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Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly-complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings. This research has been supported by the James S. McDonnell Foundation 21st Century Science Initiative in Mathematical and Complex Systems Approaches for Brain Cancer (collaborative awards 220020560 and 220020450), Ministerio de Economia y Competitividad/FEDER, Spain (grant no. MTM2015-71200-R), Junta de Comunidades de Castilla-La Mancha (grant no. SBPLY/17/180501/000154). Research in the Brain Metastasis Group is supported by MINECO grant MINECO-Retos SAF2017-89643-R (M.V.), Bristol-Myers Squibb Melanoma Research Alliance Young Investigator Award 2017 (498103) (M.V.), Beug Foundation's Prize for Metastasis Research 2017 (M.V.), Fundacion Ramon Areces (CIVP19S8163) (M.V.), Worldwide Cancer Research (19-0177) (M.V.), H2020-FETOPEN (828972) (M.V.), Fundacio La Marato de tv3 (141), Clinic and Laboratory Integration Program CRI Award 2018 (54545) (M.V.), AECC Coordinated Translational Groups 2017 (GCTRA16015SEOA) (M.V.), LAB AECC 2019 (LABAE19002VALI) (M.V.), La Caixa INPhINIT Fellowship (LCF/BQ/IN17/11620028) (P.G.-G.), La Caixa-Severo Ochoa International PhD Program Fellowship (LCF/BQ/SO16/52270014) (L.Z.). M.V. is a member of the European Molecular Biology Organization Young Investigators programme (4053). We would like to acknowledge J. Cervera and J. C. Penalver from the IVO Foundation (Valencia, Spain). No

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial success against B-cell malignancies, which has led to a growing scientific and clinical interest in extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immunosuppressive tumour microenvironment, which is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using the mathematical model, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study computationally, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. We study in silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive production of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. This strategy could benefit from the combination with PD-1 inhibitors and low tumour loads. Our computational results provide theoretical support for the treatment of different types of solid tumours using T cells engineered with combination treatments of dual CARs with on-and off-tumour activity and anti-PD-1 drugs after completion of classical cytoreductive treatments, This work has been funded by the James S. Mc. Donnell Foundation (USA) 21st Century Science Initiative in Mathematical and Complex Systems Approaches for Brain Cancer (Collaborative award 220020450), Ministerio de Ciencia e Innovación, Spain (grant number PID2019-110895RB-I00), and Junta de Comunidades de Castilla-La Mancha (grant number SBPLY/17/180501/000154). OLT is supported by a PhD Fellowship from the University of Castilla-La Mancha research plan

Immunotherapies use components of the patient immune system to selectively target cancer cells. The use of CAR T cells to treat B-cell malignancies – leukaemias and lymphomas– is one of the most successful examples, with many patients experiencing long-lasting complete responses to this therapy. This treatment works by extracting the patient’s T cells and adding them the CAR group, which enables them to recognize and target cells carrying the antigen CD19+, that is expressed in these haematological tumors.Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T-cells. The model accounts for mature and progenitor B-cells, tumor cells, CAR T cells and side effects by incorporating the main biological processes involved. The model explains the early post-injection dynamics of the different compartments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that provides the maximum CAR T cell expansion in-vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19+ tumor relapses could be the result of the competition between tumor and CAR T cells analogous to predator-prey dynamics. We discuss this fact on the light of available evidences and the possibility of controlling relapses by early re-challenging of the tumor with stored CAR T cells.

Diabetes mellitus constitutes a major health problem and its clinical presentation and progression may vary considerably. A number of standardized diagnostic and monitoring tests are currently used for diabetes. They are based on measuring either plasma glucose, glycated haemoglobin or both. Their main goal is to assess the average blood glucose concentration. There are several sources of interference that can lead to discordances between measured plasma glucose and glycated haemoglobin levels. These include haemoglobinopathies, conditions associated with increased red blood cell turnover or the administration of some therapies, to name a few. Therefore, there is a need to provide new diagnostic tools for diabetes that employ clinically accessible biomarkers which, at the same time, can offer additional information allowing us to detect possible conflicting cases and to yield more reliable evaluations of the average blood glucose level concentration. We put forward a biomathematical model to describe the kinetics of two patient-specific glycaemic biomarkers to track the emergence and evolution of diabetes: glycated haemoglobin and its labile fraction. Our method incorporates erythrocyte age distribution and utilizes a large cohort of clinical data from blood tests to support its usefulness for diabetes monitoring.