New knotted solutions of Maxwell's equations

In this note we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman's variables. This has enabled us to get a wide class of solutions from the basic configuration like constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of the Bateman's construction and discussed the conserved charges associated with the conformal group as well as a set of four types of conserved helicities. We have also given a formulation in terms of quaternions. This led to a simple map between the electromagnetic knotted and linked solutions into flat connections of $SU(2)$ gauge theory. We have computed the corresponding CS charge in a class of solutions and it takes integer values.Comment: version accepted for publication in J. Phys. A. minor changes: references added, new figure added, typos correcte

Knotted solutions, from electromagnetism to fluid dynamics

Knotted solutions to electromagnetism and fluid dynamics are investigated, based on relations we find between the two subjects. We can write fluid dynamics in electromagnetism language, but only on an initial surface, or for linear perturbations, and we use this map to find knotted fluid solutions, as well as new electromagnetic solutions. We find that knotted solutions of Maxwell electromagnetism are also solutions of more general nonlinear theories, like Born-Infeld, and including ones which contain quantum corrections from couplings with other modes, like Euler-Heisenberg and string theory DBI. Null configurations in electromagnetism can be described as a null pressureless fluid, and from this map we can find null fluid knotted solutions. A type of nonrelativistic reduction of the relativistic fluid equations is described, which allows us to find also solutions of the (nonrelativistic) Euler's equations.Comment: 36 pages, 3 figure

Is systems biology a promising approach to resolve controversies in cancer research?

At the beginning of the 21st century cancer research has reached an impasse similar to that experienced in developmental biology in the first decades of the 20th century when conflicting results and interpretations co-existed for a long time until these differences were resolved and contradictions were eliminated. In cancer research, instead of this healthy "weeding-out" process, there have been attempts to reach a premature synthesis, while no hypothesis is being rejected. Systems Biology could help cancer research to overcome this stalemate by resolving contradictions and identifying spurious data. First, in silico experiments should allow cancer researchers to be bold and a priori reject sets of data and hypotheses in order to gain a deeper understanding of how each dataset and each hypothesis contributes to the overall picture. In turn, this process should generate novel hypotheses and rules, which could be explored using these in silico approaches. These activities are significantly less costly and much faster than "wet-experiments". Consequently, Systems Biology could be advantageously used both as a heuristic tool to guide "wet-experiments" and to refine hypotheses and test predictions

Systems biology and cancer, [Editorial]

The systems approach to complex biological problems has rapidly gained ground during the first decade of this century. There are several reasons for this development. An important one is that while the achievement of sequencing the complete human genome, and those of other species, has been of great benefit to fundamental science, for example in comparative genomics and evolutionary biology, it has not led to the expected quick and simple solutions to multifactorial diseases (2010). On the contrary, cancer, cardiovascular, respiratory, metabolic and nervous diseases have all been resistant to reductionist analysis. In the case of cancer the hope that by identifying what are called oncogenes we would not only understand cancer but be led naturally to its cure has not been fulfilled ([Sonnenschein and Soto, 1999] and [Sonnenschein and Soto, 2011]). In all areas of medical science, despite the identification of hundreds more potential targets by genome sequencing, the pharmaceutical industry has been faced with a decline in the production of new successful drugs. The more we find out about the fundamental elements of biology, the DNA, RNAs, proteins, metabolites, membrane systems, organelles, the more puzzling the picture becomes. Even central biological concepts, like that of a gene, have changed and have even become difficult to define (Beurton et al., 2008 In: P.J. Beurton, R. Falk and H.-J. Rheinberger, Editors, The Concept of the Gene in Development and Evolution: Historical and Epistemological Perspectives, Cambridge University Press, Cambridge (2008).Beurton et al., 2008).\ud \ud Reassessment of the fundamental concepts of biological science is therefore necessary. This is happening in all fields, including genetics (Beurton et al., 2008), evolution ([Pigliucci and Müller, 2010], [Gissis and Jablonka, 2011] and [Shapiro, 2011]), cancer (Soto et al., 2008), development and the relationships between genomes and phenotypes ([Noble, 2011b] and [Noble, 2011a]). What once were heresies seem to be creeping back into mainstream biology.\ud \ud One of the driving forces of this development is the use of mathematical modelling in systems biology. This has brought a rigorous quantitative approach to what otherwise would be largely untestable theories. Mathematical models provide a framework in which to interpret the vast amount of experimental data generated on a daily basis and to suggest subsequent experiments necessary to test theories. The traditional verbal reasoning approach is not appropriate in many cases due to the complexity of biology (Gatenby and Maini, 2003) which renders intuition insufficient as results are often counter-intuitive, a characteristic outcome of scientific research that goes as far back as Copernicus’ proposal of an heliocentric planetary system. This vast complexity requires a mathematical approach.\ud \ud The motivation for this focussed issue of the journal is that the field of cancer is ripe for the systems biology approach. As editors we have collected an eclectic mix of articles. This is not a ‘one view fits all’ approach. It is rather one to ‘let a hundred flowers bloom’. At this stage in our understanding we cannot be sure where the next big insights are going to come from.\ud \ud Since the 18th century biologists and philosophers tried to define the place of biology1 in science and in particular its relationship with physics. A two hundred year debate followed, with biologists adopting “physicalist” or “vitalistic” stands. Was life to be explained in a totally materialistic way by the laws of physics? Or were there additional “forces” present in the living matter but absent in the inert one? Curiously, as vitalism dwindled among biologists in the 20th century, physicists like Schrödinger (1944) and Elsasser (1987) were the ones that tried to understand biological order and were prepared to find new laws that applied only to living matter.2 No new laws resulted from this search, but from the emerging field of information theories, biologists adopted information as the metaphor for the study of biological organization.3 This, however, has not produced the desired effects either, probably because the attempts to formalize this approach failed, which in turn suggests that it was conceptually wrong. Can biology achieve formalization through mathematics, a feat that physics has accomplished so successfully?\ud \ud The article by Giuseppe Longo and Mael Montevil (2011) (mathematicians), analyzes the principles of intelligibility in physics, which is based on symmetries, and posit that the role of symmetries in biology is different: in their words “the permanent change of symmetries …per se modifies the analysis of the internal and external processes of life, both in ontogenesis and evolution”. They propose to consider the roles played by local and global symmetry changes, along extended critical transitions. According to them, the mathematization of this state of extended criticality may provide the adequate frame to understand biological complexity. Paul-Antoine Miquel (2011) (a philosopher), reflects on the philosophical aspects of the theoretical analysis by Longo and Montevil and concludes that “the philosophical key point for us is that they (Longo and Montevil) interpret this mathematical space in which anti-entropy is realized in biological criticality as an extension of the classical physical theoretical frameworks.” These two contributions aim at improving our understanding on why the principles governing living organisms are different from those defining the physicality of inanimate objects and provide a conceptual frame of reference and a point of departure for constructing a mathematics for biology.\ud \ud Stuart Baker (a bio-statistician) and Barnett Kramer (a cancer epidemiologist) (2011) evaluate the potential contributions of different approaches to Systems Biology when applied to uncover buried messages in the genesis of cancer which may set new trends in research and in ways to benefit patients. They anticipate both promises and perils in applying systems biology to cancer. The great promise of systems biology comes from the idea that studying a system can provide information not available by separately studying the workings of each part. However, they perceive a divide between systems biology based on the principles of biology or biophysics, systems biology related to statistics, bioinformatics, and reverse engineering, and systems biology involving clinical predictions, sometimes without full appreciation of other viewpoints. The peril comes when the rules leading to a complex system vary over many components and the sample sizes are limited for identifying the rules and making predictions. Baker et al. have introduced the concept of “paradigm instability” when referring to current state of affairs through which the field of cancer research is traversing. Thus, they focus on a number of paradoxes that exist in this field and cautiously point at ways that might increase knowledge about the disease and also benefit patients.\ud \ud Simon Rosenfeld (2011) (a mathematical physicist) makes a critical analysis of the assumptions and concepts used in the emerging field of network biology, particularly those on the actual physics and chemistry happening inside cells. He posits that, in biology there is dual causality, that is, in addition to the constraints imposed by the laws of nature, there is the evolutionary history of the organism: “…inherent dynamical instability represents the natural laws and physico-chemical principles whereas biological robustness is the result of evolutionary history in which this dynamical instability has been effectively used for gaining evolutionary advantages and survival.” He subscribes to the notion that “Mathematics represents a systematic and orderly way of describing and organizing knowledge. In the majority of scientific disciplines, mathematical reasoning has proven to be an unparalleled and indispensable tool for understanding complex dynamics.” He forcefully argues for adopting a Systems Biology approach to resolve complex biological problems while complying with a comprehensive evolutionary perspective.\ud \ud Plankar et al. (2011) challenge the genetically determined paradigm of cancer from another angle to characterise cancer as the result of impaired coherence leading to progressive destabilisation of molecular and gene regulatory networks. As they write in their conclusion “It is becoming clear that even with potentially unlimited insight into the dynamics of genetic changes, cancer could not be sufficiently explained, and neither could it be explained in terms of separate linear molecular pathways alone. During the last decade, scientific attention has turned dramatically towards the metabolic, bioenergetic, developmental, and systems biology aspects of cancer, reflecting a gradual paradigm shift towards its non-genetic origin.”\ud \ud Enderling and Hahnfeldt (2011) analyse the dynamics of a growing solid tumour composed of cancer stem cells and cancer non-stem cells using a simple hybrid cellular automaton (CA) model. They illustrate the counter-intuitive finding that increasing the rate of apoptosis, while obviously reducing tumour size in the short-term, actually enhances growth in the long-term. They show that tumours can remain dormant for a long time but stimulation of apoptosis can cause the tumour cell population to aggressively invade. Their work suggests that the widely regarded “evading cell death” as a hallmark of cancer (Hanahan and Weinberg, 2000) needs to be revisited.\ud \ud Kim et al. (2011) begin by reviewing the interactions between a tumour and its microenvironment, highlighting how this plays an important role in the transition from benign or pre-malignant tumour to invasive cancer. They then describe a continuum model for the mechanics of a growing tumour in three spatial dimensions, and use it to investigate the effects on tumour growth of agarose gel inhomogeneities and other microenvironmental factors. This framework is extended to explore ductal carcinoma in situ (DCIS) in which the stroma is modelled as a continuum but the cells of the tumour are modelled discretely. The mechanical model is coupled to the biochemistry via a system of reaction–diffusion equations which describe the dynamics of key signalling factors. This multiscale model is solved numerically and effects of perturbing the system mechanically or biochemically are illustrated. This approach allows us to begin to understand the outcome of the nonlinear interactions of some of the fundamental processes involved in tumour growth, with the potential to then consider methods to control growth and spread.\ud \ud Gerlee and Anderson (2011) focus on mechanisms present in organisms that allow it, or parts of it, to maintain a given shape or architecture (structural homeostasis). They consider a hybrid CA model for a two-dimensional mono-layer of cells which may, for example, approximate the epithelial lining of an organ. In their model, each cell has an intracellular network which integrates the cues a cell receives from its microenvironment (for example nutrients or growth factors, whose dynamics are modelled by reaction-diffusion equations) and other cells and determines the response of the cell, in terms of its behaviour or phenotype. The problem is then reduced to finding a set of network parameters (or genotype) which maximises a fitness function such that structural homeostatis is attained. Perturbations of the system, such as wounding or mutation, are investigated.\ud \ud Vera et al. (2011) present an in-depth review which focuses on JAK-STAT (Janus kinase – signal transducer and activator of transcription) pathway in the context of cancer. This pathway plays a fundamental role in growth control, cell differentiation and maintenance of tissue homeostasis, and its dysregulation plays an important role in tumourigenesis. They review the biology of the pathway and then survey systems biology approaches that have helped elucidate the dynamics of the pathway under physiological and diseased states.\ud \ud Scianna et al., (2011) address the multiple levels of organisation involved in vascularisation, an important step enabling tumour growth and the formation of metastases. Their work forms an innovative multiscale hybrid framework within which to test potential anti-angiogenic strategies in treating cancer.\ud \ud Insuk Lee (2011) presents a holistic model of genes as a collaborative society. To the standard approaches involving protein–protein interaction networks (PPIN) and transcriptional regulatory networks (TRN) he adds the probabilistic functional gene network (PFGN) to show how robustness can arise despite noisy genomics data. Mapping epistatic interactions between genes is identified as the key way to understanding the genetic organisation of complex traits. Amongst the applications of this approach he considers epistatic interactions between hub cancer genes such as p53.\ud \ud Keith Baverstock (2011) uses models of cell regulation to address the important question of whether regulatory networks are hard wired into the genome or whether they are better represented as open systems involving an attractor interacting with the environment. In the latter case, environmental stress can trigger inherited transitions in the phenotype without necessarily involving DNA sequence changes. The second type of model works best. As he says “the power of the model lies in its ability to make evident how it is that a rigid and highly conserved coding sequence in DNA, the genotype, can give rise to phenotypic plasticity and responsiveness to environment” and that it helps to understand “the origins of non-genetic somatic and inherited disease, arising from switches to variant attractors representing phenotypes with abnormal characteristics.” The relevance to diseases like cancer is obvious.\ud \ud Taken as a whole, this set of articles not only challenges some of the current paradigms, but also lays the groundwork for alternative approaches and in many cases takes those approaches further towards the goal of understanding cancer as a systems-level process

In search of principles for a Theory of Organisms

Giuseppe Longo, Maël Montévil, Carlos Sonnenschein, Ana Soto. In Search of Principles for a Theory of Organisms. In Journal of Biosciences, Springer, pp. 955–968, 40(5), December, 2015. (LoMoSoSo-Search.pdf).International audienceLacking an operational theory to explain the organization and behaviour of matter in unicellular and multicellular organisms hinders progress in biology. Such a theory should address life cycles from ontogenesis to death. This theory would complement the theory of evolution that addresses phylogenesis, and would posit theoretical extensions to accepted physical principles and default states in order to grasp the living state of matter and define proper biological observables. Thus, we favour adopting the default state implicit in Darwin’s theory, namely, cell proliferation with variation plus motility, and a framing principle, namely, life phenomena manifest themselves as non-identical iterations of morphogenetic processes. From this perspective, organisms become a consequence of the inherent variability generated by proliferation, motility and self-organization. Morphogenesis would then be the result of the default state plus physical constraints, like gravity, and those present in living organisms, like muscular tension

On physicalism and downward causation in developmental and cancer biology

International audienceThe dominant position in Philosophy of Science contends that downward causation is an illusion. Instead, we argue that downward causation doesn't introduce vicious circles either in physics or in biology. We also question the metaphysical claim that "physical facts fix all the facts." Downward causation does not imply any contradiction if we reject the assumption of the completeness and the causal closure of the physical world that this assertion contains. We provide an argument for rejecting this assumption. Furthermore, this allows us to reconsider the concept of diachronic emergence

The Microenvironment Determines the Breast Cancer Cells' Phenotype: Organization of MCF7 Cells in 3D Cultures

Background: Stromal-epithelial interactions mediate breast development, and the initiation and progression of breast cancer. In the present study, we developed 3-dimensional (3D) in vitro models to study breast cancer tissue organization and the role of the microenvironment in phenotypic determination. Methods: The human breast cancer MCF7 cells were grown alone or co-cultured with primary human breast fibroblasts. Cells were embedded in matrices containing either type I collagen or a combination of reconstituted basement membrane proteins and type I collagen. The cultures were carried out for up to 6 weeks. For every time point (1-6 weeks), the gels were fixed and processed for histology, and whole-mounted for confocal microscopy evaluation. The epithelial structures were characterized utilizing immunohistochemical techniques; their area and proliferation index were measured using computerized morphometric analysis. Statistical differences between groups were analyzed by ANOVA, Dunnett's T3 post-hoc test and chi-square. Results: Most of the MCF7 cells grown alone within a collagen matrix died during the first two weeks; those that survived organized into large, round and solid clusters. The presence of fibroblasts in collagen gels reduced MCF7 cell death, induced cell polarity, and the formation of round and elongated epithelial structures containing a lumen. The addition of reconstituted basement membrane to collagen gels by itself had also survival and organizational effects on the MCF7 cells. Regardless of the presence of fibroblasts, the MCF7 cells both polarized and formed a lumen. The addition of fibroblasts to the gel containing reconstituted basement membrane and collagen induced the formation of elongated structures. Conclusions: Our results indicate that a matrix containing both type I collagen and reconstituted basement membrane, and the presence of normal breast fibroblasts constitute the minimal permissive microenvironment to induce near-complete tumor phenotype reversion. These human breast 3D tissue morphogenesis models promise to become reliable tools for studying tissue interactions, therapeutic screening and drug target validation