RNA viruses at the edge of chaos

Viruses and viroids are the simpler forms of replicating structures inhabiting our biosphere. They are known as the most important intracellular parasites, using genetic information from their hosts in order to replicate themselves. They can only reproduce by invading and controlling other cells as they lack the cellular machinery for self-reproduction. The term virus usually refers to those particles that infect eukaryotes, whilst the term bacteriophage or phage is used to describe those infecting prokaryotes.

We study different aspects of virus complexity, including theoretical models of evolution and coevolution, computer viruses and general models of parasite evolution. In collaboration with Santiago Elena's Lab in Valencia, we are using well-defined experimental systems (mainly viroids infecting plants) together mathematical and computer models looking for understanding of how viruses explore their worlds. Among other questions, we want to know what is the structure of their fitness landscapes, how they cope with their complexity and how they might have originated and perhaps, canalized the evolution of biological complexity. 



 Our interest in viruses is also motivated by a lack of understanding of the nature and definition of life. Viruses place themselves on the boundaries of living systems,  and can be understood as programs. However, the discovery of giant viruses carrying large genomes and defining a complex life cycle casts some doubts about the correctness of the previous statement. New models need to be developed in order to address the coevolution of viruses and their hosts and in particular the role played by genome size, instability, coevolutionary responses and the genotype-phenotype mapping.


Variability in mutational fitness effects prevents full lethal transitions in large quasispecies populations. J. Sardanyés, C. Simó, R. Martínez, R. V. Solé, Santiago F. Elena. Nature Scientific Reports 4 (2014) 4625

Viral RNA replication modes: evolutionary and dynamical implications. J. Sardanyés. Trends in Mathematics 2 (2014) 115-119

Simple genomes, complex interactions: Epistais in RNA virus  S. F. Elena, R. V. Solé, J. Sardanyés. Chaos 20 (2010) 026106

Tempo and mode of plant RNA virus escape from RNA interference-mediated resistance. G. Lafforgue, F. Martínez, J. Sardanyés, et al. J. Virol. 85 (2011) 9686-9695

Replication mode and landscape topology differentially affect RNA virus mutational load and robustness. J. Sardanyés, R. V. Solé, S.F. Elena. J. Virol. 83 (2009) 12579 - 89

Simple quasispecies models for the survival-of-the-flattest effects: the role of space. J. Sardanyés, S. F. Elena, R.V. Solé. J. Theor. Biol. 250 (2008) 560-568

Information catastrophe in RNA virus through replication thresholds. R. V. Solé, J. Sardanyés, J. Díez, A. Mas. J. Theor. Biol. 240 (2006) 353-359

The fittest versus the flattest: Experimental confirmation of the quasispecies effect with subviral pathogens. F. Codoñer, Daròs, J-A., Ricard V. Solé, S. F. Elena. Plos Pathogens 2(12), e136

Field theory for a reaction-diffusion model of quasispecies dynamics. R. Pastor-Satorras, R. V. Solé. Phys. Rev. E 64(5), 051909

Red Queen Dynamics, Competition and Critical Points in a Model of RNA Virus Quasispecies. R. V. Solé, R. Ferrer, I. González-García, J. Quer, E. Domingo. Journal of Theoretical Biology 198(1), 47-59 


Unstable cancer dynamics

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. The cooperation that maintains the integrity of a multicellular 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.

The fight against cancer has been of limited success. It is true that a number of cancers can get cured and that major advances have happened over the last 50 years in our understanding of timor progression and its origins. But the frequency of non cured tumours remains the same after all this years. Using evolutionary arguments, theoreticians have been arguing in the last decades that perhaps a new way of looking at the whole problem is needed. A new way that takes into account the Darwinian, ecological nature of the disease.

In our Lab we have been studying one particularly important aspect of cancer, namely its enormous levels of genomic instability, which are easily observable in most advanced tumours, particularly at the level of chromosomes, which appear duplicated, lost or broken in apparently disorganised patterns. Despite such degree of aneuploidy, cancer populations are capable of adapting and eventually expanding, killing the host. Are there limits to such degree of instability? How can we model this phenomenon? Since it has been shown that thresholds to cancer viability are indeed present, we have been proposing that therapeutic approaches might consider this aspect of cancer dynamics as a potential advantage.


Can a minimal replicating construct be identified as the embodiment of cancer?  R Solé,S.Valverde,C.Rodriguez-Caso and J. Sardanyés. Bioessays 38 (2014) 503-512

Catastrophic shifts and lethal thresholds in a propagating front model of unstable cancer progression. D. Rodriguez Amor and R. Solé, Phys Rev. E 90, 022710

Accelerated tumor invasion under non-isotropic cell dispersal in glioblastomas. J. Fort and R Solé. New J. Phys. 15 (2013) 055001

Phase transitions in cancer.R. Solé. In: New Challenges for Cancer Biomedicine. Springer (2012) pp.35-51.

Cancer stem cells as the engine of unstable tumour progression. R Sole, C Rodriguez-Caso, TS Deisboeck, J Saldanya. J. Theor. Biol. 253 (2008) 629-673.

An error catastrophe in cancer? R Solé and T Deisboeck. J. Theor. Biol. 228 (2004) 47-54

Phase transitions in unstable cancer cell populations. R Solé. Europ. J. Phys. 35 (2003) 117-123.

Metapopulation dynamics and spatial heterogeneity in cancer. I Gonzalez-Garcia, R Sole and J. Costa. PNAS 99 (2002) 13085-13089.