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Analytical ultracentrifugation observes concentration profiles during rotation, rather than only recovering a separated pellet. Sector-shaped sample cells rotate past optical detectors. Absorbance scans measure attenuation at selected radii. A Rayleigh interferometer compares a sample sector with a solvent reference, converting concentration-dependent refractive-index changes into fringe shifts. Repeating scans follows a sedimentation boundary or the approach to a stationary distribution.^[ref]

For a dilute solute of buoyant mass $m_b$ and translational friction $f_h$, radial force balance gives $s=m_b/f_h$, where $s$ is the sedimentation coefficient. Diffusion supplies $D=k_{B}T/f_h$. A velocity experiment resolves boundary motion and broadening; a sedimentation equilibrium experiment instead measures $d\ln c/d(r^2)=m_b{\omega }^2/(2k_{B}T)$. This follows from the Boltzmann distribution in centrifugal potential $-m_b{\omega }^2{r}^2/2$. The two approaches separate frictional size information from buoyant mass information; shape, hydration and solvent properties must be specified to infer a unique geometric dimension.

J. Michael Li is a coauthor, with Xueguang Sun and Roger M. Wartell, of the2007 study of frozen-solution conversion between an RNA hairpin and a metastable RNA dimer. The paper identifies the authors with Georgia Tech's School of Biology and gives Li's byline in this form.^[ref]

The study examined a79-nucleotide RNA with two bands in native gel electrophoresis but one in denaturing conditions. Sedimentation equilibrium supported monomer and dimer assignments. Experiments on shorter segments implicated the first21nucleotides in dimer formation.^[ref]

A useful distinction follows: two native gel bands alone do not count the number of strands in each structure. Changing the folding state can change electrophoretic mobility without changing strand mass. Combining a mobility observation with an independent association measurement addresses that ambiguity, which is central to interpreting this contribution.

Awarded to Jean Baptiste Perrin for the discontinuous structure of matter, especially sedimentation equilibrium. The Perrin sedimentation experiment describes the measurements.^[ref]

For a dilute suspended sphere in Stokes flow, the translational friction coefficient is $f_h=6\pi \eta R$, with dynamic viscosity $\eta$ and hydrodynamic radius $R$. To derive the diffusion-friction relation, put particles in a weak conservative force $F=-U^{\prime }$. Their drift velocity is $F/f_h$, while the diffusive flux is $-Ddc/dx$. At equilibrium the Boltzmann distribution gives $c^{\prime }=-c{U}^{\prime }/(k_{B}T)=cF/(k_{B}T)$. Zero total flux therefore gives $cF/f_h-DcF/(k_{B}T)=0$, hence the Stokes–Einstein relationHere $k_B$ is the Boltzmann constant, $T$ absolute temperature and $D$ the translational diffusion coefficient. The sphere, no-slip continuum-fluid and dilute thermal-equilibrium assumptions enter through the drag law and flux balance.

At $T=293.15\mathrm{K}$ and the supplied viscosity, the predicted product is $DR=2.1472\times 10^{-19}{\mathrm{m}}^3{\mathrm{s}}^{-1}$. The derived predictions and radii inferred from the measured diffusion coefficients are:

The last three agree closely at the precision of the supplied data. The ribonuclease diffusion coefficient is about $16\%$ below the spherical prediction, corresponding to a larger frictional radius than the stated radius. Hydration, shape, a different operational radius and coarse measurement precision can matter; molar mass is not an independent parameter in the spherical diffusion law. A compact constant-density globule would have $R\propto M^{1/3}$, whereas collagen's large frictional radius relative to its mass is consistent with an extended nonspherical molecule. The inferred Stokes radius is a friction-equivalent radius, not automatically a geometric half-length.

In analytical ultracentrifugation, scan the radial protein concentration while a rotor spins at known angular speed $\omega$. Optical absorbance or refractive-index interference records a moving sedimentation boundary and its diffusive broadening.^[ref] With solvent density ${\rho }_s$, partial specific volume $\bar{v}$ and molar mass $M$ in $\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$, the buoyant mass is $m_b=M(1-\bar{v}{\rho }_s)/N_A$. Force balance gives $f_{h}v=m_b{\omega }^{2}r$, so the sedimentation coefficient is $s=v/({\omega }^{2}r)=m_b/f_h$. A boundary trajectory gives $s={\omega }^{-2}d\ln r/dt$; diffusion gives $f_h=k_{B}T/D$.

Combining them gives the molar mass from sedimentation and diffusion:Known mass and buoyancy can instead determine friction from $s$ alone, and comparison with a compact sphere tests shape or hydration. In sedimentation equilibrium, the stationary radial profile obeys $d\ln c/d(r^2)=m_b{\omega }^2/(2k_{B}T)$, providing buoyant mass without a friction model. This is a sedimentation-diffusion balance in a uniform solvent, rather than density-gradient banding at an isopycnic point.

An RNA dimer is a complex containing two associated RNA molecules. The two strands can have identical or different nucleotide sequences, and they need not form one completely paired duplex. Association joins molecular partners; it is different from joining their backbones into one longer covalent RNA strand.

For an original count, two 27-nucleotide strands contain 54 residues altogether. They remain two RNA molecules in a dimer even if much of their base pairing is intermolecular. One continuous 54-residue strand with an intramolecular stem-loop has the same total residue count but a different connectivity. Strand count and RNA secondary structure are separate specifications.

A primary experiment used a 79-nucleotide RNA that gave two bands in native polyacrylamide gel electrophoresis but one band under denaturing conditions. That observation suggested alternative assemblies, but a second method was needed to test their molecular sizes. Sedimentation equilibrium measurements at 20,000 rpm used DNA standards of known size. Samples containing two native-gel bands had an apparent average molecular mass $1.6\pm 0.15$ times the monomer mass, compared with $1.1\pm 0.1$ for a preparation giving one native band. The combined evidence supported monomer and dimer assignments.^[ref]

The study also located an important 21-residue association segment and showed preparation-history effects. Heating and cooling could change the observed assembly, and some dimer states were kinetically trapped.^[ref] Thus two bands are not automatically two sequence lengths, and one predicted low-energy duplex is not sufficient experimental proof of an RNA dimer.

For a reversible self-complementary duplex, self-complementary RNA duplex population provides a quantitative two-species model. More complicated contacts, competing folds or RNA melting hysteresis require corresponding experimental and kinetic tests.

Roger M. Wartell is a biophysicist whose research connects nucleic-acid structure with physical measurements of folding and association. His Georgia Tech profile traces his training through physics degrees at Stevens and Rochester and identifies research on DNA melting, RNA-binding proteins and small RNA molecules in ice.^[ref]

With Xueguang Sun and J. Michael Li, Wartell investigated a stable RNA hairpin that could form a metastable RNA dimer in frozen solution. Their study combined gel electrophoresis, sedimentation equilibrium and temperature-dependent absorbance to distinguish structures and their interconversion.^[ref]

The scientific issue is broader than the existence of two gel bands. A band's electrophoretic mobility depends on molecular shape and experimental conditions as well as size. Independent measurements of association and thermal response help test whether the bands represent two folds of one strand or complexes containing different numbers of strands. Wartell's work illustrates how complementary physical measurements can constrain an otherwise ambiguous structural interpretation.

Sedimentation equilibrium occurs when the downward tendency of suspended particles is balanced by their diffusion, leaving a stationary concentration profile with no net particle flux. For dilute identical particles in an isothermal fluid, let $m_b=({\rho }_p-{\rho }_f)V_p$ be their buoyant mass. Balancing the gradient of ideal osmotic pressure $n{k}_{B}T$ against gravity givesHere height increases upward, and heavy particles have $m_b>0$.

The profile is a miniature atmosphere: thermal motion spreads particles upward while gravity favours lower positions. The Perrin sedimentation experiment measured particle counts at different microscope focal heights and used this competition to infer a molecular energy scale.^[ref] A stationary profile requires sufficiently slow background flow and controlled temperature; a growing deposit during ongoing settling is a different situation.