Most phenomena studied by the Natural Sciences, from Material Sciences to Astrophysics, are multi-scale processes, i.e. they involve the coupling of multiple different processes characterised by widely-ranging time and length scales, with the macroscopic behaviour emerging from the complex interactions between them. Whilst considerable progress has been done in dealing with such problems in the Physical Sciences, the success achieved so far in the Biological Sciences is rather more limited. This is partly due to the fact that the individual components of biological systems (e.g. cells) are much more complex than their counterparts in physical systems and, therefore, new methods and models are needed to analyse multi-scale processes in Biology. Such is the remit of the Computational & Mathematical Biology group at CRM: To propose new models relevant to experimental biologists and clinicians and develop the analytical and computational tools necessary for their analysis. We pay special attention to problems with clinical relevance, in particular those related to cancer.

The research activity of our group is developed along the following lines:

• Multiscale modelling of tumour growth and tumour-induced angiogenesis
• Evolutionary dynamics of populations with complex structure, in particular cell populations with hierarchical structure and genotype-phenotype map
• Mathematical modelling of the cell-cycle
• Stochastic modelling of receptor tyrosine kinases
• Tumour dormancy

Our group is focused in understanding the mathematical bases of evolution.

The main question we want to address is: how did complex organisms arise in evolution? Or more in general, how can complexity evolve also in other systems like culture, society and molecular pre-biotic systems. In the case of multicellular organisms, such as us, this main question translates into three other questions that we want to address:

1. How does a fertilized egg cell transforms into a complex adult organism? This is a complex functional organism characterized by many cells, cell types and a specific distribution of those in space. Can we understand the mathematics of such a dramatic pattern formation process?
2. How did this complexity arose by a gradual process of evolution by natural selection. This implies explaining also the evolution of the development that produces such complexity in each generation.
3. Are there some logical or mathematical requirements or principles that gene networks need to fulfill in order to be able to produce complex morphologies during development? If so, can we approach question 1 and 2 above from understanding these principles?
   Understanding question 1 is highly non-trivial: something very complex, our body, is produced from something much simpler and small, a simple cell, in a relatively short time.

This process can not be understood by looking at single genes. Embryonic development involves the interaction between huge numbers of genes and cells. Thus, for example, to understand which morphological changes will occur from specific mutations in a gene, we need to understand how that gene is embedded in a gene network and how that affects the dynamics of signaling and mechanical interactions between cells and tissues. In other words, we have a huge number of heavily interacting elements at different levels (e.g. genes, cells, tissues) that lead to the arising and variation of a macroscopic pattern, the body’s.

To address question 1 we build multi-scale models of embryonic development. Each such models includes a set of differential equations describing how genes regulate each other’s expression and a set of differential equations describing how cells move, change shape and activate cell behaviors (cell growth, cell contraction, cell division, etc…). Each cell contains the same set of genes and equations, but, as a result of model dynamics, different cells end up expressing genes at different intensities. Genes affect the mechanical properties and behaviors of the cells in which they are expressed. As a result, cells move and rearrange themselves in space and, in their turn, affect back gene expression by differentially affecting, through cell-cell signaling, where genes get expressed. The models are, essentially, reaction-diffusion models in which the shape of the compartment in which diffusion is taking place, the embryo, is changing over time as a consequence of the reactions, i.e. gene regulation, affecting cell movement. Through specific gene networks, initial conditions and regulation of cell behaviors and mechanical properties by gene products, we simulate how the morphology of adult organs develops. In other words, the model reproduces the position in 3D space and the gene expression in each cell in the adult and how that has changed over development. We do that for specific organs in collaboration with experimentalists (e.g. teeth (Salazar-Ciudad and Jernvall, 2002, 2010; Salazar-Ciudad 2008, 2012; Järvinen et al., 2006; Harjunmaa et al., 2014; Renvoise et al., 2017), fly wings (Ray et al., 2015), turtle carapaces (Moustakas-Verho, 2014) among others) but also for the ensemble of animal development (Salazar-Ciudad, 2000, 2001a, 2001b, Marin-Riera et al., 2016).

For question 2 we take two different approaches. In a populational one we combine the models of development we build for question 1 with models of mutation, natural selection and genetic drift in populations. In a way we put together the mathematical apparatus of populational genetics with that of the multiscale models of embryonic development. This way we simulate how complex morphologies arise in evolution. In the ensemble approach we build a huge number of random networks and check which ones are able to produce complex morphologies.

From both approaches we want to understand how phenotypes and development evolve and, also, if there are some logical or mathematical requirements that gene networks need to fulfill in order to be able to produce complex morphologies during development. If that would be the case, as we think it is, the study of development and evolution would be greatly simplified. The evolution of development could then be understood, as we attempt, by looking at the networks fulfilling these requirements and exploring how likely they arise from random mutation, or how likely one can be transformed into another, as compared with the adaptive value of the morphologies they produce (Salazar-Ciudad et al., 2001a, Salazar-Ciudad 2010). This will entitle us with building a general theory of how development works, and most importantly, of how it evolves.

In parallel we also explore how our evolution and development approach can be applied to evolution in culture (Salazar-Ciudad, 2010c) and in the origins of life (Salazar-Ciudad 2008b, 2013b). In these approaches development is just replaced by the processes that lead to phenotypic variation.

Part of our research also involves discussing how the insights acquired from our models modify several aspects of evolutionary theory such as developmental constraints (Salazar-Ciudad, 2006), canalization (Salazar-Ciudad, 2007), robustness (Salazar-Ciudad, 2007), novelty (Salazar-Ciudad, 2006b) or just evolutionary theory in general (Salazar-Ciudad, 2008).

In addition, we also have data-mining approaches in what we call statistical developmental biology. This is the combined analysis of massive transcriptomic and genomic databases to  quantitatively test several long-held hypothesis on the evolution of development, this goes from an explicit measurement of how complexity increases over development and anatomy (Salvador-Martinez and Salazar-Ciudad, 2015, 2017) to an estimation of a map of acting selection over the body of the fly (Salvador-Martinez et al., 2018).

We added an image, an example of a developmental mechanism with a gene network combining different cell behaviours implemented in EmbryoMaker. The left diagram show the gene network. The boxes indicate specific cell behaviours or cell mechanical properties regulated by specific genes in the network.  a) Initial conditions, hollow spheric epithelium with a single cell (yellow) expressing gene TF1. B) Outcome, after a number of iterations, of the complex developmental mechanism applied on the initial conditions in A. The left column shows, in section, the node types. Blue for basal side of cylinders, violet for the apical side of cylinders, red for mesenchymal cells and orange for extracellular matrix nodes. Middle and right column display concentrations of GF2 and TF5 respectively (yellow for high concentration, blue for low concentration).

Our laboratory is interested in understanding biological nonlinear phenomena. Our research is focused on Biomedicine (including cancer and viruses), in systems and synthetic Biology as well as in theoretical ecology. To do so we use the qualitative theory of dynamical systems and computer simulations (stochastic dynamics and spatially-extended systems).

We are especially interested in characterizing both asymptotic and transient dynamics of these systems and their sensitivity to parameter changes. That is, understand which bifurcations govern transitions in biological systems.

Publications from the last 5 years

D.Stepanova, H.M. Byrne, P.K. Maini, T. Alarcon. A multiscale model of complex endothelial cell dynamics in early angiogenesis. Posted in bioRxiv.

M.O. Bernabeu, J. Kory, J.A. Grogan, B. Markelc, A. Beardo-Ricol, M. d’Avezac, J. Kaeppler, N. Daly, J. Hetherington, T. Krueger, P.K. Maini, J.M. Pitt-Francis, R.J. Muschel, T. Alarcon, H.M. Byrne. Abnormal morphology biases haematocrit distribution in tumour vasculature and contributes to heterogeneity in tissue oxygenation. Posted in bioRxiv.

A.I. Rodriguez-Villarreal, L. Ortega-Tana, J. Cid, A. Hernendez-Machado, T. Alarcon, P. Miribel-Catala, J. Colomer-Farrarons. An integrated detection method for flow viscosity measurements in microdevices. IEEE Transactions on Biomedical Engineering. Accepted for publication (2020).

E. Cuyas, S. Verdura, B. Martin-Castillo, T. Alarcon, R. Lupu, J. Bosch-Barrera, J.A. Menendez. Tumor-cell-intrinsic immunometabolism and precision nutrition in cancer immunotherapy. 12, 1757 (2020). doi: 10.3390/cancers12071757

E. Cuyas, J. Gumizio, S. Verdura, J. Brunet, J. Bosch-Barrera, B. Martin-Castillo, T. Alarcon, J.A. Encinar, A. Martin, and J.A. Menendez. The LSD1 inhibitor iadademstat (ORY-1001) targets SOX2-driven breast cancer stem cells: A potential epigenetic therapy in luminal-B and HER2-positive breast cancer subtypes. Aging.  12, 4794-4814 (2020). doi: 10.18632/aging.102887

R.A. Barrio, T. Alarcon, A. Hernandez-Machado. The dynamics of shapes of vesicle membranes with time dependent spontaneous curvature. PLoS One. 15, e0227562 (2020). doi: 10.1371/journal.pone.0227562

J.A. Menendez, E. Cuyas, N. Folguera-Blasco, S. Verdura, B. Martin-Castillo, T. Alarcon. In silico clinical trials for anti-aging therapies. Aging. 11, 6591-6601 (2019). doi: 10.18632/aging.102180

A.V. Ponce-Bobadilla, T. Carraro, H.M. Byrne, P.K. Maini, T. Alarcon. Age-structure can account for delayed logistic proliferation of scratch assays. Bull. Math. Biol. 81, 2706-2724 (2019). Preprint version available from bioRxiv

Vidiella B, Valverde S, Fontich E, Sardanyés J, Transients in simple trophic chains with facilitation: the impact of habitat destruction. Theoretical Ecology (submitted)

Sardanyés J, Raich C, Alarcón T. Noise-induced stabilization of saddle-node ghosts. Physical Review E (submitted)

Solé R, Sardanyés J, Elena SF, Phase transitions in Virology. Virus Evolution (submitted)

Zaldo Q, Serra I, Alsedà Ll, Sardanyés J, Maneja R, Reviewing the reliability of Land Use and Land Cover Data in studies relating human health to the environment. Land Use Policy (submitted)

Vidiella B, Sardanyés J, Solé R, Synthetic soil crusts against green-desert transitions: a spatial model. Royal Society Open Science​ (submitted)

Penella C, Alarcón T, Sardanyés J, Spatio-temporal dynamics of cancer phenotypic quasispecies under targeted therapy. Proceedings of the 9th International Congress on Industrial and Applied Mathematics (ICIAM) (2020) Accepted​

Nurtay A, Hennessy MG, Alsedà Ll, Elena SF, Sardanyés J, Host-virus evolutionary dynamics with specialist and generalist infection strategies: bifurcations, bistability and chaos. Chaos (2020) Accepted​

Perona J, Fontich E, Sardanyés J, Dynamical effects of loss of cooperation in discrete-time hypercycles​. Physica D: Nonlinear Phenomena 406: 132425 (2020)

Conde-Pueyo N, Vidiella B, Sardanyés J, Berdugo M, Maestre FT, de Lorenzo V, Solé R, Synthetic biology for terraformation: lessons from Mars, Earth, and the microbiome​. Life 10(2): 14 (2020)

Alsedà Ll, Vidiella B, Solé R, Lázaro JT, Sardanyés J, Dynamics in a time-discrete food-chain model with strong pressure on preys​. Communications in Nonlinear Science and Numerical Simulation 84, 105187 (2020)

Sardanyés J, Piñero J, Solé R, Habitat loss-induced tipping points in metapopulations with facilitation​. Population Ecology 1-14 (2019)

Sardanyés J. Viruses: Agents of evolutionary invention​. The Quarterly Review of Biology 94(1): 90-91 (2019)

Nurtay A, Hennessy MG, Sardanyés J, Alsedà Ll, Elena SF, Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits: a bifurcation analysis​. Royal Society Open Science 6: 181179 (2019)
​
Fornés J, Lázaro JT, Alarcón T, Elena SF, Sardanyés J, Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis. Journal of Theoretical Biology 460: 170-183 (2019)

Daniel J. Toddie-Moore Martti P. Montanari Ngan Vi Tran Evgeniy M. Brik Hanna Antson Isaac Salazar-Ciudad Osamu Shimmi, Mechano-chemical feedback mediated competition for BMP signalling leads to pattern formation

Salazar-Ciudad, Isaac. Why call it developmental bias when it is just development?. Biology Direct, 2021, vol. 16, p. 1-13.

Milocco, L., & Salazar-Ciudad, I. (2022). Evolution of the G Matrix under Nonlinear Genotype-Phenotype Maps. The American Naturalist, 199(3), 420-435.

Hagolani, P. F., Zimm, R., Vroomans, R., & Salazar-Ciudad, I. (2021). On the evolution and development of morphological complexity: A view from gene regulatory networks. PLoS computational biology, 17(2), e1008570.

Coronado-Zamora, M., Salvador-Martínez, I., Castellano, D., Barbadilla, A., & Salazar-Ciudad, I. (2019). Adaptation and conservation throughout the Drosophila melanogaster life-cycle. Genome biology and evolution, 11(5), 1463-1482.

Hagolani, P. F., Zimm, R., Marin-Riera, M., & Salazar-Ciudad, I. (2019). Cell signaling stabilizes morphogenesis against noise. Development, 146(20), dev179309.

The I2SysBio and the Centre de Recerca Matemàtica (Mathematical Research Center) launch the associated unit Dynamic Systems and Computational Virology (DysCoVir) — News — DysCoVir website