Biophysical Reviews and Letters

This discussion about diagnostic tests for cancer incorporates a powerful branch of Physics namely X-ray diffraction. Although this technique was used to solve the DNA structure using the X-ray diffraction pictures of Rosalind Franklin,¹ and the structure of vitamin B12 by Dorothy Hodgkin² and hosts of other medical related structures, it is poorly understood by the general medical profession and the community at large. To the nonphysicist the patterns appear to have no relation to the results produced. It might as well be written in Greek. The well-known quote of Poincaré, the famous French mathematician and scientist, in 1885 comes to mind: "Science is built up with facts as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house."

In order therefore to build a true understanding of this powerful technique it is necessary to build a firm understanding of the basic facts about this technique, so that the final results will be clear to all, as they will be held up by a firm house of knowledge. So let us take up the first stone.

Type I collagen fibrils have circular cross sections with radii mostly distributed in between 50 and 100 nm and are characterized by an axial banding pattern with a period of 67 nm. The constituent long molecules of those fibrils, the so-called triple helices, are densely packed but their nature is such that their assembly must conciliate two conflicting requirements. One is a double-twist around the axis of the fibril induced by their chirality and the other is a periodic layered organization, corresponding to the axial banding, built by specific lateral interactions. We examine here how such a conflict could contribute to the control of the radius of a fibril. We develop our analysis with the help of two geometrical archetypes: the Hopf fibration and the algorithm of phyllotaxis. The first one provides an ideal template for a twisted bundle of fibres and the second ensures the best homogeneity and local isotropy possible for a twisted dense packing with circular symmetry. This approach shows that, as the radius of a fibril with constant double-twist increases, the periodic layered organization can not be preserved without moving from planar to helicoidal configurations. Such changes of configurations are indeed made possible by the edge dislocations naturally present in the phyllotactic pattern. The distribution of those defects is such that the lateral growth of a fibril should stay limited in the observed range. Because of our limited knowledge about the elastic constants involved, this purely geometrical development stays at a quite conjectural level.

In current work we investigate the interaction between polyguanylic acid and Ethidium Bromide (EtBr) and the changes of thermodynamic parameters due to those interactions by spectrophotometric methods. From the binding isotherms, binding constants were calculated for three different temperatures and the changes of Gibbs free energy, entropy and enthalpy for complex-formation were determined. Complex-formation with four-stranded poly(G) structure needs less conformational changes in contrast with poly(G)poly(C), and due to that, EtBr binds with 5 and not 4 nucleotides. Obtained results confirm the concept that polyguanylic acids may form four-stranded complex structures with intercalating ligand EtBr in the aqueous solution.

In this paper we discuss how the coincident detection of mobile particles in dual-color confocal images can be improved. Optimal coincidence detection requires a careful choice of experimental conditions and image acquisition parameters in order to maximize the overlap between the two detection volumes. By measuring this overlap with fluorescence cross-correlation spectroscopy, we show in particular that a small confocal field of view is necessary in order to maintain good coincidence. Most importantly, coincidence detection also requires a dedicated image analysis strategy. Traditionally, two approaches have been adopted to assess coincidence of mobile particles: fluorescence fluctuation measurements, notably cross-correlation spectroscopy, and single particle detection. Here we propose to combine these two approaches by calculating a cross-correlation coefficient for each of the detected single particles. We show that this allows to remove accidental coincidence events from a data set, and thus to unambiguously identify particles that instead carry two different fluorophores. This strategy can help increase the available concentration range for confocal coincidence measurements and detect rare binding events.

Special Issue Comments: This article about coincident detection of mobile particle in two-color confocal images is thematically related to several articles in this Special Issue, namely the review of FRET-based single-molecule fluorescence techniques by Ruedas-Rama et al.,¹ the single particle detection work presented by de Keersmaecker et al.² and the general considerations on the mathematical treatment of single molecule trajectories presented by Flomenbom³. Our study of single liposomes is also relevant to experiments involving proteins and liposomes, such as the enzyme experiments described in the review by Jørgensen and Hatzakis.⁴

We are developing a biophysical model of tumor biology. We follow a strictly quantitative approach where each step of model development is validated by comparing simulation outputs with experimental data. While this strategy may slow down our advancements, at the same time it provides an invaluable reward: we can trust simulation outputs and use the model to explore territories of cancer biology where current experimental techniques fail. Here, we review our multi-scale biophysical modeling approach and show how a description of cancer at the cellular level has led us to general laws obeyed by both in vitro and in vivo tumors.

Cancer can be viewed as a "tissue", where neoplastic cells are immersed into a peculiar microenvironment (the "tumor microenvironment", TME) which modulates tumor cell behaviour during multistep tumorigenesis. Based on this concept, antineoplastic therapy should be tuned to target not only tumor cells but also the cellular constituents of the TME. Such necessity is well exemplified by considering tumor angiogenesis, a major aspect of cancer biology.

Ion channels and transporters are increasingly recognized as relevant players in the tumor cell-TME cross-talk. For example, during tumor neo-angiogenesis, soluble factors as well as fixed components of the extracellular matrix (ECM) and membrane proteins determine signal exchange between the TME and the implicated cell types. The signalling network is coordinated by functional "hubs", which may be constituted by integrin receptors associated with other proteins to form macromolecular signalling platforms at the adhesive sites. These complexes often include ion channels.

The K⁺ channels encoded by the human ether-à-go-go related gene (Kv11.1, or hERG1) are frequently overexpressed in human cancers and regulate intracellular signalling by physically associating with integrin subunits and growth factor/chemokine receptors. In colorectal cancer (CRC) we recently identified a novel signalling pathway centered on hERG1 channels and integrins. This pathway involves the p53 protein, which is encoded by a tumor suppressor gene often mutated in human cancers. p53 controls angiogenesis, through a mechanism regulated by hERG1 K⁺ channels. The central role played by hERG1 in CRC angiogenesis suggests that targeting hERG1 may be an effective therapeutic option in patients with advanced CRC.

To better understand the above process, it is necessary to study the interlaced dynamics of the key microscopic actors by using dedicated mathematical models. We here review a simple model, of reductionist inspiration, that explores the intimate connections between apoptosis and hypoxia, passing through angiogenesis. We show that a dynamical switch takes place between the normoxia and cellular death conditions. When oxygen lacks, cells can cross the transition line and so gain their way towards the normoxia regime, by implementing point mutations that affect the p53 production and activation rate, with the involvement of K⁺ ion homeostasis, in agreement with the experimental observations.