Dr. M. A. Herrero
RESEARCH INTERESTS:
- EMERGENT PROPERTIES IN BIOLOGICAL POPULATIONS
An intriguing question concerning physiological and pathological behaviours of large cell aggregates making up tissues and organs is the following. How can distinct global population behaviours emerge as a result of purely individual decisions taken by individual cells?
Take for instance the example of the immune response. The capability of the human adaptive immune system to tackle on pathogens relies substantially on a sophisticated mechanism to identify antigens expressed in target cells. Key players in this process are T cells, which interact with antigens through a membrane receptor (T cell receptor or TCR) by means of a key-and-lock procedure. Specifically, antigens are presented to inactive T cells (called naïve) by innate immune cells (IICs) by means of a specific membrane receptor, the MHC (major histocompatibility complex). This cell-to-cell interaction involves the physical contact between the complex MHC/antigen and the TCR. If both structures do not match, the cellular union breaks and the naive T cell remains inactive. However, if they do match, the resulting union (called immune synapse) may last some hours, marking the beginning of T cell immune response.
In this case, the corresponding naïve T cell is activated and undergoes an asymmetric division, giving rise to two different daughter cells: an effector T cell and a memory T cell. Effector T cells then go through several rounds of cell divisions, which are able to multiply the initial population by millions in a few hours. The cells thus originated are ready to migrate to the infected tissues to kill infected host cells, thus preventing the spread of the pathogen. This rapid multiplication is crucial for success, since many pathogens have large reproduction rates, and the initial available number of T cells able to recognize a given antigen may just be on the order of hundreds.
This fascinating behaviour raises a number of significant questions. To mention but a single one, how can a T cell tell a friend (that is, an antigen produced by some internal, ordinary process in the body) from a foe (for instance an invading bacteria)? It has been widely assumed that T cells can distinguish self from non-self antigens. However, this answer cannot explain why in many cases the immune system is able to detect and destroy tumours being produced by the host, whereas in other cases it attacks well-behaved cells, thus generating autoimmune diseases.
Figure 1: A red blood cell undergoing macrophage phagocytosis.
(see http://oncologydiscovery.com/2015/11/04/trillium-therapeutics-a-pure-play-on-cd47-as-an-immuno-oncology-target/)
This and other related issues are being currently investigated. Some recent references are:
- C. F. Arias, M. A. Herrero, J. A. Cuesta, F. J. Acosta and C. Fernández-Arias. The growth threshold conjecture: a theoretical framework for understanding T-cell tolerance. R. Soc. Open Sci. 2: 150016, 2015. doi: http://dx.doi.org/10.1098/rsos.150016.
http://rsos.royalsocietypublishing.org/content/2/7/150016
- C. F. Arias, M. A. Herrero, F. J. Acosta and C. Fernández-Arias. A mathematical model for a T cell fate decision algorithm during immune response. Journal of Theoretical Biology 349, 109-120, 2014. [PDF]
Cell populations may at some point decide to change behaviour, switching from an initial phenotype to an utterly different one. An illustrative case is provided by the so-called "go or grow" alternative in glioma. This last term is used to design some types of brain tumours originating from glia cells that have a sober prognosis.
Figure 2: A schematic presentation of malignant glioma grow in human brain.
(taken from Kristian Gerhard Jebsen Brian Tumor Research Center: www.kgjebsen-btrc.no/research)
The extreme aggressiveness of gliomas has been long since associated to their efficient invasive properties. There is evidence to conclude the existence of two phenotypes characteristic of that type of tumours. One of them is called proliferative, and has high replication capability but scarce mobility. The second one, called migratory is highly motile but does not proliferate. Data suggests that switching from one phenotype to another is reversible, and some molecules that may trigger that switch have been identified. This phenotype dichotomy is referred to as the “go or grow” alternative and is currently considered as a key issue to understand the dynamics of that type of tumours.
We are interested in understanding the way in which this change in behaviour emerges from individual tumour cells decisions reacting to changes in their local microenvironment. A result in this direction is provided in:
- Böttger K, Hatzikirou H, Voss-Böhme A, Cavalcanti-Adam EA, Herrero MA, Deutsch A (2015) An Emerging Allee Effect Is Critical for Tumor Initiation and Persistence. PLoS Comput Biol 11(9): e1004366. doi:10.1371/journal.pcbi.1004366.
http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004366
- MATHEMATICAL MODELLING IN RADIOTHERAPY
Radiotherapy plays an important role in the treatment of solid tumours. On fact, over 50% of patients suffering from such disorders will be prescribed radiotherapy during their illness, whether on its own or as an adjunct to surgery, chemotherapy or other medical techniques. Radiotherapy consists in the use of ionizing radiation to achieve suitable tumour control over the so-called PTV (Planning Target Volume). The latter is selected to be a region as small as possible that strictly contains the tumour to be treated. Consideration of this type of regions is due to the uncertainty related to the resolution limits of medical imaging techniques currently used to locate tumours (see Figure 3).
Figura 3: Representation of a PTV (Planning Target Volume) for a patient
diagnosed with a brain tumour.
A key limiting aspect in the use to of Radiotherapy dosimetries is the need to minimize radiation effects on organs at risk (OAR) and healthy tissues (HT) located near the target to be irradiated (see Figure 4).
Figura 4: Representation of a PTV (purple) and surrounding OARs for a patient
diagnosed with a Meningioma.
Therefore, when a radiotherapy treatment is planned, two often conflicting goals should be kept in mind. On the one hand, a large enough radiation dose has to be delivered on the PTV to achieve tumour control. On the other, only sufficiently small doses should be deposited on neighbouring OAR and HT. To this day, the choice of the treatment actually delivered to every patient relies basically on the experience accumulated by clinicians and radiophysicists in charge of such treatments. This makes particularly relevant the search of theoretical ground for the design of radiation protocols and algorithms to compare them, that could provide efficient decision-making tools in clinical practice.
Additional details can be found in the following references:
- J. C. L. Alfonso, M. A. Herrero and L. Núñez (2015) A dose-volume histogram based decision-support system for dosimetric comparison of radiotherapy treatment plans. Radiation Oncology 10(1): 1-9. doi:10.1186/s13014-015-0569-3.
http://ro-journal.biomedcentral.com/articles/10.1186/s13014-015-0569-3
- J. C. L. Alfonso, G. Buttazzo, B. García-Archilla, M. A.Herrero and L. Núñez (2012). A class of optimization problems in Radiotherapy dosimetry planning. Discr. Cont. Dyn. Systems B 17, 6; pp. 1651-1672.
https://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=7351
- A. Cappuccio, M. A. Herrero and L. Núñez. Biological optimization of tumour radiosurgery (2009). Medical Physics 36, 1; pp. 98-104.
- A. Cappuccio, M. A. Herrero and L. Núñez. Tumour radiotherapy and its mathematical modelling (2009). In Mathematics, Developmental Biology and Tumour Growth, F. Giráldez and M. A. Herrero editors. 492; pp. 77-102.
- MODELS OF VASCULAR DEVELOPMENT
Vasculogenesis is a developmental process whereby blood vessels of different lengths and widths are generated and assembled to give raise to the vascular system in vertebrates. The latter is the first system that becomes fully functional in human embryos. Indeed, an adequate supply of oxygen and nutrients and an efficient disposal of metabolic waste is crucial for embryo growth, which rapidly goes over the reduced size where passive transport mechanisms as diffusion are enough to fulfil such tasks. A question that has been a challenge for scientists since ancient times is the large variety of forms, compatible with a precise regularity in their development, that can be observed as a vascular system unfolds from a virtually homogeneous initial state (see Figure 5).
Figura 5: Different snapshots of vascular system development in quail embryo.
It is well known that the development of geometric structures as those represented in Figure 1 is regulated by chemical cues. One may naturally wonder how structures with so high a degree of space heterogeneity can be generated under the guidance of chemical signals which may well be of a homogeneous or random nature.
Using mathematical models, which include cellular automata of hybrid type allows to formulate a model of paracrine (that is, induced by long-range cues) signalling, different to those of autocrine (whereby a cell produces chemicals that act on itself) nature, mostly favoured to this day. More precisely, according to the former proposal, early development of polygonal networks as shown in Figure 1 may occur in response to: 1) A release of a growth factor (namely VEGF: vascular endothelium growth factor) taking place at the endoderm, located near the mesoderm population which will form blood vessels, 2) Binding of VEGF to the extracellular matrix (ECM) around the endothelial cells which will eventually produce blood vessels, and 3) Amplification of VEGF signalling following their local retention by ECM, altogether resulting in a quite different effect to that due to free VEGF diffusion (see Figure 6).
Figura 6: A sketch of differences between autocrine and paracrine
signalling in vascular network formation.
For additional details, see:
- A. Köhn-Luque, W. De Back, Y. Yamaguchi, K. Yoshimura, M. A. Herrero and T. Miura (2013). Dynamics of VEGF matrix retention in vascular network patterning. Phys. Biol. : 10, 066007. doi:10.1088/1478-3975/10/6/066007.
http://iopscience.iop.org/1478-3975/10/6/066007
- A. Köhn-Luque, W. De Back, J. Starrruss, A. Mattiotti, A. Deutsch, J. M. Pérez-Pomares and M. A. Herrero (2011). Early embryonic vascular patterning by matrix-mediated paracrine signalling: a mathematical model study. PLoS ONE 6(9), e24175. doi:10.371/Journal.pone.0024175.
http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0024175
- SOCIAL DYNAMICS
Living beings often gather in large groups, within which they interact according to rules than can be highly sophisticated. The formation and internal stability of such groups turns out to have a very positive impact on species survival. In the course of their interaction, a number of emergent behaviours result that affect both the internal structure of the community formed and the species environment. The evolution, both in time and space, of any such community will be referred to as social dynamics.
Figura 7: Collective dynamics of human and insect populations.
The study of social dyanmics in human populations is an exciting research topic, where use is being increasingly made of mathematical modellig and simulation that go beyond the application of statistical methods, however important the latter are. In this broad area, we have been concerned with mathematical models to assess the impact of social and economical mobility between classes in the dynamics and stability of human societies. We have also considered the consequences of some aspects of cheating in the global wealth of a society. Moreover, we have discussed the feedback between political and economical unrest, and the possible onset of significant crisis that their interplay might trigger.
Some works were these questions are addressed are the following:
- N. Bellomo, M. A.Herrero and A. Tosin (2013). On the dynamics of social conflicts: looking for the black swan. Kinetic and Related Models 6; pp. 459- 479.
http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=8657
- J. C. Nuño, M. A. Herrero and M. Primicerio (2011). A mathematical model of a criminal-prone society. Discrete and Continuous Dynamical Systems S 4,1; pp. 193-207.
http://aimsciences.org/journals/displayArticles.jsp?paperID=5534
- J. C. Nuño, M. A. Herrero and M. Primicerio (2010). Fighting cheaters: how and how much to invest. European Journal of Applied Mathematics 21, 4-5; pp. 459-478.
