Quantum vacuum energy and the Casimir effect

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: Joan SolàAn overview of the Casimir e ect is presented. The area of study is historically introduced, together with a basic presentation on the zero-point energy concept in relation with the quantization of elds. After this, the Casimir force between parallel plates is calculated under two di erent regularization schemes. The brief overview is completed with a compilation of experimental results and implications of the e ect in di erent elds of physics

Quantum vacuum energy and the Casimir effect

Abstract: An overview of the Casimir effect is presented. The area of study is historically introduced, together with a basic presentation on the zero-point energy concept in relation with the quantization of fields. After this, the Casimir force between parallel plates is calculated under two different regularization schemes. The brief overview is completed with a compilation of experimental results and implications of the effect in different fields of physics

Cancer as a complex adaptive system : Mathematical models of tumor ecology, evolution and development

Despite decades of scientific effort, cancer remains a major cause of death worldwide. Through the accumulation of genome alterations, tumor populations evolve the capacity to circumvent the selective barriers of tissue homeostasis, eventually adapting to resist therapeutic stress. Furthermore, extensive Darwinian evolution is accompanied by an ecological engineering of the surrounding tissue micro-environment together with the alteration of cellular maturation hierarchies. To understand cancer complexity, therefore, we need a picture that spans through the domains of ecology, evolution and development. In an effort to gain understanding of the underlying patterns of treatment resistance, the present PhD thesis introduces a mathematical approach to cancer complexity that takes into account its dynamical nature across these three axes. The resulting modeling endeavor is focused on two major fields of current research: immunotherapy and cancer epigenetics and differentiation, with the aim of providing both treatment design rationale and a comprehensive perspective that merges cancer ecological, evolutionary and developmental complexity.Malgrat dècades d’esforços científics, el càncer continua sent una de les principals causes de mort arreu del món. Mitjançant l’acumulació d’alteracions del genoma, les poblacions tumorals evolucionen la capacitat d’eludir les barreres selectives de l’homeòstasi del teixit, fins al punt d’adaptar-se per resistir l’estrès terapèutic. A més, l’extensa evolució darwiniana s’acompanya d’una enginyeria ecològica del teixit circumdant, juntament amb l’alteració de les jerarquies de maduració cel·lular. Per entendre la complexitat del càncer, per tant, necessitem una imatge que abasti els dominis de l’ecologia, l’evolució i el desenvolupament. En un esforç per comprendre els patrons subjacents de resistència al tractament, al llarg d’aquesta tesi doctoral introduı̈m un enfocament matemàtic de la complexitat del càncer que té en compte la seva naturalesa dinàmica en els tres eixos. L’esforç de modelització resultant se centra en dos grans camps de la investigació actual: la immunoteràpia i l’epigenètica i la diferenciació del càncer, amb l’objectiu d’oferir tant un fonament pel disseny terapèutic com una perspectiva integral que combini la complexitat ecològica, evolutiva i del desenvolupament del càncer

Tumour neoantigen heterogeneity thresholds provide a time window for combination immunotherapy: Tumour neoantigen heterogeneity thresholds provide a time window for combination immunotherapy

Following the advent of cancer immunotherapy, increasing insight has been gained on the role of mutational load and neoantigens as key ingredients in T cell recognition of malignancies. However, not all highly mutational tumours react to immune therapies, and initial success is often followed by eventual relapse. Heterogeneity in the neoantigen landscape of a tumour might be key in the failure of immune surveillance. In this work, we present a mathematical framework to describe how neoantigen distributions shape the immune response. The model predicts the existence of an antigen diversity threshold level beyond which T cells fail at controlling heterogeneous tumours. Incorporating this diversity marker adds predictive value to antigen load for two cohorts of anti-CTLA-4 treated melanoma patients. Furthermore, our analytical approach indicates rapid increases in epitope heterogeneity in early malignancy growth following immune escape. We propose a combination therapy scheme that takes advantage of preexisting resistance to a targeted agent. The model indicates that the selective sweep for a resistant subclone reduces neoantigen heterogeneity, and we postulate the existence of a time window before tumour relapse where checkpoint blockade immunotherapy can become more effective

The ecology of cancer differentiation therapy

A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.This work was supported by the Botín Foundation by Banco Santander through its Santander Universities Global Division, the Spanish Ministry of Economy and Competitiveness, grant FIS2016-77447-R MINECO/AEI/FEDER, an AGAUR FI 2018 grant, and the Santa Fe Institute where most of this work was done.Peer reviewe

Transition Therapy: Tackling the Ecology of Tumor Phenotypic Plasticity.

Phenotypic switching in cancer cells has been found to be present across tumor types. Recent studies on Glioblastoma report a remarkably common architecture of four well-defined phenotypes coexisting within high levels of intra-tumor genetic heterogeneity. Similar dynamics have been shown to occur in breast cancer and melanoma and are likely to be found across cancer types. Given the adaptive potential of phenotypic switching (PHS) strategies, understanding how it drives tumor evolution and therapy resistance is a major priority. Here we present a mathematical framework uncovering the ecological dynamics behind PHS. The model is able to reproduce experimental results, and mathematical conditions for cancer progression reveal PHS-specific features of tumors with direct consequences on therapy resistance. In particular, our model reveals a threshold for the resistant-to-sensitive phenotype transition rate, below which any cytotoxic or switch-inhibition therapy is likely to fail. The model is able to capture therapeutic success thresholds for cancers where nonlinear growth dynamics or larger PHS architectures are in place, such as glioblastoma or melanoma. By doing so, the model presents a novel set of conditions for the success of combination therapies able to target replication and phenotypic transitions at once. Following our results, we discuss transition therapy as a novel scheme to target not only combined cytotoxicity but also the rates of phenotypic switching

Genetic instability as a driver for immune surveillance

Background: Genetic instability is known to relate with carcinogenesis by providing tumors with a mechanism for fast adaptation. However, mounting evidence also indicates causal relation between genetic instability and improved cancer prognosis resulting from efficient immune response. Highly unstable tumors seem to accumulate mutational burdens that result in dynamical landscapes of neoantigen production, eventually inducing acute immune recognition. How are tumor instability and enhanced immune response related? An important step towards future developments involving combined therapies would benefit from unraveling this connection. Methods: In this paper we present a minimal mathematical model to describe the ecological interactions that couple tumor adaptation and immune recognition while making use of available experimental estimates of relevant parameters. The possible evolutionary trade-offs associated to both cancer replication and T cell response are analysed, and the roles of mutational load and immune activation in governing prognosis are studied. Results: Modeling and available data indicate that cancer-clearance states become attainable when both mutational load and immune migration are enhanced. Furthermore, the model predicts the presence of well-defined transitions towards tumor control and eradication after increases in genetic instability numerically consistent with recent experiments of tumor control after Mismatch Repair knockout in mice. Conclusions: These two main results indicate a potential role of genetic instability as a driver of transitions towards immune control of tumors, as well as the effectiveness of increasing mutational loads prior to adoptive cell therapies. This mathematical framework is therefore a quantitative step towards predicting the outcomes of combined therapies where genetic instability might play a key role.This work has been supported by the Botín-Foundation by Banco Santander through its Santander Universities Global Division, a MINECO grant FIS2015-67616-P (MINECO/FEDER, UE) fellowship, an AGAUR grant 2018 by the Universities and Research Secretariat of the Ministry of Business and Knowledge of the Generalitat de Catalunya and the European Social Fund and by the Santa Fe Institute

Adaptive dynamics of unstable cancer populations: the canonical equation

In most instances of tumour development, genetic instability plays a role in allowing cancer cell populations to respond to selection barriers, such as physical constraints or immune responses, and rapidly adapt to an always changing environment. Modelling instability is a nontrivial task, since by definition evolving instability leads to changes in the underlying landscape. In this article, we explore mathematically a simple version of unstable tumour progression using the formalism of adaptive dynamics (AD) where selection and mutation are explicitly coupled. Using a set of basic fitness landscapes, the so-called canonical equation for the evolution of genetic instability on a minimal scenario associated with a population of unstable cells is derived. We obtain explicit expressions for the evolution of mutation probabilities, and the implications of the model on further experimental studies and potential mutagenic therapies are discusse

Genetic instability as a driver for immune surveillance

Background: Genetic instability is known to relate with carcinogenesis by providing tumors with a mechanism for fast adaptation. However, mounting evidence also indicates causal relation between genetic instability and improved cancer prognosis resulting from efficient immune response. Highly unstable tumors seem to accumulate mutational burdens that result in dynamical landscapes of neoantigen production, eventually inducing acute immune recognition. How are tumor instability and enhanced immune response related? An important step towards future developments involving combined therapies would benefit from unraveling this connection. Methods: In this paper we present a minimal mathematical model to describe the ecological interactions that couple tumor adaptation and immune recognition while making use of available experimental estimates of relevant parameters. The possible evolutionary trade-offs associated to both cancer replication and T cell response are analysed, and the roles of mutational load and immune activation in governing prognosis are studied. Results: Modeling and available data indicate that cancer-clearance states become attainable when both mutational load and immune migration are enhanced. Furthermore, the model predicts the presence of well-defined transitions towards tumor control and eradication after increases in genetic instability numerically consistent with recent experiments of tumor control after Mismatch Repair knockout in mice. Conclusions: These two main results indicate a potential role of genetic instability as a driver of transitions towards immune control of tumors, as well as the effectiveness of increasing mutational loads prior to adoptive cell therapies. This mathematical framework is therefore a quantitative step towards predicting the outcomes of combined therapies where genetic instability might play a key role.This work has been supported by the Botín-Foundation by Banco Santander through its Santander Universities Global Division, a MINECO grant FIS2015-67616-P (MINECO/FEDER, UE) fellowship, an AGAUR grant 2018 by the Universities and Research Secretariat of the Ministry of Business and Knowledge of the Generalitat de Catalunya and the European Social Fund and by the Santa Fe Institute

Transition Therapy: Tackling the Ecology of Tumor Phenotypic Plasticity

Phenotypic switching in cancer cells has been found to be present across tumor types. Recent studies on Glioblastoma report a remarkably common architecture of four well-defined phenotypes coexisting within high levels of intra-tumor genetic heterogeneity. Similar dynamics have been shown to occur in breast cancer and melanoma and are likely to be found across cancer types. Given the adaptive potential of phenotypic switching (PHS) strategies, understanding how it drives tumor evolution and therapy resistance is a major priority. Here we present a mathematical framework uncovering the ecological dynamics behind PHS. The model is able to reproduce experimental results, and mathematical conditions for cancer progression reveal PHS-specific features of tumors with direct consequences on therapy resistance. In particular, our model reveals a threshold for the resistant-to-sensitive phenotype transition rate, below which any cytotoxic or switch-inhibition therapy is likely to fail. The model is able to capture therapeutic success thresholds for cancers where nonlinear growth dynamics or larger PHS architectures are in place, such as glioblastoma or melanoma. By doing so, the model presents a novel set of conditions for the success of combination therapies able to target replication and phenotypic transitions at once. Following our results, we discuss transition therapy as a novel scheme to target not only combined cytotoxicity but also the rates of phenotypic switching.This work was supported by the Botín Foundation by Banco Santander through its Santander Universities Global Division, the Spanish Ministry of Economy and Competitiveness, grant FIS2016-77447-R MINECO/AEI/FEDER, an AGAUR FI 2018 grant, and the Santa Fe Institute where most of this work was done.Peer reviewe