Systems Biology Hierarchical Modelling


in a Cardiovascular Context



The content of my previous site is transferred on this site.





     Hierarchical or Multiscale modelling is currently extensively developed in a specific scientific discipline, Cardiovascular Science. Therefore, this scientific context serves in this site as a paradigm for the illustration of the approach. Some elements of Cardiovascular Physiology are given below.






      The human organism in order to maintain itself needs nutrient fuels that will be consumed in its internal combustion engine using oxygen. The equivalent of the combustion engine are the different cells in our entire body. Both nutrients and oxygen have to be delivered in all cells. The organism accommodates this need by using a set of “pipes”, the vessels, and a liquid medium, the bloodstream. It also needs a “pump” to set the liquid medium in motion and to keep it circulating. This is the role of the heart; it acts as a pump that facilitates delivery of nutrients and oxygen to all cells.

     The heart pump has to propel the liquid medium carrying nutrients and oxygen. After it receives a volume of blood that fills it entirely, it contracts and thereby it moves the blood forward. Subsequently, it relaxes and is filled again with blood. The contraction and relaxation is accompanied by sound and constitutes the heartbeat. The continuous contraction and relaxation of the heart ensures proper blood circulation.

     Teleologically speaking, that is if we were to accept that causes, design, and purpose (greek "telos" *) exist in nature, what mechanism has nature designed to mediate contraction of the heart muscle and, in particular, coordinated contraction of all heart cells that compose the organ? First, to generate contraction, muscle cells are equipped with special contractile apparatuses, the sarcomeres, composed of thick (myosin) and thin (actin) filaments (Figure 1). The latter are made to contract when they bind a specific substance, calcium. Therefore, when calcium is increased in the muscle cell, sarcomeres will contract. In order to mediate the repetitive contraction and relaxation of the heart muscle, nature had to devise a mechanism to increase and subsequently decrease the concentration of calcium inside the cell in a repetitive manner. 



Figure 1Contractile apparatuses (sarcomeres) in relaxed and contracted positions. Sarcomeres are comprosed primarily of myosin (red) and actin (blue) filaments (image from wikipedia).

Image author: Richfield, David. "Medical gallery of David Richfield 2014". Wikiversity Journal of Medicine 1 (2). DOI:10.15347/wjm/2014.009. ISSN 2001-8762. - Licensed under CC BY-SA 3.0 via Commons -



     On the surface of the cell membrane there is a calcium channel, which can mediate calcium influx from the extracellular space, if activated. Again, nature had to devise a mechanism for repetitive activation and deactivation of the calcium channel. For this purpose, it attributed a specific functional feature to this channel: this opens when the voltage of the membrane is approximately -20mV. The voltage value of the cardiomyocyte membrane at rest is about -80mV, with the inside «being more negative » than the outside. Another feature of the calcium channel is that it closes very quickly after calcium has been increased in the cell.

     Now, only a mechanism that changes the voltage of the membrane in a repetitive manner had to be discovered. To this purpose, a group of cells that generate electricity were « placed » in the heart. These cells, which are called "pacemaker cells" (as they set the pace), create electric signals that travel in the entire heart. When this signal arrives on the membrane of a heart cell, it induces the opening of another type of channel, the sodium channel. As a result, sodium ions, which are positively charged, enter massively from the extracellular space inside the cell and increase the voltage (from its initial value of -80mV). As mentioned, when the voltage increases to -20mV, the calcium channels will be activated and will mediate calcium influx that will activate the sarcomeres and the contraction of the muscle cell. Shortly afterwards, othen channels or pumps will extrude the ions that entered the cell and will normalize the voltage of the cell membrane. In this way, the cell is ready for the next arrival of the electric signal, that will repeat the procedure.

     In the above simplifying description only two currents were mentioned, a sodium current and a calcium current. However, many other currents have been identified, each with its own characteristics e.g. voltage of activation, duration of activation, amount of ions transported etc. In order to analyse simultaneously all these currents, only a computational approach can be followed. This is the aim of electrophysiology, which uses computational modelling in order to represent these events.

     Once this fundamental mechanism has been successfully represented computationally, it is possible to add additional cellular mechanisms, e.g. how the modelled ion currents are translated to cardiomyocyte contraction, or how nutrients are used to generate energy to support these processes. In this way, we can represent and simulate the behaviour of the cell as a whole. Then, it is possible to combine the behaviour of cells and extracellular components, in order to model the behaviour of the tissue. We can further proceed to modelling the whole organ and obtain a simulation of heart function. Finally, it is possible to add adjacent organs and create a computational model of an organic system. This hierarchical modelling approach and relevant modelling standards that have been generated to implement it are described in this site.




     Hierarchical or Multiscale modelling aims in representing in a unified manner different scales of biological organization, from molecule, to cell, tissue, organ and organic system. For instance:

     From modelling a molecule,

     e.g. the sodium or the calcium channel;

     to cardiomyocyte modelling;

     how electricity arrives on the cardiomyocytes, how it activates different channels and how ion currents are created (e.g. calcium current), how currents move contractile units to generate movement, how the cardiomyocyte processes nutrients it receives to generate energy to support these processes, which ultimately produce movement, and how different signal transduction pathways orchestrate its response to different stresses;

     to tissue modelling; 

     if we have figured out how electric signals are propagated in a cardiomyocyte, can we predict how they are transferred in a tissue which is composed of these cells in different arrangements and of different materials e.g. glue-like materials like collagen?

     Can we predict how the whole tissue will move by changing its form?


     to organ modelling;

     if we know how tissue bits behave can we put them in place following the example of a builder who places small pieces on a scaffold or a sculptor who places these on a mould in different orientations in order to create a heart? If we combine them successfully, will we be able to predict the function of the heart?


     to organic system modelling;

     Can we try to integrate adjacent organs and create an organic system?       

     Towards this direction “ the torso model” has been proposed.



     The Physiome Project was initiated by Denis Noble and Jim Bassingthwaighte of the International Union of Physiological Sciences (IUPS). The Heart Physiome Project represents the most developed part of the Physiome Project at this point. It can be accessed at the following link: (for referenceHunter, P. J. and T. K. Borg (2003) Nat Rev Mol Cell Biol 4(3): 237-243Hunter, P. J., E. J. Crampin, et al. (2008) Brief Bioinform 9(4): 333-343).

     The Heart Physiome Project aims in the representation of the heart as a physiological entity composed of different levels of biological organization, of spatial and temporal nature. It addresses different spatial scales i.e. molecule, biomacromolecule, cell, tissue, organ and organic system and different temporal scales i.e. μs time interval required for molecular interactions to human lifespan. To this aim, it works in the direction of multiscale modelling, as it will be described further below.

     The heart is an organ comprised primarily of cardiac muscle cells and which produces electrical activity, transmits it throughout its entity and generates contraction. Electrical activity arriving at the cardiomyocyte membrane mediates the «electrical» activation of the cardiomyocyte. The first in a series of events is the activation of the sodium channel which is responsible for the extremely rapid voltage change of the cardiac muscle cell membrane. This voltage change will activate the calcium channel which will increase the calcium concentration of the cell, which in its turn will switch on the cardiomyocyte contractile apparatus to generate contraction. Finally, the potassium channel will amend the changed voltage and will return the cell to its resting state.

     The series of ion channel activation in the heart has been studied and modelled extensively in the electrophysiology field initially by Denis Noble (Oxford University) who was inspired by the Hodgin-Huxley nerve model. Additionally, individual molecular channel models of the Hodgin-Huxley model type exist. These molecular models constitute the first degree/element in the spatial hierarchy mentioned above and are to be incorporated in the electrophysiology cellular models.






     In order to model biological processes at the cellular level, markup languages based on the XML world wide web language, have been developed, e.g. SBML or CellML. These standards allow for a representation of biological function in a set of ordinary differential equations (ODEs). The Heart Physiome Project is using the CellML standard.

     The SBML standard is described at

     The CellML standard is described at

     In order to model tissue processes, which are influenced by the spatial variations of the tissue, a different standard has been developed, FieldML which uses partial differential equations (PDEs).

     The FieldML standard is described at

* telos (greek) = purpose, end. E.g. "To this end" = For this purpose


Hunter, P. J. and T. K. Borg (2003). "Integration from proteins to organs: the Physiome Project." Nat Rev Mol Cell Biol 4(3): 237-243.
Hunter, P. J., E. J. Crampin, et al. (2008). "Bioinformatics, multiscale modeling and the IUPS Physiome Project." Brief Bioinform 9(4): 333-343.


     The images of the main figure of the site, from left to right, have been taken from the following sources: link to 1st image2nd image (presentation slide 30)3rd image4th image

     The first from the left image could represent a traditional “pencil and paper” first draft of an otherwise computationally intensive discipline. The second image represents a tissue section (with numbered cells) which is a very common task/technique in many biological labs. Although the reconstruction of a tissue block by joining individual sections is an automated task with today’s microscopes, coding of spatial information is a technique performed by specialists; a step of this process is demonstrated in the third image. Processing of spatial information with sophisticated computational techniques results in representations that resemble an art form, as demonstrated in the fourth image.