It is possible to \"weigh\" DNA molecules and other biological particles by meas
ID: 1915877 • Letter: I
Question
It is possible to "weigh" DNA molecules and other biological particles by measuring the influence of their mass on a nano-oscillator. The figure shows a thin rectangular cantilever etched out of silicon (? = 2300 kg/m3 ) with a small gold dot at the end. If pulled down and released, the end of the cantilever vibrates with simple harmonic motion, moving up and down like a diving board after a jump. When bathed with DNA molecules whose ends have been modified to bind with gold, one or more molecules may attach to the gold dot. The addition of their mass causes a very slight-but measurable-decrease in the oscillation frequency. A vibrating cantilever of mass M can be modeled as a block of mass M/3 attached to a spring. (The factor of 1/3 arises from the moment of inertia of a bar pivoted at one end.) Neither the mass nor the spring constant can be determined very accurately-perhaps to only two significant figures-but the oscillation frequency can be measured with very high precision simply by counting the oscillations. In one experiment, the cantilever was initially vibrating at exactly 12 MHz (1MHz = 10 6 Hz). Attachment of a DNA molecule caused the frequency to decrease by 58 Hz. (1) What is the spring constant of the cantilever? (2) What is the mass of the DNA that is adsorbed? (3) Such a configuration also permits sensitive detection of biological particles by monitoring the shift in oscillation frequency. Suppose the cantilever surface were chemically modified to enable binding to glycoproteins of HIV. How much would the vibration frequency of the cantilever shift if a single HIV virion were to bind to the end of the cantilever? Assume the virus is 120 nm in diameter and has a density of 1100 kg/m3 . (4) Would it be possible to detect the virus loading without the cantilever oscillating, for example, via shear deformation? The shear modulus for silicon is S = 79.92 GPa.Explanation / Answer
Nanomechanical biosensing relies on changes in the movement and deformation of micro- and nanoscale objects when they interact with biomolecules and other biological targets. This field of research has provided ever-increasing records in the sensitivity of label-free detection but it has not yet been established as a practical alternative for biological detection. We analyze here the latest advancements in the field, along with the challenges remaining for nanomechanical biosensors to become a commonly used tool in biology and biochemistry laboratories.
(1) A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by moment and shear stress. Cantilever construction allows for overhanging structures without external bracing. Cantilevers can also be constructed with trusses or slabs.
This is in contrast to a simply supported beam such as those found in a post and lintel system. A simply supported beam is supported at both ends with loads applied between the supports.
Cantilevers are widely found in construction, notably in cantilever bridges and balconies (see corbel). In cantilever bridges the cantilevers are usually built as pairs, with each cantilever used to support one end of a central section. The Forth Bridge in Scotland is an example of a cantilever truss bridge.
Temporary cantilevers are often used in construction. The partially constructed structure creates a cantilever, but the completed structure does not act as a cantilever. This is very helpful when temporary supports, or falsework, cannot be used to support the structure while it is being built (e.g., over a busy roadway or river, or in a deep valley).
(2) If the solution is pure, one can use a spectrophotometer to measure the amount of ultraviolet radiation absorbed by the bases. DNA can also be quantified by measuring the UV-induced emission of fluorescence from intercalated ethidium bromide. This method is useful if there is not enough DNA to quantify with a spectrophotometer, or if the DNA solution is contaminated. Strategies for accurately quantifying nucleic acids using these approaches are discussed here.
Example of Calculation
A sample of dsDNA was diluted 50X. The diluted sample gave a reading of 0.65 on a spectrophotometer at OD260. To determine the concentration of DNA in the original sample, perform the following calculation:
dsDNA concentration = 50 g/mL × OD260 × dilution factor
dsDNA concentration = 50 g/mL × 0.65 × 50
dsDNA concentration = 1.63 mg/mL
DNA isolation is a routine procedure to collect DNA for subsequent molecular or forensic analysis. There are three basic and two optional steps in a DNA extraction:
Study of a cantilever oscillation is a rather science - intensive problem. In many cases the general solution to the cantilever equation of motion can not be obtained in an analytical form. However, if cantilever deflections from the equilibrium position are small, oscillations of the system will be described by well-known theories.
In chapter 2.1.1 it is shown that the Hooke's law properly describes the cantilever beam deflections from the equilibrium position. That is why small amplitude oscillations of the cantilever with one clamped end are qualified as oscillations of the spring pendulum having stiffness k and some effective mass meff [1]. The difference between the effective mass meff and the real cantilever mass is that not all cantilever oscillates with the same amplitude. The largest deflection takes place near the free end with a decay to zero at the clamped end. Chapter 2.1.6 presents calculations of the effective mass of the cantilever with given dimensions.
In this chapter we consider in detail problems of possible cantilever linear oscillations modeling it as a spring pendulum. Oscillatory systems described by linear motion equation are called linear.
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