Neurogastroenterology & Motility
Modelling ion channels
Gastrointestinal (GI) motility disorders are complex, heterogeneous, and poorly understood. Patients suffer from reduced quality of life and incur huge costs. Multi-scale computational models are important towards improving our understanding of motility, and in medical treatments.
The interstitial cells of cajal (ICC) and smooth muscle cells (SMC) present in the walls of GI organs such as the stomach and small intestine are critical in motility. There is evidence that suggests genetic mutations of ion channels in ICC and SMC are involved in the pathophysiology of GI motility disorders. However, the mechanistic link between these genetic perturbations to phenotype is still missing, and limited by experimental challenges. To address this gap requires multiple spatial scale models ranging from sub-cellular ion channels to multi-cellular constructs of ICC and SMC.
In ion channel modelling, a variety of methods were applied and investigated to develop a collection of computer models describing ion channel electrophysiology. Notably, variants of SCN5A (sodium) channels including those whose functions were altered by mutation were modelled and validated. Integrative in silico experiments using selected suitable ion channel models and higher spatial scale models suggest pathogenic potential of these genetic variants.
(Right upper figure shows a six-state Markov model that can describe SCN5A sodium channel electrophysiology. Right lower figure shows a sample of the simulated voltage-temporal plot of SCN5A channel open probability)
Poh YC, Beyder A, Strege P, Farrugia G and Buist ML. Quantification of gastrointestinal sodium channelopathy. J Theor Biol, 293:41–8, Sept 2012. (doi:10.1016/j.jtbi.2011.09.014)
Poh YC and Buist ML. A computational approach to understanding gastrointestinal motility in health and disease. Conf Proc IEEE Eng Med Biol Soc, 2011:429–32, 2011. (doi:10.1109/IEMBS.2011.6090057)
Single cell electrophysiology
We have developed the first biophysically based models of a gastric smooth muscle cell (SMC), an interstitial cell of Cajal (ICC, see figure on the upper right) as well as the first human jejunal (small intestine) smooth muscle (hJSMC) model (see figure on the lower right). These models contain a realistic description of the major ion channels that are believed to contribute to the development and propagation of the slow waves. Relevant descriptions of intracellular processes such as calcium dynamics are also included in the model. The ICC model is self-excitatory, i.e., it does not need any stimulus current, and it produces simulated slow waves at 3 cycles per minute. The SMC model predicts the volatge and calcium profiles in the cell in response to activation by a slow wave generated by a neighbouring ICC.
The equations for each of the ion channels are validated, wherever possible, against published patch clamp epxeriments performed on the specific ion channel in isolation. All the equations are then combined in a Hodgkin and Huxley-type electrical circuit where the ion channels are modelled as parallel conductances and the cell membrane as a capacitor. Further validation is performed by comparing the model predictions of whole cell voltage versus time with relevant published current clamp experiments.
Please visit our downloads section to obtain the freely available implementation code in several formats.
Poh YC, Corrias A, Cheng N. and Buist ML. A quantitative model of human jejunal smooth muscle cell electrophysiology. PLoS ONE, 7(8):e42385, Aug 2012 (doi:10.1371/journal.pone.0042385)
Corrias A and Buist ML. Quantitative cellular description of gastric slow wave activity. Am J Physiol Gastrointest Liver Physiol, 294(4):G989–G995, Apr 2008 (doi:10.1152/ajpgi.00528.2007)
Corrias A and Buist ML. A Quantitative Model of Gastric Smooth Muscle Cellular Activation. Ann Biomed Eng, 35(9):1595–1607, September 2007. (doi:10.1007/s10439-007-9324-8)
Modelling generation of active contraction
A mathematical model to study the relationship between intracellular calcium concentration and active contraction in gastric smooth muscle cells (SMC) has been developed. Motility in the gastrointestinal system is brought about by the co-ordinated contraction and relaxation pattern of the smooth muscle layers. First, contraction triggered by calcium dependent activation of Myosin Light Chain Kinase (MLCK) which is the primary mechanism has been described in terms of two interacting modules. The first module describes the activation of MLCK through its interactions with calmodulin and Ca2+. The second module describes myosin phosphorylation and cross-bridge formation between actin and myosin. Second, the role of Myosin Light Chain Phosphatase (MLCP) in the regulation of the force behavior has been studied and a hypothesis of activation of MLCP for rapid relaxation has been tested and modelled. The model has been simulated with calcium data, both measured from spontaneously active SMCs and experimentally induced and the force behaviors have been predicted and compared to experimental results. Using the primary MLCK-MLCP model, an experimentally observed phenomenon called calcium desensitization has also been studied by describing two secondary regulatory pathways – (i) enhanced activation of MLCP and (ii) down regulation of MLCK activation through its phosphorylation.
Gajendiran V and Buist ML. A quantitative description of active force generation in gastrointestinal smooth muscle. International Journal for Numerical Methods in Biomedical Engineering, 27(3):450?460, March 2011. (doi:10.1002/cnm.1419)
Whole organ models
Integration of cellular activity into whole tissue and organ models is an important step towards the implementation of a fully coupled multi-scale modelling framework. The propagation of electrical activity generated by the ICC is normally described by a set of PDE (for propagation) coupled with a set of ODE (the cell model). There are several important questions of clinical relevance that can be addressed with robust and fully validated whole organ models: how is the slow wave propagation pattern affected by a particular disease? Can the motility pattern be restored by means of electrical stimulation? Is it possible to diagnose a GI motility disorder by looking at the signals picked up non-invasively via electrogastrography?
Buist ML, Cheng LK, Sanders KM, and Pullan AJ. Multiscale modelling of human gastric electric activity: can the electrogastrogram detect functional electrical uncoupling? Exp Physiol, 91(2):383–390, Mar 2006. (doi:ol.2005.031021)
The tissue microstructure of the GI musculature is extremely complex and, unlike the cardiac counterpart, it is made up of at least two distinct cell types: smooth muscle cells and interstitial cells of Cajal. For this reason, our group recently proposed an extension to the classical mono/bidomain framework in order to incorporate multiple cell types into tissue and whole organ models (see Figure on the right). In suche framework, the functional unit in which the geometry is discretised is made up of two distinct cell types (ICC and SMC in this case) in communication with each other via gap junction. Each of the cell types have a different set of ionic conductances.
Large scale models tend to be computationally demanding. We make use of state-of-the-art parallel computing software to solve the equations of propagation coupled with cellular activities at a small scale.
Corrias A, Pathmanathan P, Gavaghan D and Buist ML. Modelling tissue electrophysiology with multiple cell types: applications of the extended bidomain framework. Integr Biol (Camb), 4(2):192–201, Feb 2012. (doi:10.1039/c2ib00100d)
Buist ML and Poh YC. An extended bidomain framework incorporating multiple cell types. Biophysical journal, 99 (1):13–8, July 7 2010. (doi: 10.1016/j.bpj.2010.03.054)
Buist ML, Corrias A, and Poh YC. A model of slow wave propagation and entrainment along the stomach. Ann Biomed Eng, 38(9):3022–3030, 2010. (doi:10.1007/s10439-010-0051-1)
Nonlinear viscoelasticity of GI tissues
The mechanical properties of GI tissues exhibited a characteristically nonlinear viscoelastic behaviour. A speicific model was created to capture the unique mechanical properties.
Chung CW and Buist ML. A novel nonlinear viscoelastic solid model. Nonlinear Analysis: Real World Applications, 13:1480–1488, June 2012. (doi:10.1016/j.nonrwa.2011.11.011)