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

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

4.4.2 Nanogravimeters

Research in space medicine has discovered that micron-scale elements of the immune system have extraordinary sensitivity to gravity. One study found that bone marrow-derived (B6MP102) macrophage single cells respond after 8 seconds to exposure to a 10^-2 g hypogravity environment as indicated by increased cell spreading,⁴⁶⁸ a well-known marker of cell activation. Individual immune system cells placed in microgravity exhibit enhanced growth but depressed differentiation,⁴⁶⁸ decreased activation by concanavalin A,⁴⁷⁰ a 20% reduction in glucose metabolism, increased resistance to antibiotics, increased number of pseudopodia on monocytes, and changes in cytoplasmic streaming velocity and frequency.⁴⁶⁹

As of 1998, the exact mechanism by which the leukocyte "gravity sensor" operates remained unknown. It has been speculated that differences in densities of several organelles, such as the nucleolus, the ribosomes, and the centrioles, could generate detectable pressures on the structure of the cytoskeleton under gravitational loading^469,471 mediated through mechanosensitive stretch-activated ion channels or the extracellular matrix.⁴⁶⁸ While indirect gravitational effects that modify the cellular environment (such as reduced sedimentation or decreased thermal convection due to hypogravity) could also be responsible, a direct interaction of the gravitational force with cellular structures^472,473 appears to be the most likely sensor mechanism. For instance, if a change in gravitational loading equivalent to the force generated by a natural molecular motor (F ~ 1 pN; Section 4.4.1) is detectable by the cytoskeleton, and this force is applied to the entire mass of a (10 micron)³ cell (m ~ 10^-12 kg), then the minimum detectable gravitational acceleration is g ~ F/m ~ 1 m/sec² = 0.1 g, which should be adequate to detect the onset of hypogravity.

A nanomechanical gravity sensor of similar size to a macrophage cell may be at least 100,000 times more sensitive. For example, the energy of a tethered mass swinging freely in a uniform gravity field is approximately E_g ~ m g Dh, where Dh is the maximum vertical amplitude of the motion. To be detectable, oscillator energy must exceed thermal noise energy, so SNR ~ ln (m g Dh N_meas^1/2 / kT), giving g_min = kT e^SNR / m Dh N_meas^1/2 ~ kT e^SNR / r L⁴ N_meas^1/2 for a bob mass of density r and size L³, N_meas independent measurements, and assuming Dh ~ L. If T = 310 K, SNR = 2, N_meas = 1, and r = 21,450 kg/m³ (Pt), then g_min = 0.1 g for L ~ 1 micron, 0.01 g for L ~ 2 microns, 10^-5 g for L ~ 11 microns, and 10^-6 g for L = 20 microns, the size of the average human tissue cell (Section 8.5.1).

Regarding nanogravimeter design, for a pendulum of length L in a gravity field g ~ 9.81 m/sec² (1 g), the resonant period of the motion T_res = 2 p (L/g)^1/2 = 2 x 10^-3 sec for L = 1 micron, 9 x 10^-3 sec for L = 20 microns. If Dt_min = 1 nanosec is the minimum detectable decrease in resonant period caused by an increase in gravity from g to g + Dg, then the minimum detectable change in gravitation force is

{Eqn. 4.24}

for a medical nanorobot, where k_g = (Dt_min / 2 p) + (L/g)^1/2. For L = 1 micron, Dg / g ~ 10^-6; for L = 20 microns, Dg / g ~ 2 x 10^-7.

Last updated on 17 February 2003