**Nanomedicine,
Volume I: Basic Capabilities**

**©
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/sec^{2} = 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 L^{4} N_{meas}^{1/2}
for a bob mass of density r and size L^{3},
N_{meas} independent measurements, and assuming Dh
~ L. If T = 310 K, SNR = 2, N_{meas} = 1, and r
= 21,450 kg/m^{3} (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/sec^{2} (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

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