.RunAgain(). Note that it is not possible to change the input parameters once a scan has been run, if this is required a new Scanner object should be created.

• sc1.getResultMatrix(stst=False) return the scan results as an array containing both input and output. If stst = True append the steady-state fluxes and concentrations to the user output so that output has dimensions [scan_parameters]+[state_species+state_flux]+[Useroutput], otherwise return the default [scan_parameters]+[Useroutput].

• sc1.UserOutputList the list of output names

• sc1.UserOutputResults an array containing only the output

• sc1.ScanSpace the generated list of input parameters.

## Parallel parameter scans¶

When performing large multi-dimensional parameter scans, PySCeS has the option to perform the computation in parallel, either on a single machine with a multi-core CPU, or on a multi-node cluster. This requires a working ipyparallel installation (see also Installation). The functionality is accessed via the pysces.ParScanner class, which has the same methods as the pysces.Scanner class (see above) with a few multiprocessing-specific additions.

The parallel scanner class is instantiated with a loaded PySCeS model object:

>>> sc1 = pysces.ParScanner(mod, engine='multiproc')


The additional engine argument specifies the parallel computation engine to use:

• 'multiproc' - use Python’s internal multiprocessing module (default)

• 'ipcluster' - use ipcluster (refer to ipyparallel documentation)

There are two ways to run the scan:

• sc1.Run() - runs the scan with a load-balancing task client; tasks are queued and sent to nodes as these become available.

• sc1.RunScatter() - compute tasks are evenly distributed amongst compute nodes (“scattered”) and the results are returned (“gathered”) once all the computations are complete. No load balancing is performed. May be slightly faster than sc1.Run() if the individual tasks are very similar. Not available with multiproc !

Further input and output processing is as for pysces.Scanner. A few example scripts illustrating the parallel scanning procedure are provided in the pysces/examples folder of the installation.

# Plotting¶

The PySCeS plotting interface has written to facilitate the use of multiple plotting back-ends via a Unified Plotting Interface (UPI). Using the UPI we ensure that a specified subset of plotting methods is back-end independent (although the UPI can be extended with back-end specific methods). So far Matplotlib (default) and GnuPlot back-ends have been implemented.

The common UPI functionality is accessible as pysces.plt.* while back-end specific functionality is available as pysces.plt.m (Matplotlib) and pysces.plt.g (GnuPlot).

While the Matplotlib is activated by default, GnuPlot needs to be enabled (see Configuration section) and then activated using pysces.plt.p_activateInterface('gnuplot'). All installed interfaces can be activated or deactivated as required:

>>> pysces.plt.p_activateInterface(interface)
>>> pysces.plt.p_deactivateInterface(interface)


where interface is either 'matplotlib' or 'gnuplot'. The PySCeS UPI defines currently has the following methods:

plot(data, x, y, title='', format='') plot a single line data[y] vs data[x]

• data the 2D-data array

• x x column index

• y y column index

• title is the line legend text (key)

• format is the backend format string (default=’’)

plotLines(data, x, y=[], titles=[], formats=['']) plot multiple lines, i.e. data[y1, y2, ] vs data[x]

• data the data array

• x x column index

• y is a list of line indexes, if empty all of y not including x is plotted

• titles a list of line keys, if empty Line1, Line2, etc. is used

• formats a list (per line) of format strings, if formats only contains a single item, this format is used for all lines.

splot(data, x, y, z, title='', format='') plot a surface, i.e. data[z] vs data[y] vs data[x]

• data the data array

• x x column index

• y y column index

• z z column index

• title the surface key (legend text)

• format a format string (default=’’)

splotSurfaces(data, x, y, z=[], titles=[], formats=['']) plot multiple surfaces, i.e. data[z1, z2, ] vs data[y] vs data[x]

• data the data array

• x x column index

• y y column index

• z a list of z column indexes, if empty all data not including x, y are plotted

• titles a list of surface keys, if empty Surf1, Surf2, etc. is used

• formats is a list (per line) of format strings (default=’’). If formats only contains a single item, this format is used for all surfaces.

replot() replot the current figure using all active interfaces (useful with GnuPlot type interfaces)

save(name, directory=None, dfmt='\%.8e') save the plot data and (if possible) the back-end specific format file

• filename the filename

• directory optional (default = current working directory)

• dfmt the data format string (default= '\%.8e')

export(name, directory=None, type='png') export the current plot as a <type> file (currently only PNG is guaranteed to be available on all back-ends).

• filename the filename

• directory optional (default = current working directory)

• type the file format (default= 'png').

setGraphTitle(title='PySCeS Plot') set the graph title, unset if title=None

• title (string, default=’PySCeS Plot’) the graph title

setAxisLabel(axis, label='') sets one or more axis labels

• axis x, y, z, xy, xz, yz, zyx

• label label string (default= None). When alled with only the axis argument, clears the label of that axis.

setKey(value=False) enable or disable the current plot key, no arguments removes key.

• value boolean (default= False)

setLogScale(axis) set axis to log scale

• axis is one of x, y, z, xy, xz, yz, zyx

setNoLogScale(axis) set axis to a linear scale

• axis is one of x, y, z, xy, xz, yz, zyx

setRange(axis, min=None, max=None) set one or more axis ranges

• axis is one of x, y, z, xy, xz, yz, zyx

• min is the range(s) lower bound (default=None, back-end auto-scales)

• max is the range(s) upper bound (default=None, back-end auto-scales)

setGrid(value) enable or disable the graph grid

• value (boolean) True (on) or False (off)

plt.closeAll() Close all active Matplolib figures.

# Displaying data¶

## Displaying/saving model attributes¶

All of the showX() methods, with the exception of mod.showModel() operate in exactly the same way. If called without an argument, they display the relevant information to the screen. Alternatively, if given an open, writable (ASCII mode) file object as an argument, they write the requested information to the open file. This allows the generation of customised reports containing only information relevant to the model.

• mod.showSpecies() prints the current values of the model species (mod.M).

• mod.showSpeciesI() prints the initial values of the model species (mod.Mi), as parsed from the input file.

• mod.showPar() prints the current values of the model parameters.

• mod.showState() prints the current steady-state fluxes and species.

• mod.showConserved() prints any moiety conserved relationships (if present).

• mod.showFluxRelationships() shows the relationships between dependent and independent fluxes at steady state.

• mod.showRateEq() prints the reaction stoichiometry and rate equations.

• mod.showODE() prints the ordinary differential equations.

Note

The mod.showModel() method is not recommended for saving models as a PySCeS input file, use the Core2 based pysces.interface.writeMod2PSC method instead:

>>> pysces.interface.writeMod2PSC(mod, filename, directory, iValues=True, getstrbuf=False)

• filename: writes <filename>.psc or <model_name>.psc if None

• directory: (optional) an output directory

• iValues: if True (default) then the model initial values are used (or the current values if False)

• getstrbuf: if True a StringIO buffer is returned instead of writing to disk

For example, assuming you have loaded a model and run mod.doState() the following code opens a Python file object (rFile), writes the steady-state results to the file associated with the file object (results.txt) and then closes it again:

>>> rFile = open('results.txt','w')
>>> mod.showState()      # print the results to screen
>>> mod.showState(rFile) # write the results to the file results.txt
>>> rFile.close()


## Writing formatted arrays¶

The showX() methods described in the previous sections allow the user a convenient way to write the predefined matrices either to screen or file. However, for maximum flexibility, PySCeS includes a suite of array writers that enable one to easily write, in a variety of formats, any array to a file. Unlike the showX() methods, the Write_array methods are specifically designed to write to data to a file.

In most modelling situations it is rare that an array needs to be stored or displayed that does not have specific labels for its rows or columns. Therefore, all the Write_array methods take list arguments that can contain either the row or column labels. Obviously, these lists should be equal in length to the matrix dimension they describe and in the correct order.

There are currently three custom array writing methods that work either with a 1D (vector) or 2D (matrix) array. To allow an easy comparison of the output of these methods, all the following sections use the same example array as input.

### Write_array()¶

The basic array writer is the Write_array() method. Using the default settings this method writes a ‘tab delimited’ array to a file. It is trivial to change this to a ‘comma delimited’ format by using the separator = ',' argument. Numbers in the array are formatted using the global number format.

If column headings are supplied using the Col = [] argument they are written above the relevant column and if necessary truncated to fit the column width. If a column name is truncated it is marked with a * and the full length name is written as a comment after the array data. Similarly row data can be supplied using the Row = [] argument in which case the row names are displayed as a comment which is written after the array data.

Finally, if the close_file argument is enabled the supplied file object is automatically closed after writing the array. The full call to the method is:

>>> mod.Write_array(input, File=None, Row=None, Col=None, separator=' ')


which generates the array

## Write_array_linear1_11:12:23
#s0           s1           s2
-3.0043e-001  0.0000e+000  0.0000e+000
1.5022e+000 -5.0217e-001  0.0000e+000
0.0000e+000  1.5065e+000 -5.0650e-001
0.0000e+000  0.0000e+000  1.0130e+000
# Row: R1 R2 R3 R4


By default, each time an array is written, PySCeS includes an array header consisting of the model name and the time the array was written. This behaviour can be disabled by setting: mod.write_array_header = 0

### Write_array_latex()¶

The Write_array_latex() method functions similarly to the generic Write_array() method except that it generates a formatted array that can be included directly in a LaTeX document. Additionally, there is no separator argument, column headings are not truncated and row labels appear to the left of the matrix.

>>> mod.Write_array_latex(input, File=None, Row=None, Col=None)


which generates

%% Write_array_latex_linear1_11:45:03
$\begin{array}{r|rrr} & \small{s0} & \small{s1} & \small{s2} \\ \hline \small{R1} &-0.3004 & 0.0000 & 0.0000 \\ \small{R2} & 1.5022 &-0.5022 & 0.0000 \\ \small{R3} & 0.0000 & 1.5065 &-0.5065 \\ \small{R4} & 0.0000 & 0.0000 & 1.0130 \\ \end{array}$


and in a typeset document appears as:

 s0 s1 s2 R1 -0.3004 0.0000 0.0000 R2 1.5022 -0.5022 0.0000 R3 0.0000 1.5065 -0.5065 R4 0.0000 0.0000 1.0130

# Installing and configuring¶

PySCeS is developed primarily in Python and has been designed to operate on multiple operating systems, i.e. Linux, Microsoft Windows and macOS. PySCeS makes use of NumPy and SciPy for a number of functions and needs a working SciPy stack (https://www.scipy.org) to install and run.

## General requirements¶

• Python 3.6+

• Numpy 1.14+

• SciPy 1.0+

• Matplotlib (with TkAgg backend)

• GnuPlot (optional, alternative plotting back-end)

• IPython or the Jupyter notebook (optional, highly recommended for interactive modelling sessions)

• libSBML (optional). Python bindings for SBML support can be installed via

$pip install python-libsbml  This software stack provides a powerful scientific programming platform which is used by PySCeS to provide a flexible Systems Biology Modelling environment. PySCeS itself has been modularised into a main package and a (growing) number of support modules which extend its core functionality. It is highly recommended that the following packages/modules are also installed: By default PySCeS installs with a version of ZIB’s NLEQ2 non-linear solver. This software is distributed under its own non-commercial licence. Please see https://github.com/PySCeS/pysces for details. ## Installation¶ Binary install packages for all three OSs and Python versions 3.6-3.9 are provided. Anaconda users can conveniently install PySCeS with: $ conda install -c conda-forge -c pysces pysces


Any dependencies will be installed automatically, including the optional dependencies Assimulo, ipyparallel and libSBML.

Alternatively, you can use pip to install PySCeS from PyPI. Core dependencies will be installed automatically.



### macOS build¶

The Anaconda build method, described above for Windows, should also work on macOS.

Alternatively, Python 3 may be obtained via Homebrew and the compilers may be installed via Xcode.

Clone the source from Github as described above, change into the source directory and run:

$python setup.py install  ## Configuration¶ PySCeS has two configuration (*.ini) files that allow one to specify global (per installation) and local (per user) options. Currently the multiuser options are only fully realised on Linux based systems. Global options are stored in the pyscfg.ini file which is created in your PySCeS installation directory upon install. The example below is a Windows version; the exact values of install_dir and gnuplot_dir (if available) will depend on your individual OS and Python setup and are determined on install. [Pysces] install_dir = c:\Python38\Lib\site-packages\pysces gnuplot_dir = c:\model\gnuplot\binaries model_dir = os.path.join(os.path.expanduser('~'),'Pysces','psc') output_dir = os.path.join(os.path.expanduser('~'),'Pysces') silentstart = False change_dir_on_start = False  The [Pysces] section contains information on the installation directory, the directory where the GnuPlot executable(s) can be found and the default model file and output directories. This section also contains two further key-value pairs. If silentstart (default False) is set to True, informational messages about the PySCeS installation are not printed to the console on startup. The key change_dir_on_start specifies if the working directory should be changed to the PySCeS output directory (typically $HOME/Pysces or %USERPROFILE%\Pysces) on startup. When set to False (the default), the working directory is not changed.

As we shall see some of these defaults can be overridden by the local configuration options.

[ExternalModules]
nleq2 = True

[PyscesModules]
pitcon = True


These sections define whether third-party algorithms (NLEQ2 and PITCON) are available for use, while the last section allows the alternate plotting backends to be enabled or disabled:

[PyscesConfig]
gnuplot = True
matplotlib = True


The user configuration file (pys_usercfg.ini) is created when PySCeS is imported/run for the first time. On Windows this is in %USERPROFILE%\Pysces while on Linux and macOS this is in \$HOME/Pysces. Once created, the user configuration files can be edited and will be used for every subsequent PySCeS session.

[Pysces]
output_dir = C:\mypysces
model_dir = C:\mypysces\pscmodels
gnuplot = False


For example, the above user configuration on a Windows system customises the default model and output directories and disables GnuPlot (enabled globally above). If required, gnuplot_dir can also be set to point to an alternate location on a per-user basis. The configuration keys silentstart and change_dir_on_start can also be overridden here on a per-user basis.

Once you have PySCeS configured to your personal requirements you are ready to begin modelling.

# References¶

Footnotes

1

Hofmeyr, J.-H.S. (2001) Metabolic control analysis in a nutshell, in T.-M. Yi, M. Hucka, M. Morohashi, and H. Kitano, eds, Proceedings of the 2nd International Conference on Systems Biology, pp. 291-300.

2

Kacser, H. and Burns, J. A. (1973), The control of flux, Symp. Soc. Exp. Biol. 32, 65-104.

3

Heinrich and Rappoport (1974), A linear steady-state treatment of enzymatic chains: General properties, control and effector strength, Eur. J. Biochem. 42, 89-95.