Nanostructure sensor of presence and concentration of a target molecule

• US 7,549,338 B1
• Filed: 09/28/2007
• Issued: 06/23/2009
• Est. Priority Date: 09/28/2006
• Status: Expired due to Fees

• Current Assignee: USA As Represented By The Administrator Of The NASA
• Original Assignee: United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration
• Inventors: Schipper, John F.
• Primary Examiner(s): Williams; Hezron
• Assistant Examiner(s): SAINT SURIN, JACQUES M
• Application Number:
  US11/973,998
• Time in Patent Office: 634 Days
• Field of Search: 735/92, 73/405.A, 735/79, 735/90, 735/96, 356/301
• US Class Current: 73/592
• CPC Class Codes: G01H 3/08 Analysing frequencies present in complex vibrations, e.g. comparing harmonics present acoustic presence detection G01V1/001

Abstract

Method and system (i) to determine when a selected target molecule is present or absent in a fluid, (2) to estimate concentration of the target molecule in the fluid and (3) estimate possible presence of a second (different) target molecule in the fluid, by analyzing differences in resonant frequencies of vibration of a thin beam suspended in the fluid, after the fluid has moved across the beam.

Claims

1. A method for sensing at least one or presence of, and concentration of, a target molecule that may be present in a fluid, the method comprising:

providing a first thin beam, having a strip of a selected chemical substance of a selected length D, oriented substantially parallel to a longitudinal axis of the beam, on at least one surface of the beam, where the selected chemical substance binds to a selected target molecule;

providing a first resonant frequency ω

1 of vibration of the first beam and the at least one strip;

allowing a selected test fluid, which may contain a target molecule in an unknown concentration, to flow past the first beam for a selected time duration Δ

t, to provide a modified first beam;

providing an estimated second resonant frequency ω

2(est) of vibration of the modified first beam;

providing a measured second resonant frequency ω

2(meas) of vibration of the modified first beam, where ω

2(est) is substantially different from ω

1;

when the frequency ω

2(meas) is substantially equal to ω

1, interpreting this condition as indicating that the target molecule is not present in the fluid; and

when the frequency ω

2 (meas) is substantially equal to ω

2(est), interpreting this condition as indicating that the target molecule is present in the fluid.

2. The method of claim 1, wherein said process of providing said first resonant frequency ω

1 comprises;

providing a mathematical solution for a partial differential equation that expresses an amplitude u(r,t) of a longitudinal vibration of said first reference beam with at least one selected boundary condition imposed, where r represents a vector of at least one location coordinate x for an arbitrary location on said first beam and t represents a time variable, where x is measured along said first beam longitudinal axis; and

estimating said first resonant frequency ω

1 from a first dispersion relation that relates ω

1 to at least a first parameter k_x that is determinable from the at least one boundary condition imposed on the solution u(r,t) for said first beam, where said target molecule is not present.

3. The method of claim 2, wherein said process of providing said estimated frequency ω

2(est) comprises;

providing a mathematical solution for a partial differential equation that expresses an amplitude u′

(r,t) of a longitudinal vibration of said modified first beam with at least one selected boundary condition imposed, where r represents a vector of at least one location coordinate x for an arbitrary location on said modified first beam and t represents a tine variable, where x is measured along said modified first beam longitudinal axis; and

estimating said first resonant frequency ω

2(est) from a second dispersion relation that relates ω

2 to at least one wavenumber parameter k′

_x that is determinable from the at least one boundary condition imposed on the solution u′

(r,t) for said modified first beam, where said target molecule is assumed to be present and to be attached to said modified first beam.

4. The method of claim 3, further comprising:

providing an estimate of a minimum frequency difference Δ

ω

(min)=min{|ω

2(est)−

ω

1|}, where at least one of said target molecule is present on said modified first beam; and

when an estimated frequency difference |ω

2−

ω

1| is substantially less than the minimum frequency difference Δ

ω

(min), interpreting this condition as indicating that at least one molecule, other than said target molecule, is attached to said modified first beam.

5. The method of claim 1, further comprising selecting said chemical substance to comprise either avidin or streptavidin and choosing said target molecule to comprise biotin.

6. The method of claim 1, comprising:

(i) providing an ordered sequence of N−

1 supplemental beams, numbered m=2, . . . , N(N≧

3), each substantially identical to and spaced apart from and substantially parallel to said first beam, numbered m=1, and each supplemental beam having a strip of said selected chemical substance of length substantially equal to D on at least one surface, where supplemental beam .no.m is spaced apart downstream from said first beam by a distance of approximately (m−

1)Δ

s in a direction of flow of said test fluid;

(ii) allowing said test fluid, having a known initial concentration, η

=η

1 of said target molecule, to flow across said first beam and across the N−

1 supplemental beams to provide N modified first beams, numbered m′

=1, . . . , N;

(iii) determining, for the N modified beams, whether beam no. m′

has said target molecule attached thereto;

(iv) determining a number ν

(n) of beams, among the beams no. m′

=1, . . . , n, that have said target molecule attached thereto;

(v) estimating a value, α

=α

0(η

), for which an error sum

$\mathrm{\varepsilon <br><br>}<br><br>\left(\mathrm{\alpha <br><br>}\right)=\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br><br><br>w_n<br><br><br><br>\mathrm{\nu <br><br>}<br><br>\left(n\right)-\mathrm{\eta <br><br>1exp}<br><br>\left\{-\mathrm{\alpha <br><br>}·<br><br>n·<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>s\right\}<br><br>$

is minimized, where w_n is a selected non-negative value;

(vi) repeating steps (ii)-(v) for said test fluid, having a known initial concentration, η

=η

2 (≈

η

1) of said target molecule in said test fluid;

(vii) repeating steps (ii)-(v) for said test fluid, having a known initial concentration, η

=η

3 (≈

η

1, ≈

η

2) of said target molecule in said test fluid; and

(viii) estimating a relationship, α

0=α

0(η

), between the value α

0 and a concentration η

of said target molecule in said fluid from the values α

0(θ

1), α

0(η

2) and α

0(η

3).

7. The method of claim 6, further comprising:

(ix) providing said first beam, numbered m=1, and said ordered sequences of N−

1 supplemental beams, numbered m=2, . . . , N (N≧

3), each substantially identical to and spaced apart from and substantially parallel to said first beam, numbered m=1, and each supplemental beam having said strip of said selected chemical substance of length substantially equal to D on at least on surface, where supplemental beam .no. m is spaced apart downstream from said first beam by a distance of approximately (m−

1)Δ

s in a direction of flow of said test fluid;

(x) allowing said selected test fluid, having said unknown concentration of said target molecule, to flow across said first beam and across said N−

1 supplemental beams to provide said N modified first beams, numbered m′

=1, . . . , N;

(xi) determining, for said N modified beams, whether said beam no. m′

has said target molecule attached thereto;

(xii) determining a number ν

′

(n) of beams, among said modified beams, no. m′

=1, . . . , n, that have said target molecule attached thereto;

(xiii) estimating a concentration value η

′

for said target molecule in said selected test fluid for which an error sum

${\mathrm{\varepsilon <br><br>}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\alpha <br><br>}<br><br><br><br>0\right)=\underset{n=1}{\overset{N}{\sum <br><br>}}<br><br><br><br>w_n<br><br><br><br>{\mathrm{\nu <br><br>}}^{\mathrm{\prime <br><br>}}<br><br>\left(n\right)-{\mathrm{\eta <br><br>}}^{\mathrm{\prime <br><br>}}<br><br>\exp <br><br>\left\{-\mathrm{\alpha <br><br>}<br><br><br><br>0<br><br>\left({\mathrm{\eta <br><br>}}^{\mathrm{\prime <br><br>}}\right)·<br><br>n·<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>s\right\}<br><br>$

is minimized; and

(xiv) interpreting this condition as indicating that said concentration value for said target molecule in said selected test fluid is approximately η

′

.