Research Project from the ICREA/Complex Systems Lab, Universitat Pompeu Fabra-GRIB



Main Researchers: Ricard V. Solé, , Carlos Rodriguez-Caso, & Sergi Valverde

Cancer is an example of a complex, robust system. To a large extent, the plasticity and adaptability exhibited by tumors stems from their high diversity resulting from internal instabilities. We are exploring the role of genetic instability in tumor progression at different scales. Our research in this area involves the development of both mathematical and computer models of unstable tumors and the impact of increasing levels of instability in cancer progression. Part of this research is done within the recent NIH INTEGRATIVE CANCER BIOLOGY .

The goal of this initiative is to promote the analysis of cancer as a complex biological system, with the ultimate goal of developing reliably predictive computational models of various cancer processes, facilitating the development of cancer interventions. This will be achieved through the integration of experimental and computational approaches towards the understanding of cancer biology. This initiative will encourage the emergence of integrative cancer biology as a distinct field by establishing research programs in integrative cancer biology, which bring together cancer biologists and scientists from fields such as mathematics, physics, information technology, imaging sciences, and computer science to work on a common cancer biology problem.

1/1/2005    Start of Modelling Cancer Instability project, funded under NIH Integrative Cancer Biology Program

24/3/2005    NIH Integrative Cancer Biology Meeting, Boston, USA.




Order and disorder in cancer

Cancer is the result of a system's breakdown that arises in a cell society when a single cell (due to a mutation or set of mutations) starts to display uncontrolled growth \cite{Andersson}. The cooperation that maintains the integrity of a multicelular organism is thus disrupted. Further changes in the population generated by such abnormal cell can lead to malignant tumor growth, eventually killing the host. From an evolutionary point of view, tumor progression is a microevolution process in which tumors must overcome selection barriers imposed by the organism.

Left: the P53 network: by drawing the links connecting different proteins related to the tumor supressor gene p53, a network of complex relations is obtained, strongly suggestive of an electronic design. P53 is actually highly connected to many others, given its key role in maintaining genome integrity. Right: a picture of cancer cells with mutated p53.

A multicellular system is a society whose individual members are cells, reproduced in a collaborative way and organized into tissues. In this sense, understanding it requires concepts that are well-known in population dynamics, such as birth, death, habitat and the maintenance of population sizes. Under normal conditions, there is no need to worry about selection and mutation: As opposed to the survival of the fittest, the cell society involves cooperation and, when needed, the death of its individual units. Mutations occur all the time but sophisticated mechanisms are employed in detecting them and either repairing the damage or triggering the death of the cell displaying mutations. Abnormal cells can be indentified from within (i.e. through molecular signaling mechanisms operating inside the damaged cell) or by means of interactions with other cells. The first is strongly tied to the network of molecular interactions, whereas the later involves cellular immune responses.

The understanding of how cancer emerges and develops requires a system's view of the whole, since multiple links relate genes directly or indirectly associated to tumor development. In this context, cancer is an example of a broader class of complex systems (see for example: Kitano, H. Cancer as a robust system: implications for anticancer therapy. Nature Reviews Cancer. 4, 3, 227-235, 2004. A better understanding of how cancer develops requires the study of tumors as spatially distributed, adaptive systems but also understanding the topological patterns of gene-gene interactions inside cancer cells. Uncovering the origins of cancer robustness will help developing new treatments and provide powerful insight into future experimental approaches.



Cancer quasispecies: mathematical models of unstable tumor dynamics

Selection barriers (such as the attack from the immune system or physical barriers of different types) can be overcome by a tumor provided that the diversity of mutant cells is high enough to generate a successful strain. High mutation rates are thus a way to escape from the host responses and it is actually known that most human cancers are genetically unstable. Genetic instability results from mutations in genes that are implicated in DNA repair or in maintaining the integrity of chromosomes. As a result, mutations accumulate at very high rates. RNA viruses are actually a good example of replicating systems involving mutation and it was early shown that such systems involve an error threshold: beyond a critical mutation rate, a phase transition occurs towards a random replication phase. At the subcritical, low-mutation phase, the population is able to maintain hereditary information and a heterogeneous distribution of molecules is observed: the so-called quasispecies. At the supercritical phase, populations experience random drift through sequence space and no genetic information can be maintained.

Left: tumor cells have to face a number of selective barriers, including the attack of the immune system (here T cells attack a cancer cell). Right: Predicted domains of tumor growth dynamics from the mathematical model of cancer quasispecies. Here the instability level (horizontal axis) and the competitive advantage (vertical) of the unstable population are used as parameters. A critical line exists separating a phase of rapid growth (blue) from a phase of slow growth (black). The transition is sharp and involves a threshold phenomenon in the allowed instability levels compatible with cancer progression.

An important implication of the previous observation is that the threshold-like character of the phase transition allows to conjecture that non-viable virus populations might be obtained by slightly increasing the mutation rate beyond criticality. This has been done in vitro and in vivo therapies are in progress. A similar scenario has been suggested within the context of cancer. Since cancer also displays some common traits with RNA viruses it has been suggested that unstable cancer populations might also display threshold levels of mutation parallel to those observed in viral populations (Solé, 2003; Solé and Deisboeck, 2004). If true, strategies based on targeting unstable cancer cells and increasing their mutation rate would successfully inhibit tumor progression.

See our related papers:

Phase transitions in unstable cancer cell populations, R.V Solé, European Phys. J. B. 35 (2003) 117-124
An error catastrophe in cancer?. R. V. Solé and T.Deisboeck, J. Theor. Biol., 228 (2004) 47-54 .



Evolving unstable tumors with stochastic cellular automata models

Tumor progression is a coevolution process in which cancer population responses are modulated by the host response. In this sense, further work should consider this host-tumor interaction, which eventually might tune mutation and replication rates, as it seems to be the case with RNA viruses. The previous models are an oversimplified picture of cancer cells populations. Even for RNA viruses the assumption of a single-peak fitness function is a very strong one, and experimental evidence shows that the structure of the landscape is case-dependent. Tumor population would actually evolve through adaptive walks. Additionally, the previous analysis was performed under the assumption of stationarity, i. e. a maximum cell population size is allowed and competition takes place under this population constraint. Real tumors are nonequilibrium systems and as such are growing structures. Besides, spatial degrees of freedom seem to be relevant in maintaining and propagating genetic heterogeneity in such a way that competition among different clones is effectively reduced under the local character of cell-cell interactions.

Left: An example of the three-dimensional structure of a small unstable tumor as evolved from our in silico simulation model (the CANCERLAB package being currently developed at the CSL). Areas with different colors correspond to cells with different levels of instability. The right picture shows a tumor spheroid from a scanning electron micrograph .

See our related papers:

Metapopulation Dynamics and Spatial Heterogeneity in Cancer,
I. González-Garcia, R. V. Solé and J. Costa, Procs. Natl. Acad. Sci. USA 99 (2002) 13085-13089

Spatial Dynamics in Cancer,
Ricard V. Solé, Isabel González-García and Josep Costa In: Complex Systems in Biomedicine, Deisboeck et al., eds. Kluwer., pp.557-572