1^st Prize Winner

Mr Wang Fei, Department of Mathematics, National University of Singapore

This paper is an exploration of introductory topics in algebraic geometry, focusing on plane curves. It contains a brief on projective space and on the group law on cubic curves. The key research objective is developing an algebraic relation for the 9 points of intersection of 2 or more cubics.

This leads to some original results (Theorem 3.2 and Corollary 3.3) for the case of degenerate cubic curves. Conjecture 3.4 relating the algebraic sum of 9 general points on a cubic to the number of cubics passing through the 9 points can be derived from these results. A construction of the homeomorphism of a nonsingular plane cubic in P2C and a torus over real numbers, with self-programmed graphics showing the transformation, is
included in the appendix.

2^nd Prize Winner

B-RAF, a frequently mutated protein in cancer, is an attractive target for colorectal cancer (CRC) drug treatment. However, resistance to B-RAF inhibitor drugs has been a significant clinical challenge. Effective strategies to overcome B-RAF inhibitor drug resistance are therefore urgently needed. Here, we identify that drug resistance is perpetrated by the development of Inverse Regulation Cross-Talk between the MAPK and PI3K/AKT signaling pathways. We further find that this cross-talk resistance mechanism can be intercepted by various combinatorial inhibitor-based therapies. Our study not only establishes mechanisms of drug resistance in CRC cells, but also proposes robust strategies to overcome it, thus contributing to our concerted progress towards a cure for CRC.

3^rd Prize Winner

Dr Charlotte A.E. Hauser & Mrs Archana Mishra, Institute of Bioengineering and Nanotechnology, A*STAR

Studies on the self-assembly properties of a class of ultrasmall amphiphilic peptides by critical micelle concentration (CMC) measurements: Are these peptides able to form micelles?

Amphiphilic, self-assembling, surfactant-like peptides are interesting as they can spontaneously self-assemble into well-ordered nanostructures and aggregates, such as vesicles and micelles. Therefore they have potential applications in the field of tissue engineering, cosmetics and pharmaceuticals.

A rationally designed class of ultrasmall, amphiphilic, aliphatic peptides (tri-to heptamer) self-assemble to form nanostructures, fibrous scaffolds and hydrogels. These peptides have a characteristic motif: an amino acid tail chain of decreasing hydrophobicity capped by a polar amino acid head group. To further understand their aggregation and surfactant properties due to their amphiphilicity, this project aims to investigate if these peptides are able to form micelles.

These peptides are synthesized by solid phase synthesis and characterized by liquid chromatography-mass spectrometry and thermogravimetry. The hydrogels formed by these peptides are characterized by rheometry. The putative micelle structures are assessed by critical micelle concentration (CMC) measurements: (1) using the fluorescence probe: pyrene and (2) determining contact angles of peptide solutions. The CMC of commercially-available surfactants are also tested to verify the methods. The peptides are dissolved in water and salt solutions that mimic buffers and biological environments to study the peptide potential as biocompatible surfactants. From this class of peptides, it was observed that the trimer could form putative normal micelles.

This study provides insight into the effect of ionic solutions, peptide size and concentration on the peptide self-assembling properties. This study also demonstrates the peptides potential as easily synthesized and less toxic self-assembling surfactants. Therefore, these peptides have possible applications in biomedical, cosmetic and food industries.

Raffles Institution

 Dr Kenneth Hung, Department of Gastroenterology, Tufts Medical Center

Treatment of BRAF(V600E) in Colorectal Cancer

B-RAF, a frequently mutated protein in cancer, is an attractive target for colorectal cancer (CRC) drug treatment. However, resistance to B-RAF inhibitor drugs has been a significant clinical challenge. Effective strategies to overcome B-RAF inhibitor drug resistance are therefore urgently needed. Here, we identify that drug resistance is perpetrated by the development of Inverse Regulation Cross-Talk between the MAPK and PI3K/AKT signaling pathways. We further find that this cross-talk resistance mechanism can be intercepted by various combinatorial inhibitor-based therapies. Our study not only establishes mechanisms of drug resistance in CRC cells, but also proposes robust strategies to overcome it, thus contributing to our concerted progress towards a cure for CRC.

NUS High School of Mathematics and Science

e-AID: Enabling Assistance and Independence to Home-Alone Elderly

e-AID is a smarthome system designed to help home-alone elderly who are otherwise incapable of taking care of themselves. Through the placement of sensors and actuators in high-activity regions of the house, we can accurately determine the activity of the user, assess the danger level at all times and provide assistance if necessary. e-AID is unintrusive, cost-effective and highly customisable, allowing it to effectively ensure aging-in-place without affecting the user’s life or daily activities excessively. This system also hopes to improve communication between the elderly user and his or her family members by informing them via SMS whenever a dangerous scenario is detected, giving them the peace of mind that their relative is being well taken care of.

Ananya Kumar & Ang Yan Sheng

NUS High School of Mathematics and Science

Mr. Chai Ming Huang, NUS High School

Generalized Quantum Tic-Tac-Toe

Quantum tic-tac-toe (QT3) elegantly extends the popular game of tic-tac-toe based on quan-tum physics principles. Yet, despite the interesting and challenging gameplay, not much research has been done on it. Hence in this paper we explore the game in terms of extension, analysis and solution. We first conjecture and prove a graph theory theorem that enables a generalization of the game (GQT3) to make it a better metaphor for quantum physics. We then show that our generalized game can always be successfully completed in a finite number of moves. Then, we begin game analysis. Firstly, we investigate the game tree size; we find that QT3 has 18 trillion possible games, substantially higher than tic-tac-toe`s 400 thousand. Next, we explore GQT3 games where players play their moves randomly; for a 3-by-3 board the expected score is a player 1 win by 0.417 points. Thereafter, we examine the Nash Equilibrium of the game; the result if two perfect players play the game against each other. We find that in this scenario, the first player will win by 0.5 points. To make the game fairer, we suggest minor variations which make the Nash Equilibrium a draw. Note that standard methods to analyze most of these would take at least a year, but our programs take only a few minutes due to various optimizations. Finally, we extend our programs into an artificial intelligence that is a perfect solution to the game.

Establishment of a proof-of-concept high content screen for small molecules inhibiting glioma growth

Reactive Oxygen Species (ROS), superoxide (O2-) and hydrogen peroxide (H2O2) have been found to play a part in the sensitivity and resistance of glioblastoma multiforme (GBM) cells to apoptotic triggers. We explored ROS as a central modulator of chemoresistance in GBM, where chemoresistance is a balance of the two species, O2- and H2O2. We used the glioma cell line U87-MG for the in vitro experiments, where we pharmacologically increased or lowered the O2-:H2O2 levels. We utilized flow cytometry and viability assays to measure the effects of manipulating these ROS levels, followed by cisplatin treatment. Next, we converted flow cytometric signals to fluorescence intensity readout, establishing the confocal microscopy platform as an imaging tool for high content screening. Lastly, we implanted pre-treated U87-MG cells reflecting in vitro conditions of elevated and lowered O2-:H2O2 orthotopically in mice. We show that a reduction in O2-:H2O2 sensitized glioma cells to apoptotic triggers while an increase in O2-:H2O2 conferred chemoresistance. We also provide proof-of-concept evidence that flow cytometry calibrates sensitivity and resistance corresponding to a decrease and increase in O2-:H2O2 respectively, and can be translated to confocal microscopy as an imaging platform for small molecule drug screening.

Shuan Lim Choon Hoh and Lloyd Yeo Wei De

Project Title

Wearable device for stroke patients

Project Category

Engineering: Materials & Bioengineering

This project explores the potential use of wearable tracking devices in stroke tele-rehabilitation. It aims to establish an affordable tracking system for doctors to remotely monitor patient exercises.