Graphene and its derivatives such as graphene oxide (GO) and reduced GO (rGO) offer excellent electrical, mechanical and electrochemical properties. Further, due to the presence of high surface area, and a rich oxygen and defect framework, they are able to form nanocomposites with metal/semiconductor nanoparticles, metal oxides, quantum dots and polymers. Such nanocomposites are becoming increasingly useful as electrochemical biosensing platforms. In this review, we present a brief introduction on the aforementioned graphene derivatives, and discuss their synthetic strategies and structure–property relationships important for biosensing. We then highlight different nanocomposite platforms that have been developed for electrochemical biosensing, introducing enzymatic biosensors, followed by non-enzymatic biosensors and immunosensors. Additionally, we briefly discuss their role in the emerging field of biomedical cell capture. Finally, a brief outlook on these topics is presented.

We consider the cutoff phenomenon in the context of families of ergodic Markov transition functions. This includes classical examples such as families of ergodic finite Markov chains and Brownian motion on families of compact Riemannian manifolds. We give criteria for the existence of a cutoff when convergence is measured in $L^p$-norm, $1 < p < \infty$. This allows us to prove the existence of a cutoff in cases where the cutoff time is not explicitly known. In the reversible case, for $1 < p\le \infty$, we show that a necessary and sufficient condition for the existence of a max-$L^p$ cutoff is that the product of the spectral gap by the max-$L^p$ mixing time tends to infinity. This type of condition was suggested by Yuval Peres. Illustrative examples are discussed.

Diabetes has become a chronic metabolic disorder, and the growing diabetes population makes medical care more important. We investigated using a portable and noninvasive contact lens as an ideal sensor for diabetes patients whose tear fluid contains glucose. The key feature is the reversible covalent interaction between boronic acid and glucose, which can provide a noninvasive glucose sensor for diabetes patients. We present a phenylboronic acid (PBA)-based HEMA contact lens that exhibits a reversible swelling/shrinking effect to change its thickness. The difference in thickness can be detected in a picture taken with a smartphone and analyzed using software. Our novel technique offers the following capabilities: (i) non-enzymatic and continuous glucose detection with the contact lens; (ii) no need for an embedded circuit and power source for the glucose sensor; and (iii) the use of a smartphone to detect the change in thickness of the contact lens with no need for additional photo-sensors. This technique is promising for a noninvasive measurement of the glucose level and simple implementation of glucose sensing with a smartphone.

Graphene oxide (GO), a derivative of graphene, and its related nanomaterials have attracted much attention in recent years due to the excellent biocompatibility and large surface area of GO with abundant oxygen functional groups, which further enable it to serve as a nano-bio interface. Herein, we demonstrate the induction of blue fluorescence in GO suspensions via a mild thermal annealing procedure. Additionally, this procedure preserves the oxygen functional groups on the graphene plane which enables the conjugation of cancer drugs without obvious cytotoxicity. Consequently, we demonstrate the capability of GO to simultaneously play the dual-role of a: (i) cellular imaging agent and (ii) drug delivery agent in CT26 cancer cells without the need for additional fluorescent protein labeling. Our method offers a simple, controllable strategy to tune and enhance the fluorescence property of GO, which shows potential for biomedical applications and fundamental studies.

Recent advances in the development of immunosensors using polymeric nanomaterials and nanoparticles have enabled a wide range of new functions and applications in diagnostic and prognostic research. One fundamental challenge that all immunosensors must overcome is to provide the specificity of target molecular recognition by immobilizing antibodies, antibody fragments, and/or other peptides or oligonucleotide molecules that are capable of antigen recognition on a compact device surface. This review presents progress in the application of immobilization strategies including the classical adsorption process, affinity attachment, random cross-linking and specific covalent linking. The choice of immobilization methods and its impact on biosensor performance in terms of capture molecule loading, orientation, stability and capture efficiency are also discussed in this review.