© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

4.2.5 Chemical Nanosensor Theoretical Limits

Berg and Purcell³³⁷ estimated that an ideal concentration sensor, limited only by diffusion constraints and drawing through a spherical boundary surface of radius r_s, provides a minimum detectable concentration differential Dc / c of

{Eqn. 4.6}

where Dt = time (sec), D is diffusion coefficient ~10^-9 m²/sec for small molecules (Table 3.3), and c = concentration (molecules/m³). Using a sample chamber with r_s = 10 nm, a concentration of c = 3 x 10^-3 nm^-3 for serum glucose could be measured with 1% uncertainty in Dt ~ 260 microsec, or with 0.01% uncertainty in 2.6 sec. A dedicated micron-scale nanodevice using a 10-sec sampling time could at best distinguish a 0.0005% concentration differential for small common molecules like serum glucose but only a 27% concentration differential for large rare serum molecules like somatotropin.

Berg and Purcell³³⁷ also found that the capture of small molecules at nanorobot surfaces can be surprisingly efficient. Specifically, for a spherical nanodevice of radius R, across whose surface are uniformly distributed N_r receptor spots of radius r_r, the maximum diffusion current absorbed by the receptor array, J_array, is

{Eqn. 4.7}

where J = maximum diffusive intake current, given by Eqn. 3.4. For r_r = 1 nm and R = 1 micron, the J_array is fully 50% of J using only N_r = 3100 surface receptors, which occupy a mere 0.1% of the total device surface area.

For a purely sensory spherical nanodevice, a uniform distribution of a relatively small number of chemoreceptors confers optimal sensitivity. However, in applications where sensors (which attract and then release) are in competition with pumps (which strongly attract and then remove) for the same target molecules at the nanodevice surface, greater sensing efficiency may be achieved by clustering the sensors, as in a "nose" organ.⁴³⁷

Proteins may be modified as they age within biological cells. For instance, under steady state conditions, ~10% of protein molecules may exhibit carbonyl (oxidation) modifications,²¹³⁸ glycosylation (non-enzymatic), and dysfunctional proteins may be ubiquitinized (Chapter 13) and phosphorylated under enzyme control. Heat shock also modifies proteins. Chemosensor receptors must be carefully designed to accommodate changes in target ligand structures or sites that are likely to be subject to such alterations.

Last updated on 17 February 2003