Marriages of Mathematics and Physics: A Challenge for Biology

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences

Polymer-graphene nanoassemblies and their applications in cancer theranostics

Background and Objective: Graphene-based nanomaterials have received increasing attention due to their unique physical-chemical properties including two-dimensional planar structure, large surface area, chemical and mechanical stability, superconductivity and good biocompatibility. On the other hand, graphene-based nanomaterials have been explored as theranostics agents, the combination of therapeutics and diagnostics. In recent years, grafting hydrophilic polymer moieties have been introduced as an efficient approach to improve the properties of graphene-based nanomaterials and obtain new nanoassemblies for cancer therapy. Methods and Results: This review would illustrate biodistribution, cellular uptake and toxicity of polymer-graphene nanoassemblies and summarize part of successes achieved in cancer treatment using such nanoassemblies. Conclusion: The observations showed successful targeting functionality of the polymer-GO conjugations and demonstrated a reduction of the side effects of anti-cancer drugs for normal tissues

Cyclodextrin-based nanosystems as drug carriers for cancer therapy

Background and Objective: Cyclodextrins have been of great interest as excellent candidates for fabricating versatile nano-drug delivery systems due to their commercial availability, easy functionalization, low immunogenicity, biocompatibility and safety. The possibility of reversible inclusion complex formation between cyclodextrins and various guest molecules in association with versatile exclusive properties of cyclodextrins offer a route towards the fabrication of highly sophisticated nanostructures with enormous potential for cancer treatment. Methods and Results: The current review discusses important recent advances in the fabrication and development of cyclodextrin-based nanostructures for cancer therapy. Firstly, the formation of inclusion complexes between cyclodextrin derivatives and anticancer compounds, as well as their application, are summarized. Sec-ondly, the cyclodextrins-based nanosystems including cyclodextrin-containing polymers, cyclodextrin-based supramolecular necklaces, which consist of polyrotaxanes and polypseudorotaxanes and cyclodextrin based hydrogels accompanied by their applications in cancer treatment are highlighted. In the end, the future perspective of this field is discussed.Conclusion: Numerous investigations in this area pave the way for the flourishing of the next generation of nano-therapeutics towards enhanced cancer therapy