The effect of AFM probe geometry on diffusion to micrometer-scale reactive (electrode) interfaces is considered. A disk-shaped substrate electrode was held at a potential to reduce a species of interest (aqueous Ru(NH 3) 6 (3+)) at a diffusion-controlled rate and the current response during AFM imaging provided information on local mass transport to the interface. This approach reveals how the AFM probe influences diffusion to a reactive surface, which is of importance in more clearly delineating the conditions under which in-situ AFM can be treated as a noninvasive probe of surface processes involving mass transport (e.g., electrode reactions and crystal dissolution and growth). An assessment has been made of three types of probes: V-shaped silicon nitride contact mode probes; single beam silicon probes; and batch-fabricated scanning electrochemical-atomic force microscopy (SECM-AFM) probes. Two disk electrodes, (6.1 microm and 1.6 microm diameter) have been considered as substrates. The results indicate that conventional V-shaped contact mode probes are the most invasive and that the batch-fabricated SECM-AFM probes are the least invasive to diffusion at both of the substrates used herein. The experimental data are complemented by the development of simulations based on a simple 2D model of the AFM probe and active surface site. The importance of probe parameters such as the cantilever size, tip cone height, and cone angle is discussed, and the implications of the results for studies in other areas, such as growth and dissolution processes, are considered briefly.
We present a new approach or framework to model dynamic regulatory genetic activity. The framework is using a multi-scale analysis based upon generic assumptions on the relative time scales attached to the different transitions of molecular states defining the genetic system. At micro-level such systems are regulated by the interaction of two kinds of molecular players: macro-molecules like DNA or polymerases, and smaller molecules acting as transcription factors. The proposed genetic model then represents the larger less abundant molecules with a finite discrete state space, for example describing different conformations of these molecules. This is in contrast to the representations of the transcription factors which are-like in classical reaction kinetics-represented by their particle number only. We illustrate the method by considering the genetic activity associated to certain configurations of interacting genes that are fundamental to modelling (synthetic) genetic clocks. A largely unknown question is how different molecular details incorporated via this more realistic modelling approach lead to different macroscopic regulatory genetic models which dynamical behaviour might-in general-be different for different model choices. The theory will be applied to a real synthetic clock in a second accompanying article (Kirkilioniset al., Theory Biosci, 2011).
We model in detail a simple synthetic genetic clock that was engineered in Atkinson et al. (Cell 113(5):597-607, 2003) using Escherichia coli as a host organism. Based on this engineered clock its theoretical description uses the modelling framework presented in Kirkilionis et al. (Theory Biosci. doi: 10.1007/s12064-011-0125-0 , 2011, this volume). The main goal of this accompanying article was to illustrate that parts of the modelling process can be algorithmically automatised once the model framework we called 'average dynamics' is accepted (Sbano and Kirkilionis, WMI Preprint 7/2007, 2008c; Kirkilionis and Sbano, Adv Complex Syst 13(3):293-326, 2010). The advantage of the 'average dynamics' framework is that system components (especially in genetics) can be easier represented in the model. In particular, if once discovered and characterised, specific molecular players together with their function can be incorporated. This means that, for example, the 'gene' concept becomes more clear, for example, in the way the genetic component would react under different regulatory conditions. Using the framework it has become a realistic aim to link mathematical modelling to novel tools of bioinformatics in the future, at least if the number of regulatory units can be estimated. This should hold in any case in synthetic environments due to the fact that the different synthetic genetic components are simply known (Elowitz and Leibler, Nature 403(6767):335-338, 2000; Gardner et al., Nature 403(6767):339-342, 2000; Hasty et al., Nature 420(6912):224-230, 2002). The paper illustrates therefore as a necessary first step how a detailed modelling of molecular interactions with known molecular components leads to a dynamic mathematical model that can be compared to experimental results on various levels or scales. The different genetic modules or components are represented in different detail by model variants. We explain how the framework can be used for investigating other more complex genetic systems in terms of regulation and feedback.
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