Computational Modelling of Wire Biosensor with Competitive Substrates Conversion Vytautas Aˇ seris Member, IAENG Abstract—Glucose biosensors are analytical devices used mainly for the recognition of glucose in blood. A wire biosensor utilizing a competitive substrates conversion is analysed in this paper. Two substrates (oxygen and glucose) are competing over the single enzyme (Aspergillus niger glucose oxidase) in the analysed reactions. However, oxygen concentration is not of any importance in this case and it is considered as disturbance. The purpose of this work was to define the parameter values of the biosensor, at which oxygen concentration does not affect the response of the biosensor. The behaviour of the biosensor is defined by the mathematical model with reaction-diffusion equations of non-linear type. The suggested mathematical model is solved numerically, by using finite difference technique, as the analytical solutions exist only for a very few selected cases because of the non-linearity in the reaction term. The simulations showed complex biosensor dynamics at various values of enzymatic membrane thickness and concentration. The calibration curves signifying the effective range of the biosensor operation were provided. Index Terms—Biosensor, modelling, competitive substrates conversion, glucose, oxygen. I. I NTRODUCTION B IOSENSORS are reliable sensing devices used for the detection of a specific substance (substrate) in the analysed solution [1]. During the biosensor action, biosensor- specific product appears which is detected and transmitted to the biosensor output device with a help of transducer element. According to the transducer type, biosensors are classified into electrochemical, electrical, optical, piezoelec- tric, thermometric [2]. Various biosensors are constantly being developed and applied in point-of-care testing, home diagnostics, environmental monitoring, research laboratories, process industry, security and biodefense and others [3], [4]. In the medical field, a majority of biosensors are included in glucose meters, blood gas analysers, electrolyte analysers, metabolite analysers and various drug detectors [1], [5], [6], [7]. The creation of new biosensors or the optimization of the existing ones by means of physical experiments is troublesome and tedious process. Part of the experiments can be replaced by using mathematical modelling [8], [9]. In most cases a biosensor is modelled as a reaction-diffusion system [4]. However, such systems usually include non-linear reaction term, which complicates the solving of the model, as the exact analytical solutions exist only for a specific set of parameter values [10]. To simulate biosensor operation in wide ranges of parameter values a digital simulations are employed [11]. Manuscript received March 14, 2014; revised April 09, 2014. This research is funded by the European Social Fund under the Global Grant measure, Project No. VP1-3.1- ˇ SMM-07-K-01-073/ MTDS-110000-583. V. Aˇ seris, PhD, is with the Department of Software Engineering, Faculty of Mathematics and Informatics, Vilnius University, LT-08303, Vilnius. e- mail: vytautas.aseris@mif.vu.lt. Glucose biosensors occupy more than 85% of all the biosensor market [12]. This type of biosensor is a compact instrument with an exceptional technology for the accurate and rapid diagnoses of blood glucose level. Various glucose biosensors were developed and analysed by using mathemat- ical modelling as long as since 1976 [13]. Consideration of insulin ”age structure” for modelling blood glucose dynamics is analysed in [14]. The dual use of horseradish peroxidase and glucose oxidase for the glucose biosensor is analysed in [15]. The effect of membrane permeability and selectivity on the performance of such sensor is analysed in [16]. A layer by layer assembling of the biosensor model is common for various biosensors, including glucose sen- sors [17]. The same approach is applied in this work to build the mathematical model of the wired biosensor. Biosen- sor with competitive substrates conversion in this work is modelled and targeted as the glucose detection sensor. Two substrates - glucose and oxygen - are capable of binding with one of the more common and relatively cheap enzymes analysed in this paper - Aspergillus niger glucose oxidase. However, only the detection and recognition of glucose is im- portant. The purpose of this work was to analyse biosensors behaviour numerically and to define the configuration of the biosensor, at which the influence of the oxygen concentration is minimal. II. PROPERTIES OF THE BIOSENSOR Physical biosensor is considered as a system consisting of wire electrode, which is covered with enzyme layer. The cross-section of this bioelectrode is displayed in Fig. 1. En- zyme (Aspergillus niger glucose oxidase) reacts with oxygen and glucose in the cyclic reaction: E ox + GlucoseGGGA E red + δ-glucolactone, (1) E red +O 2 GGGA E ox +H 2 O 2 . (2) In the terms of substrates and product the reaction scheme (1-2) can be written as follows: E ox +S gl k 1 GGGGGGB F GGGGGG k -1 ES k 2 GGGA E red +P 1 , (3) E red +S o k 3 GGGGGGA E ox +P, (4) where E ox , E red and ES stand for the oxidized enzyme, the reduced enzyme and the enzyme-substrate complex, respectively, P and P 1 are the reaction products, similarly as in [18]. The large difference of the timescales [19] in the reaction network (3) and (4) creates difficulties for simulating the temporal evolution of the network and for understanding Proceedings of the World Congress on Engineering 2014 Vol II, WCE 2014, July 2 - 4, 2014, London, U.K. ISBN: 978-988-19253-5-0 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2014