Professor Ashraf Alam led a team of engineers at Purdue University, Indiana, in creating the mathematical model, which can relate the shape of a biosensor to its performance. "Many universities and companies are conducting experiments in biosensors," Alam said. "The problem is that until now there has been no way to consistently interpret the wealth of data available to the research community. Our work provides a completely different perspective on how to analyze their data and how to interpret them." Biosensors are portable devices that integrate electronic circuitry with biological molecules such as antibodies or DNA. They are designed to capture and detect specific target molecules, allowing them to identify pathogens, DNA or other substances. As such they have a myriad of uses, ranging from drug research and delivery, through medical diagnostics to environmental monitoring. In efforts to design more sensitive devices, engineers have created sensors with various geometries: some capture the biomolecules on a flat, or planar surface, others use a single cylindrical nanotube as a sensing element, and others use several nanotubes, arranged in a crisscrossing pattern like overlapping sticks. Although it has been clear for several years that smaller devices, specifically those built on the scale of nanometres, are more sensitive, Alam explained that researchers haven't known why. "Everyone presumes that the nanometre-scale sensors are better simply because they are closer to the size of the target molecules," he said. The idea is that if the sensor is too large, the target molecule is dwarfed and too hard to locate once it's caught by the sensor.Alam likened this to "trying to see a small speck on a large surface". On the other hand, if the sensor is a similar size to the target, then it's much easier to spot.When they tested this theory, what the engineers actually found was that the smaller sensors work better because they can capture the target molecules better, rather than detect them better. "It's not what happens after the molecule is captured that determines how well the sensor works. It's how fast the sensor actually captures the molecule to begin with that matters most." The distinction is important for the design of biosensors and it explains why biosensors with a single nanotube perform better than sensors containing several nanotubes or flat planar sensors. A single nanotube eliminates a phenomenon called 'diffusion slow down'. As a result, target molecules move faster toward the nanotube. The reason smaller sensors capture molecules more effectively is because using a single nanotube sensor eliminates a phenomenon called "diffusion slow down." As a result, target molecules move faster toward single nanotubes than other structures. One obstacle that has prevented researchers from finding this out before is that biosensor analysis is too computationally difficult to perform with conventional approaches. To get round this, Alam and his team, including his student Pradeep Nair, used a mathematical technique called 'Cantor transformation' to simplify the calculations. "That is the most important aspect of this work," Nair said. "You could not effectively analyse the physics behind these biosensors by using brute force with massive computing resources. It either could not be done, or you would not be able to get consistent results." The researchers tested and validated their model with experimental data from various other laboratories. The work is published in the 21 December edition of the journal Physical Review Letters. They will now concentrate on applying the model to analyse the performance of a 'fractal sponge', a shape containing many pores which has applications in drug delivery and filtration. As Alam pointed out, the new model does prove smaller is better but also that the increased sensitivity is thanks to molecule speed. "This acceleration starts coming in when you make sensors on the size scale of tens of nanometres. That is when you will get a real advantage," he added.