Suicide is painless, it brings on many changes...

Cell suicide does indeed bring on many changes, but it's far from painless, or at least modelling it is. To get an example of just what's involved, I'd recommend having a look at the wonderfully well written paper by Cho et al. The authors use first order ordinary differential equations (ODEs) to show how the protein TNFa (Tumour Necrosis Factor-alpha) triggers a sequence of protein interactions that lead to the release of NFkb (Nuclear Factor-kappa-beta), a bound group of proteins heavily involved the response of the immune system. NFkb activity is closely associated, for example, with inflammation and cell termination (known as apoptosis).

The pathway is written as a series of chemical reactions where each reaction is catalysed by an enzyme. These reactions can be described using the law of mass action, which says that the rate of a reaction is proportional to the product of the concentration of the reactants. In a chain of reactions, the products of each reaction combine with other reactants to fuel further reactions and the behaviour of the whole chain is heavily dependent on the reaction rate constants. If they're too mismatched the pathway can swell with proteins in the middle or be starved of fuel. This picture is complicated by the recycling of the enzymes and the reverse reactions which accompany only part of the catalysis process.

What makes this sort of modelling challenging is that so few of the rate constants are known. To quote Cho et al., "The exact value of parameters, such as the concentration of each signaling protein, the rate constants for the generation and degradation, etc., are difficult to obtain because their numerical values not only depends on the species and tissue, but also on the physiological state of the cells/organism." So the rate constants used are just educated guesses. Nonetheless, Cho et al. show that by adding a dollop of TNFa to the pathway, it leads to a surge in the amount of NFKB produced.

The two plots shown are taken from their paper. The first shows the dose of TNFa (pure dashed line) at time zero and the second shows the NFKB response (pure solid line), which gets into its stride at about 50 seconds. It is clear from their results that TNFa plays an powerful role in triggering the immune response.

Reference
Cho, K. (2003). Investigations Into the Analysis and Modeling of the TNFÂ -Mediated NF-Â B-Signaling Pathway. Genome Research, 13(11), 2413-2422. DOI: 10.1101/gr.1195703

I am a model, you know what I mean (and I do my little turn on the catwork)

I recently started a project to model certain signalling pathways in our favourite macrophage cell and it's been an eye-opening experience. Once its complete, we will learn volumes about the role of cholesterol in the immune system. But at this stage, just working out the angles has been fascinating. The challenges don't come from the directions you might think.

At first, I thought they'd be computational. People have been modelling pathways for years, so I reasoned that all the straight forward work must have been done. In established fields, the new challenges come from the projects that push computing power to its limit, so I assumed that ours must have been computationally complex. But it turns out that this isn't the case. Few trusted models of signalling pathways exist and those that do are quite simple, so they are pretty straight forward to simulate.

If the challenges weren't computational, then I thought they might surround model validity. A living cell is a complex beast. So much is happening inside that to isolate one pathway, without including any others, is a risky business. Doing so might invalidate the results of the model. Well, in some cases this might be true, but the real problems occur before we get a chance to see.

The true obstacles aren't computation or simplification, they're come from something much more old-fashioned. People.

When you dig into the papers, you find that genes and proteins have been given a bunch of different names by different research groups and each name can have a bunch of different abbreviations. This makes them hard to cross reference. The papers aren't stored in any single central database, but across many databases and they aren't catalogued or indexed in a friendly way. This makes them hard to find. The papers rarely systematically explore pathways, so the proteins they describe tend to freely appear and disappear as they are needed. This makes their behaviour hard to describe.

Combined, these problems make modelling hard and it takes a strong will and plenty of sweat to pull a model out of the mire. For this reason alone, pathway modellers have gone up in my estimation. They've earned my respect.

Ground control to Major Tom.

In the last post, I mentioned that I work on exploring the complex network of interactions between genes, proteins and microRNAs that mediate a cells response to its environment. This field is known as cell signalling and the possible routes through the network are signalling pathways.

To give you an example of how a typical pathway might work, suppose a cell is attacked by a virus. The virus might emit a protein that the cell, over millions of years of evolution, has learned to recognize as indicative of that threat. In this case, it will have evolved so that the viral protein binds to another protein on the cell surface, triggering a cascade of protein-protein and protein-gene interactions within the cell. The triggering happens because the binding causes a third protein to detach from the interior of the cell surface, which then floats off into the cell interior. Along the way it interacts with many other proteins in a huge variety of ways. For example, it might bind to another protein in such a way that causes the bound pair migrate towards the cell nucleus, before binding to a third protein that allows the bound state to pass into the nucleus. Once there, the three bound proteins could separate and one could then bind to a different protein, causing the travelling protein to change its configuration. After the change, the reconfigured protein might detach itself and bind to a gene, instigating the manufacture of a new protein. Perhaps the new protein binds to another gene, triggering the production of another new protein and, as the last link in the chain, this protein could be shuttled to the cell surface in order to help with the fight against the virus.

Whilst this is a wildy hypothetical example, its also wildy over simple. Real pathways are much more complicated. The reality is that they contain ten times to a hundred times more proteins and genes and exploit feedback to create complex patterns of signals. Studying these signals is complicated further by the dramatic interweaving between different pathways. Cell's don't conveniently mediate their signals with a set of distinct pathways, insulated from each other. The various pathways have a significant overlap and for a given triggering protein, there will be many stimulated pathways.

All this makes it damn hard to study what's going on in a cell. At the outset, you have no clue about how the network or pathways works and its only through expensive and time consuming experiments that this picture can be put together, literally one link at a time. The whole process is like trying to assemble a 10,000 piece jigsaw with no picture on the box.

But despite the overwhelming scale of the challenge, we persevere because there is the potential to exploit the pathway structures to develop extraordinary medical therapies. By understanding these tapestries of pathways, we can learn how to correct the malfunctions cause disease. This will lead us to better designed treatments that have a maximised impact on the ailment with a minimised number of side effects. Viva la revolution!

If you'd like to read more about cell signalling, here's a good review in Nature.