TemplateSB: A template processor for readable and reusableuse kinetics models for systems biology

TemplateSB is a template processor for use in kinetics models for systems biology. The work was motivated by modeling in Antimony, a system for expression kinetics models in Tellurium.

The motivation for TemplateSB is as follows. Often, realistic kinetics models require representing a large number of reactions. The resulting model is difficult to write, and difficult to understand.

Fortunately, the set of reactions can often be simplified due to independence assumptions used in the model. To illustrate this, consider a part of the chemotaxis model for E. coli in Spiro (PNAS, 1997). We focus on receptor methylation. The state of a receptor is determined by three factors: whether or not it is bound to a ligand; whether or not it is phosphorylated; and its methylation level. Methylation may occur once a receptor (in any state) is bound to CheR (herein denoted by R). The reactions for a methylation level of 2 are:

T2R -> T3 + R; k2*T2R
LT2R -> LT3 + R; k2*LT2R
T2pR -> T3p + R; k2*T2pR
LT2pR -> LT3p + R; k2*LT2pR

Note that the reactions are independent of phosphorylation and ligand binding in that the kinetics constants do not change with these receptor states. To represent the complete set of methylation reactions in the Spiro model, we’d consider methylation levels of 3 and 4 as well, resulting in 12 reactions.

With TemplateSB, the complete set of 12 reactions can be expressed in a more compact way. Templates provide a way to describe model elements using template expressions. A template expression is either a template variable (which is defined in a manner described below) or a python expression consisting of template expressions. A template expression is surrounded by curly braces ({, }). A templated reaction is a reaction with one or more template expressions.

One templated reaction can expression all of the above non-templated reactions. This is done using two template variables, L and p. L has as two expansions: L and ""; p has defined in the same way.

{L}T2{p}R -> {L}T3{p} + R; k2*{L}T2{p}R

The template processor expands this expression into the above four reactions. That is, the first reaction above is realized by assigning '' (the null string) to both {L} and {p}. The other four reactions are constructed by using the other three combinations of the values of template variables. Note that both kinetics expressions and reaction labels can use template variables.

TemplateSB responds to several commands dictating how lines should be expanded. Commands are enclosed in double braces ({{ and }}). Supported commands are: {{ DefineVariables Begin }} - beginning of Python codes to execute {{ DefineVariables End }} - end of Python codes to execute

Below is a description of the function of these commands.

• Codes between DefineVariables Begin and DefineVariables End commands are used to specify template variables used in expansions. This is done using the api object. For example,

  {{ DefineVariables Start }}
  api.addDefinitions({'p': ['p', '']})
  {{ DefineVariables End }}
  

  Defines the variable "p" as having the values '' and 'p'.

Below is a representation in templates of the 64 methylation reactions in the Spiro model. TemplateSB uses a Python code to specify how processing should proceed based on opertions on the object api. In particular, api.addDefinitions takes a dictionary as its arguement. The keys are template variables; the associated values are the possible values that can be assigned to the template variable.

{{ DefineVariables Start }}
api.addDefinitions({‘p’:[‘p’,‘’], ‘L’:[‘L’,‘’], ‘r’:[‘R’,‘’], ‘m’:[‘2’, ‘3’, ‘4’]})
{{ DefineVariables End }}
 
J1{L}{m}{p}: {L}T{m}{p} + R -> {L}T{m}{p}R; k1{m}*{L}T{m}{p}*R
J2{L}{m}{p}: {L}T{m}{p}R -> {L}T{m}{p} + R; k2{m}*{L}T{m}{p}R
J3{L}2{p}: {L}T2{p}R -> {L}T3{p} + R; k32*{L}T2{p}R
J3{L}3{p}: {L}T3{p}R -> {L}T4{p} + R; k33*{L}T3{p}R

Here's an example using a template variable expression to describe an increase in methylation level. Note that the template expression has a python expression, me+1. In TemplateSB, a template expression can be an arbitrary python expression.

{{ DefineVariables Begin }}
api.addDefinitions({
                    'p': ['p', ''],  # Phosphorylation
                    'me': [2, 3],  # Increase methylation
                  })
{{ DefineVariables End }}
J1_{me}{p}R: T{me}{p}R -> T{me+1}{p} + R; k1c*T{me}{p}R

TemplateSB expands the singl templated reaction to:

J1_2pR: T2pR -> T3p + R; k1c*T2pR
J1_3pR: T3pR -> T4p + R; k1c*T3pR
J1_2R: T2R -> T3 + R; k1c*T2R
J1_3R: T3R -> T4 + R; k1c*T3R

Since TemplateSB is intended to be applied to many source languages, various elements can be configured to adapt to different source inputs. This is described in config.yaml.

One possible extension is to permit having a python expression inside a template instance (within { and }). This feature would eliminate one of the templated model lines in the above model by using {m+1} as a template instance.

The repository is organized as follows:

• The Code directory contains the python code and tests for the template preprocessor.
• The Examples directory contains an example of a template input and the output produced by TemplateSB.
• setup.py installs prerequisites for running TemplateSB.
• python3 run.py is runs TemplateSB using stdin and stdout.
• Examples/Demo contains a demo. Use bash python3 demo.sh