Mean survival times of absorbing triply periodic minimal surfaces

Block copolymer microparticles comprising inverse bicontinuous phases prepared via polymerization-induced self-assembly

Traditionally, post-polymerization processing routes have been used to obtain a wide range of block copolymer morphologies. However, this self-assembly approach is normally performed at rather low copolymer concentration, which precludes many potential applications. Herein, we report a facile method for the preparation of block copolymer particles exhibiting complex internal morphology via polymerization-induced self-assembly (PISA). More specifically, a series of diblock copolymers were synthesized by reversible addition-fragmentation chain transfer (RAFT) alternating copolymerization of styrene (St) with N-phenylmaleimide (NMI) using a poly(N,N-dimethylacrylamide) (PDMAC) stabilizer as a soluble precursor. Conducting such PISA syntheses in a 50 : 50 w/w ethanol/methyl ethyl ketone (MEK) mixture leads directly to the formation of micrometer-sized PDMAC-P(St-alt-NMI) diblock copolymer particles at 20% w/w solids. Adjusting the degree of polymerization (DP) of the core-forming P(St-alt-NMI) block to target highly asymmetric copolymer compositions provides convenient access to an inverse bicontinuous phase. TEM studies of intermediate structures provide useful insights regarding the mechanism of formation of this phase. SEM studies indicate that the final copolymer particles comprise perforated surface layers and possess nanostructured interiors. In addition, control experiments using 1,4-dioxane suggest that the high chain mobility conferred by the MEK co-solvent is essential for the formation of such inverse bicontinuous structures. One-pot PISA formulations are reproducible and involve only cheap, commercially available starting materials, so they should be readily amenable to scale-up. This augurs well for the potential use of such nanostructured micrometer-sized particles as new organic opacifiers for paints and coatings.

Biomimetic block copolymer particles with gated nanopores and ultrahigh protein sorption capacity

The design of micro- or nanoparticles that can encapsulate sensitive molecules such as drugs, hormones, proteins or peptides is of increasing importance for applications in biotechnology and medicine. Examples are micelles, liposomes and vesicles. The tiny and, in most cases, hollow spheres are used as vehicles for transport and controlled administration of pharmaceutical drugs or nutrients. Here we report a simple strategy to fabricate microspheres by block copolymer self-assembly. The microsphere particles have monodispersed nanopores that can act as pH-responsive gates. They contain a highly porous internal structure, which is analogous to the Schwarz P structure. The internal porosity of the particles contributes to their high sorption capacity and sustained release behaviour. We successfully separated similarly sized proteins using these particles. The ease of particle fabrication by macrophase separation and self-assembly, and the robustness of the particles makes them ideal for sorption, separation, transport and sustained delivery of pharmaceutical substances.

Toward an Ising model of cancer and beyond

The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review the research work that we have done toward the development of an 'Ising model' of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which cells transition between states (proliferative, hypoxic and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to study the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. A discussion about the need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented. Finally, we propose the possibility of using optimization techniques, which have been used profitably to understand physical phenomena, in order to devise therapeutic (chemotherapy/radiation) strategies and to understand tumorigenesis itself.