=Paper=
{{Paper
|id=None
|storemode=property
|title= Support for Agent Based Simulation of Biomolecular Systems
|pdfUrl=https://ceur-ws.org/Vol-710/paper33.pdf
|volume=Vol-710
|dblpUrl=https://dblp.org/rec/conf/maics/KorukondaP11
}}
== Support for Agent Based Simulation of Biomolecular Systems==
https://ceur-ws.org/Vol-710/paper33.pdf
Support for Agent Based Simulation of Biomolecular Systems
Harika Korukonda and Carla Purdy
School of Electronic and Computing Systems, University of Cincinnati
contact: carla.purdy@uc.edu
Abstract The disadvantages of modeling using traditional
We describe our work developing GenericSystem, which techniques include: the spatial dynamics of the systems
contains the basic classes and functions necessary to model cannot be modeled; systems with both continuous and
and simulate a typical biomolecular system. GenericSystem discrete behavior cannot be modeled; the high complexity
is user-friendly and extensible. It consists of well-defined and stochasticity of the system cannot be taken into
functions which can be readily customized to reduce account; and most of these methods tend to aggregate the
development time for a biomolecular simulation. Five values during modeling, which may lead to incorrect
systems-- bioluminescence in Vibrio fischeri bacteria, skin results [14]. ABM, on the other hand, has many
regulatory system, phage lambda in E. coli, epithelial cells advantages: ABM describes a system in a way which is
growth cycle and Wnt signaling pathway--have been closest to it in reality [1]; randomness is applied in the most
successfully implemented using the GenericSystem tool. appropriate way instead of just adding a noise term to an
We show some results for one of these systems and equation; ABM captures emergence phenomena of the
describe the process to translate a typical differential system which are the result of interactions between
equation-based system description into a GenericSystem individual entities of the system; and ABM is flexible, i.e.,
model.
it provides a natural framework for tuning the complexity
of the agents. The behavior, degree of rationality, ability to
Introduction learn and evolve and rules of interactions are adjustable
[1]; the levels of agglomeration can be varied. i.e., dealing
For molecular systems, traditional modeling techniques are with single agents and groups of agents simultaneously
known as equation based modeling (EBM) [2] and include becomes easy; the interactions can be changed
ordinary differential Equations (ODE), partial differential dynamically, since they are defined at the agent level; and
equations (PDE) [3], stochastic differential equations positive and negative feedback can be modeled. For
(SDE), Petri nets [4] and Pi-calculus [5]. The main systems in which activities describe the system better than
disadvantage of these approaches is their inability to processes and in which stochasticity applies to an agent’s
consider the spatial dynamics and heterogeneity of the behavior, ABM is often the most appropriate way of
system. Petri nets and Pi-calculus are graph based modeling [1]. It can also be applied to problems where the
techniques. Graph-based techniques have several population is heterogeneous or the topology of the
additional shortcomings such as basic modeling constructs interactions is heterogeneous and complex. There are
which are quite primitive and hence they fail to model several situations when ABM is the only resort. When the
complex systems successfully. Also spatial representation behavior of individual entities of a system cannot be clearly
of the system can get very complex with respect to time defined through aggregate transition rates, ABM is
and effort. Another main disadvantage is the inefficiency especially useful. As the individual behavior grows in
of representing priorities or ordering of events which is complexity, the complexity of differential equations
essential in systems modeling. Because of these modeling them also grows exponentially and thus becomes
shortcomings, graph-based modeling techniques are not unmanageable. ABM has no such overhead and has proved
well-developed and hence rarely used. The other class of successful in modeling several complex systems [7].
models comprising of ODE, PDE and SDE form the
equation based modeling class of techniques. This gamut Project Goals
of approaches essentially represents the system by
identifying the system variables. These variables are The goals of this project were:
integrated and sets of equations relating these variables are • To design GenericSystem, a generic easy-to-use
formed. Evaluation of these equations forms the basis of simulation model using the agent-based modeling
EBM. The fact that this approach has been in use for technique which can efficiently model many of the
several decades essentially showcases its ability to model a commonly found biological systems.
system satisfactorily. But as the complexity of the system • To implement GenericSystem using MASON
increases, this approach starts to fail. This happens mainly [9,10] and make the right use of the advantages available in
because the equations involved become too complex to the tool. MASON was chosen as the basis for our system
handle. A clear comparison between agent based after a thorough analysis of the available tools. A summary
modeling and the equation based approach is given in [2]. of many of the tools we considered is available in [8].
• To incorporate as many features as possible into • Size : Generic unit which can be interpreted as
the generic system so that it can successfully be used to the user wishes. It can be specified by using the scale
model systems with entities of various complex shapes. function of display class.
• To provide a procedure for transforming a • Velocity: Can be interpreted as generic unit of
biomolecular system modeled traditionally into an ABM time or generic unit of length as per user’s convenience.
version using our tool • Container : The large rectangular box which
• To provide case studies of specific system containes all the simulations elements. It can be interpreted
models, including examples previously developed as the entire simulation space where the reactions are
individually in our lab (bioluminescence in Vibrio fischeri taking place. It is assumed that all the reactions take place
[12], skin cell regulation (normal and wound conditions) within the container.
[13] and phage-lambda in E. coli acting as a biological For all the systems to be implemented, the chemical
inverter [11]). reactions and their reaction rates have been found from the
• To provide an example of translating a literature. The lifetimes and binding times of the molecules
differential equations-based simulation to an ABM are calculated from the respective reaction rates. In [6] a
simulation in GenericSystem, based on the Wnt signaling relation between rate constants and the reactions times has
pathway [16,17]. been established. The inverse of the rate constant is
. considered as the reaction time measure. This is because
GenericSystem any two given reactions with the same initial concentration
of reactants proceed with velocities that have the same
GenericSystem was designed using AUML, an agent based ratio as their reaction rate constant ratio. If v1 and v2 are
extension of UML [15]. There are three main classes of reaction velocities of reactions with rate constants K1 and
agents, Stationary, Mobile, and Vibrating. Users can K2, then the relation between them defined in [6] is
extend these classes or add new classes which are derived v1/K1 = v2/K2..
from the base class Agent. Initial subclasses included in
the system are Rectangular Sheet. Rectangular Box, Building a GenericSystem Model
Spherical, Cylindrical, Sticky Rectangular Sheet
(Stationary), Sphere, Dumbbell, Rectangular Box, We illustrate the use of GenericSystem through the model
Rectangular Sheet (Mobile), and Rectangular Box, of the Wnt signaling pathway and some simulations of its
Rectangular Sheet, U- Shaped (Vibrating). Figure 1 shows behavior. The Wnt xignaling pathway describes a set of
an AUML diagram for a GenericSystem class. Notice how proteins most commonly known for their effect on
the diagram facilitates modeling communication between embryogenesis and cancer tumors. A protein called β-
the agent and its environment. catenin acts as a transcriptional coactivator for cancer
causing tumor cells. Other important proteins which form
part of the Wnt signaling pathway are APC and Axin,
which is required for degradation of β-catenin. The
reactions taking place in the Wnt pathway are shown in
Figure 2.
Figure 1. AUML diagram of Agent class.
Experimental Setup and Base Parameters of
Simulations
The computer used to run the experiments has the 1.6GHz
Intel Core 2 Duo processor. The operating system used is a
32bit Windows 7 OS. The RAM installed in the computer
is 2GB. Figure 2. Reactions in Wnt pathway [16,17].
The software versions used in the work are:
• MASON version 14 This forms a transcriptional regulation of Wnt genes. When
• Java ™ SDK 6 update 11 Wnt signal is absent, APC directly associates with
• Java 3D version 1.5.1 TCF/LEF binding site on Wnt target genes and mediates
• Eclipse platform version 3.4.1 (IDE for Java) exchange between coactivator and corepresser complex
Model design parameters are: proteins. This represses concentration of β-catenin. Also
when Wnt signal is absent, APC transports β-catenin from Now we categorize the molecules to match agent types
the nucleus to the destruction complex where it available in the GenericSystem. The agents chosen to
phosphorylates and is recognized by β-TrCP. This also implement the system molecules are provided in Table 1.
results in further degradation of β-catenin protein. On the Molecule Agent
other hand, when Wnt signal is present, the Molecule
Dshi Mobile Spherical
phosphorylation of β-catenin is inhibited, leading to its
Agent
dissociation from the Axin-assembled destruction complex Dsha Mobile Spherical
[18]. The stabilized β-catenin reaches the nucleus and Agent
binds to the TCF/LEF resulting in activation of Wnt target apc*/axin*/gsk3 Mobile Spherical
genes. The chemical reactions taking place in the system Agent
are shown in Figure 3 and Figure 4. A differential apc/axin/gsk3 Mobile Spherical
equation based model of the Wnt pathway was previously Agent
developed in our lab [19]. Here we use the GenericSystem Gsk3 Mobile Spherical
procedure to translate that model into an ABM model. Agent
Apc/axin Mobile Spherical
Agent
Apc Mobile Spherical
Agent
β-catenin/apc* Mobile Spherical
Agent
β-catenin Mobile Spherical
*/apc*/axin*/gsk3 Agent
β-catenin * Mobile Spherical
Agent
β-catenin Mobile Spherical
Agent
Axin Mobile Spherical
Agent
Tcf Stationary
Rectangular Box
β-catenin/tcf Mobile Spherical
Agent
β-catenin/apc Mobile Spherical
Agent
TCF/LEF Binding Stationary
site Rectangular Box
Table 1. Wnt molecules and corresponding agents.
The chemical reactions are interpreted as collisions
between the corresponding molecules. The rate of reaction
is modeled as the velocity of corresponding molecules. The
functions used are listed in Table 2.
Chemical Function of
Reaction GenericSystem
Bonding to another Attach()
molecule
Unbond from Detach()
another molecule
Grow in size GrowInSize()
Decay DeleteAgent()
React with another DetectCollision()
agent
Move freely Move()
Figures 3 and 4. Wnt equations.
React and form new DeleteAgent(),
molecule CreateAgent()
Table 2. Agent functions and chemical reactions.
The number of molecules and their lifetimes are based on The lifetimes of the molecules that decay are calculated by
the concentrations given in [16]. The rate constants Ki are taking the rate of decay and relating it the total simulation
given in Figure 5. time. Table 4 tabulates the lifetimes of the molecules.
Molecule Lifetime
Dshi 1000
Dsha 10000
Axin 500
β-catenin* 300
Figure 5. Rate constants for Wnt equations. β-catenin 100
The concentrations of molecules in this experiment are Table 4. Molecule lifetimes.
spread over a large range starting from 0.00049 to 100.
Hence directly relating the concentration to the number of Snapshots of simulation
molecules is not possible in this case. So the number of
molecules are selected according to their concentration The system was successfully modeled using
levels. Taking the number of molecules to the limiting GenericSystem. Snapshots of the simulation are shown in
number, i.e., the maximum allowed by the tool, is not Figurea 6, 7, 8, and 9.
advisable since the movement of the molecules is hindered
and this reduces the rate of reactions. Hence the maximum
number is taken to be 100 and accordingly other molecule
numbers are selected. Molecules which are very low in
concentration are assigned number 1. A series of
experiments are run with various combinations of numbers
of molecules. The numbers of molecules in the base case
and their lifetimes are given in Table 3 and Table 4.
Molecule Number
Dshi 100
Dsha 0
apc*/axin*/gsk 5
3 Figure 6. System at time step 500.
apc/axin/gsk3 3
Gsk3 1
Apc/axin 3
Apc 100
β-catenin/apc* 1
β-catenin 1
*/apc*/axin*/g
β-catenin * 1
β-catenin 20 Figure 7. System at time step 900.
Axin 2
Table 3. Numbers of molecules.
Figure 11. Apc*/Axin*/gsk3 molecules vs time.
Figure 8. System at time step 1100.
The results obtained by the differential equations method
in [19] are shown in Figures 12 and 13. We see that in this
case the ABM simulation results match well with the
results in [19].
Figure 9. System at time stop 7000.
Description of Results and Comparison to
Literature Figure 12. Concentration of β-catenin vs time [19].
The numbers of the molecules β-catenin and
Apc*/Axin*/gsk3 have been observed throughout the
simulation. As Wnt changes from 0 to 1, the number of β-
catenin molecules increases from 20 to 500. The number
of Apc*/Axin*/gsk3 molecules decreases from 5 to 1.
These results are plotted in Figures 10 and 11
Figure 13. Concentration of Apc*/Axin*/Gsk3 vs time [19].
Conclusions and Future Work
Here we have compared our ABM model with a
differential equations model. In the case we considered,
Figure 10. β-catenin molecules vs time. we see that qualitatively we are getting the same behavior.
Similar results were obtained for the other systems
mentioned above. Details about these systems can be
found in [21]. The agent based model and stochastic
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