Movement and communication in multiscale/multilevel models of biological systems
David Gilbert, Leverhulme Emeritus Research Fellow
Project dates: August 2021 – September 2023
Abstract:
We worked on the design, construction and use of a system
to support the use of agent based models to describe complex
biological entities representing single celled organisms which can move
according to external stimuli, communicate and act collaboratively in
space. Our methodology is based on the use of Coloured Petri Nets
and a stepwise simulator. The internal descriptions of the organisms
include biological mechanisms such as transcription and translation, as
well as enzymatic-based activity – metabolic pathways and signalling
networks, and transport into and out of the cell. The organisms
interact with the external environment by the detection of biochemicals
which can diffuse in space, and by broadcast communication of
biochemical signals.
The project focussed on single celled organisms exhibiting motile behaviour in a colonial context as a tractible example of biological
systems,
and the modelling formalism chosen was Coloured Petri nets.
We applied our methodology to two examples, both of
which involve collaborative colonial behaviour: the aggregation phase
in slime mould (Dictyostelium), and quorum sensing driven biofilm
formation in bacteria.
The aim of the project was to develop a method to model
movement and communication in multiscale/multilevel models of biological systems.
The objectives of the project were to
- develop a method to support efficient movement and
communication by encapsulating location within an entity,
- apply the method to existing models of single celled organisms,
- incorporate appropriate intracellular pathways
and protein behaviour into the models to yield rich multilevel models at 3 levels:
- intercellular,
- intracellular networks,
- enzyme behaviour.
Previous modelling approach:
Our previous approach for modelling motile systems in a spatial environment was based on representing 1, 2 or 3D spatial location using
Coloured Petri Nets to encode a grid, and a copy of the Petri net describing the motile entity is placed in every grid location.
In this grid method, movement in space is achived by having only one copy of the entity model `live', say at location (x,y) in a 2D setting, and all the others dead (their
transitions containing no tokens). Movement is simulated by making a copy of the model at another location (x',y') live and making the
copy at (x,y) dead.
This approach has several disadvantages:
- it is not efficient in terms of memory because the model must be replicated everywhere,
- it is inefficicent in terms of processing time, bacause all locations must be check for their live or dead status,
- and the most serious - it cannot represent the movement of complex entities comprising more than one place because there is no atomic lock
available in the current Petri net system.
Technical summary:
We developed methods to
- efficiently represent 2D and 3D location in effectively unrestricted size of space in Petri net models of agents with complex
internal structure – called the ‘coordinates approach’
- interface these models in a hybrid manner to the existing ‘grid approach’ where large amounts of small entities (e.g. small
molecules) are represented on a spatial grid.
The Coordinates approach:
Each entity is effectively an `agent', which has an
internal description of its location as a coordinate tuple. Movement can be achieved by merely updating the coordinate tuple [Gilbert et
al., 2019].
Advantages:
- There is no computational penalty associated with size of the space in which the agent[s] are situated - because there
is effectively no concept of size of space.
- Infinite space can be achieved by the use of natural numbers as components of the coordinate tuple (this facilitates modelling
multiple agents being at one location), or indeed the use of real numbers -- where agents may be extremely close but not actually at the
same location.
- Complex entities can be moved in an atomic manner because all components of an entity have access to the same coordinate tuple.
Disadvantages:
- Some special basic computational mechanisms need to be implemented in order to permit entities to detect each other
in space.
- All entities have to be explicitly modelled as agents, and thus e.g. it is very computationally expensive to model the diffusion of a
large number of molecules, because each molecule has to be individually modelled
Hybrid approach:
We achieved our main technical advances by exploiting interruptive simulation available in the
Spike simulator part of the
PetriNuts Software Platform.
This requires writing complex code in our chosen meta-level language, Python. To facilitate this, we developed the
SPC-python-builder script which automatically generates the Spike code and the associated Petri net file to design models requiring
mobility using the hybrid approach.
Using our hybrid approach we were able to model intercommunicating and interacting mobile agents with complex internal structure in an
environment containing diffusing small molecules. We applied these methods to model behaviours in two example organisms: clumping in
Dictyostelium, and quorum sensing driven biofilm formation in bacteria.
We refined our models using target-driven optimisation on large computer clusters, and explored the effects in silico of modifying the
activity at the intracellular level)of key proteins on the individual and colonial behaviour of the modelled organisms.
Conclusions:
We showed that we could effectively model movement and communication in single-celled organisms at the intercellular level (broadcast
communication, chemotaxis and colonial behaviour), as well as the intracellular level (transcription, translation, protein interaction,
biochemical networks and signal export/import). We also developed a computational system to support this
using Coloured Petri nets and a step-wise simulator,
and a set of example models of
selected biological systems.
Acknowledgements:
This research was funded by the Leverhulme Trust under their Emeritus Fellowship scheme, Project number EM-202-0-086\9, value £23,900,
carried out from August 2021 to September 2023 together with
Francesco Rinaldi
(undergraduate student research assistant), in collaboration with Professor Monika
Heiner (Brandenberg Technical University) and building on earlier work by
Dr. Leila Ghanbar (Brunel University London).
Software, user guide & examples:
Materials
Related papers
- L. Ghanbar and D. Gilbert (2023):
Application of Coloured Petri Nets to Model Communication, Movement, Death and Duplication of Unicellular Organisms,
BBCC 2023
-
L. Ghanbar (2022):
Application of bio-model engineering to model abstract
biological behaviours, PhD thesis, Brunel University London, UK
-
D. Gilbert, M. Heiner, L. Ghanbar and J. Chodak (2019):
Spatial quorum sensing modelling using coloured hybrid Petri
nets and simulative model checking.
BMC Bioinformatics 20, Article number 173, Supplement 4 (2019).
http://dx.doi.org/10.1186/s12859-019-2690-z
-
F. Liu, M. Heiner and D. Gilbert (2023):
Protocol for biomodel engineering of unilevel to multilevel
biological models using colored Petri nets;
STAR Protocols, 2023. (accepted: September 2023).
http://dx.doi.org/https://doi.org/10.1016/j.xpro.2023.102651