top of page

MNat lines

Mnat lines
I. Mathematical Foundation, Models, and Methods in Nature

I.1 Analysis of Singular Interfaces and Fronts: Cell and Tumor Dynamics; Pressure and Biomechanical variables; Nonlinear diffusion and stochastic processes; Pattern formation (travelling waves, kinks, and solitons); Fluxes and Interfaces in Fluids; Granular Flows; Geometric variational problems: modeling and interfaces; Computational and discrete geometry; Kinetic and macroscopic models: analytical and numerical approaches.

I.2. Multiscale models in Life and Society, from nano to macro: Non-symmetric interactions between agents and interaction between clusters in population dynamics; Modeling neuroscience; Cell communication and cytonemes; Behavioral crowds and swarms; Beyond pairwise interactions; Forced dynamical systems with both classical and nonstandard agents; Multiscale models in epidemiology; Optimal network architectures in ecological models; Fragmentation-Coagulation processes; Complex neural networks and multiscale models; Emergent behaviour; Living systems as soft matter (kinetic and macroscopic models); Modeling transport of molecules, charges, and nanoparticles in 2D materials.

I.3. Mathematical foundations in data analysis and multiscale modeling in biological and ecological processes: Patterns in experimental data mining and their use in multiscale models; PDEs on graphs; Topological and graph data structures and applications in dynamics; Modeling trans-omic multilayer complex networks; Deep learning and multiscale models.

Photo by J. Soler


II. Modeling Cell Communications and Tumor Dynamics

II.1. Modeling of cell dynamics: Cell-to-cell communication (cytonemes, EVs, microenvironment); Cell-to-cell interactions (tumor-neurons or tumor- immune cells); Multiscale models (DNA, genes, microRNAs, proteins -Hh, Wnt- cells, ECM, and tissue scales); Nanoarchitectures based on triggering mechano-transduction pathways; Driving Stem Cells; Predictive models from experimental data mining and analysis of emerging patterns; Modeling cancer and cell dynamics as intricate interactive networks subjected to ecological processes (mutualism, competition, cooperation, ...).


II.2. Cell-gene therapy for cancer treatment: Genetic manipulation of T-cells; Targeted suicide therapeutic genes; Efficacy and toxicity on new in vitro and in vivo models; Interplay with multiscale mathematical models, mutual feedback, and prediction.


II.3. Modeling biochemical and biomechanical changes in biomimetic cells and tissues: tissue and tumor heterogeneity; Cell plasticity; Effects of external interactions on tumor development with direct intervention in cell communication, mechanical waves, microenvironment conditions, targeted drugs, synthetic biology, or nanoparticles; 3D Bioprinted mimetic tissues with regenerative properties and mathematical modeling of ECM dynamical processes; Multi-organs on-a-chip mimicking primary tumors and metastasized tissues.

II.4. Mathematical models to predict hypoxia-dependent gene expression and hypoxia-dependent hypermethylation events during tumor development and aberrant tumor angiogenesis: Feedback between micro (Ang, Tie, VEGF, PARP...) and macro scales (pressure, tumor and endothelial cells); hypoxia-related signaling pathways and effects of targeted therapies on tumor progression; hypoxia cycle effects on tumor cells, adaptation to harsh environments, and therapy-resistant phenotypes.

Images by E. López Ruiz & M. Perán.


III. Modeling Bio-Nanotechnology. New Materials and Bio-Engineering.

III.1. Bioinspired self-assembled architectures in soft matter composites: Emergent dynamics; Anisotropic magnetic nanoparticles as nanosensors and theranostic agents; Modeling living systems (swarms, cells, aggregates of aquatic polymeric particles); Artificial cell-like microcompartments; Sustainable water remediation and circular recovery of resources.


III.2. Multiscale modeling of bioinspired 2D smart electronic materials for sustainable applications: Neuromorphic computing; Optoelectronic devices; Flexible electronics; Transparent electrodes with human vascular tissue-inspired metal-nanowire networks; Devices and technologies for energy harvesting and storing; Biosensors for early diagnostic; 2D-bio-inspired metamaterials; E-noses for environmental and food control.

III.3 Modeling interactions between nanomaterials and biological agents: Drug targeting; Resistance and resilience of living matter (synthetic proteins, ECM reconstruction); New renewable materials, sustainable research with animals and circular economy; Analysis of drug toxicity and possible alternative solutions.

Images by J. de Vicente, K. Shahrivar, J.R. Morillas


IV. Modeling complex and dynamic adaptive systems at multiple scales. Computational Biology

IV.1. Information flows in biological systems: The interaction between genotype and environment. Gene coexpression networks; Transcriptomic regulation and its role on the development of complex phenotypes; Phenotypic plasticity; Epigenetic marks, sRNAs, and transgenerational epigenetic inheritance in evolution; Cancer as a complex process driven by Darwinian principles; Eco-evolutionary dynamics of metastasis


IV.2. Complex networks to understand biological systems: Functional integration of ecological networks; Variations in interaction outcomes and the continuum from mutualism to antagonism; Ecological networks across organization levels; The multilayer nature of ecological networks; Context- dependent network architecture and topology.


IV.3. Mechanisms boosting biological diversity: Eco-evolutionary dynamics at multiple scales; Hybridisation, polyploidy, local adaptation, and speciation. Interaction and trade-off based eco-evolutionary models; Holobionts as hotspots of diversity and ecosystem functions.

IV.4. Patterns emergence in biological systems: The analysis of collective behavior from molecules to organisms and societies; Biophysical processes promoting self-assembling, coagulation, and phase transitions; Dissolved colloids and exopolymers released by organisms and their aggregation into particles; Effects of sedimentation in the global carbon cycle; Biofilms and microbial communication.



Photo by the SeaWiFS Project, NASA/Goddard Space Flight Center, and ORBIMAGE



Image by Javier Valverde


bottom of page