FCS is a fluorescence technique conventionally used to study the kinetics of fluorescent molecules in a dilute solution. Being a non-invasive technique, it is now drawing increasing interest for the study of more complex systems like the dynamics of DNA or proteins in living cells. Unlike an ordinary dye solution, the dynamics of macromolecules like proteins or entangled DNA in crowded environments is often slow and subdiffusive in nature. This in turn leads to longer residence times of the attached fluorophores in the excitation volume of the microscope and artifacts from photobleaching abound that can easily obscure the signature of the molecular dynamics of interest and make quantitative analysis challenging.We discuss methods and procedures to make FCS applicable to quantitative studies of the dynamics of DNA in live prokaryotic and eukaryotic cells. The intensity autocorrelation is computed function from weighted arrival times of the photons on the detector that maximizes the information content while simultaneously correcting for the effect of photobleaching to yield an autocorrelation function that reflects only the underlying dynamics of the sample. This autocorrelation function in turn is used to calculate the mean square displacement of the fluorophores attached to DNA. The displacement data is more amenable to further quantitative analysis than the raw correlation functions. By using a suitable integral transform of the mean square displacement, we can then determine the viscoelastic moduli of the DNA in its cellular environment. The entire analysis procedure is extensively calibrated and validated using model systems and computational simulations.
Fluorescence correlation spectroscopy (FCS) is an optical technique in which the fluctuations in fluorescence intensity are quantified. The time correlation function gives insight into the dynamics of the molecule in its environment: typically the diffusion coefficient in a dilute solution is measured, but the technique has been expanded to uses in more complex environments, including living cells. In these environments photobleaching and dye-dissociation can substantially introduce artifacts in the FCS data. We present a technique to correct for the artifacts introduced by photobleaching and study dye dissociation in DNA solutions.
We are using tethered particle motion (TPM) microscopy to observe protein-mediated DNA looping in the lactose
repressor system in DNA constructs with varying AT / CG content. We use these data to determine the persistence
length of the DNA as a function of its sequence content and compare the data to direct micromechanical measurements
with constant-force axial optical tweezers. The data from the TPM experiments show a much smaller sequence effect on
the persistence length than the optical tweezers experiments.
We have used constant force axial optical tweezers to understand the subtle eects of sequence variations on the
mechanical properties of DNA. Using designed sequences of DNA with nearly identical curvatures, but varied AT
content, we have shown the persistence length to be highly dependent on the elasticity of DNA. The persistence
length varies by almost thirty percent between sequences containing 61% AT and 45% AT. The biological
implications of this can be substantial, as the need to bend DNA is involved in a host of regulatory schemes,
ranging from nucleosome positioning to the formation of protein-mediated repressor and enhancer loops.
Forces on the order of a hundred femtonewtons can drastically prevent the formation of protein-mediated DNA loops,
which are a common regulatory component of cellular function and control. To investigate how such an acutely sensitive
mechanism might operate within a noisy environment, as might typically be experienced within a cell, we have studied
the response of DNA loop formation under an optically induced, fluctuating, mechanical tension. We show that
mechanical noise strongly enhances the rate of loop formation. Moreover, the sensitivity of the loop formation rate to
mechanical fluctuations is relatively independent of the baseline tension. This suggests that tension along the DNA
molecule could act as a robust means of regulating transcription in a noisy <i>in vivo</i> environment.
We have measured the entropic elasticity of ds-DNA molecules ranging from 247 to 1298 base pairs in length, using
axial optical force-clamp tweezers. We show that entropic end effects and excluded-volume forces become significant
for such short molecules. In this geometry, the effective persistence length of the shortest molecules decreases by a factor
of two compared to the established value for long molecules, and excluded-volume forces extend the molecules to about
one third of their nominal contour lengths in the absence of any external forces. We interpret these results in the
framework of a modified wormlike chain model.
Optical tweezers have become an important tool for the manipulation of single biomolecules. However, their application
to stretching biopolymers is usually limited to molecules that are several microns in length because conventional optical
tweezers manipulate molecules laterally in the focal plane of the microscope objective, a mode in which steric
hindrances from the attached microsphere and the surface are substantial. In order to study the properties of short DNA
fragments that are typically 1000 bp long, we used optical tweezers in the axial direction to pull microsphere away from
the cover glass surface. The microsphere was held in the linear region of the optical potential where the optical force is
least sensitive to the bead position. By varying the laser intensity, different stretching forces were applied to the DNA
molecule, and the axial position of the tethered microsphere was obtained from its diffraction pattern. The results
indicate that the wormlike chain model is still valid for such short DNA fragments.
Protein-mediated DNA loop formation is an important biological process that regulates key functions such as
transcription. We present a mechanical model for these DNA-protein complexes that can take effects of the
DNA sequence such induced curvature into account. This model provides the equilibrium shape and elastic
energy of the DNA loop, using boundary conditions from the protein crystal structure. We then construct
a Hamiltonian for small perturbations of the DNA around the equilibrium shape, which in turn allows us to
calculate the eigenmodes and the entropic contributions of the thermal fluctuations to the free energy of the
DNA loop. Here we present computations related to the short wild-type lactose repressor loop of <i>Escheria
coli (E. coli), </i>and find that the entropic contributions are significant and amount to up to 3.9 k<sub>B</sub>T of the free
energy. We also show that this entropic contribution from the stiffening of the DNA loop depends strongly
on the phase angle between the two operator sites, which adds to the known phasing effect of the elastic
energy of the loop.
Studying the thermal fluctuations of DNA molecules reveals not only a wealth of interesting equilibrium and nonequilibrium statistical mechanics, but is also of importance for understanding the dynamics of DNA in vivo. An instance of the latter is in the context of regulatory functions that require collaborative interactions of distant operator sites on the DNA molecule. These thermal fluctuations are extremely sensitive to mechanical constraints, such as supercoiling or mechanical tension in the DNA. The natural force scale fc on which these fluctuations are sensitive to tension is related to the persistence length l<sub>p</sub> by f<sub>c</sub> = k<sub>B</sub>T/l<sub>p</sub> = 80 fN, which is generally considered small for a crowded cellular environment. We are studying the dynamics of single DNA molecules under tension under equilibrium and non-equilibrium conditions using a modified scanning-line laser trap. This technique allows us to apply a constant force between 20 fN and 3 pN to a λ-DNA molecule while we study its behavior under two different conditions: 1) nonequilibrium studies in which we observe the relaxation trajectory of a highly extended DNA molecule as it returns to its equilibrium conformation against an applied optical force, and 2) equilibrium studies which measure fluctuations in the extension of the molecule about its mean with sub-millisecond time resolution as a function of its extension. In the nonequilibrium studies we find a marked deviation from predictions derived from the wormlike-chain (WLC) model for extended DNA molecules. In the equilibrium studies we compute the time-correlation functions of the fluctuations to determine their time constants, and model them with a simple bead-and-spring model. We observe a decrease of the fundamental time constant with increasing extension of the molecule. This suggests that the change in spring constant dominates changes in the intra-chain hydrodynamic coupling between segments as the Gaussian coil unravels into an extended conformation.
Studying the thermal fluctuations of DNA molecules reveals not only a wealth of interesting equilibrium and non-equilibrium statistical mechanics, but is also of importance for understanding the dynamics of DNA in vivo. An instance of the latter is in the context of regulatory functions that require collaborative interactions of distant operator sites on the DNA molecule. These thermal fluctuations are extremely sensitive to mechanical constraints, such as supercoiling or mechanical tension in the DNA. The natural force scale f<sub>c</sub> on which these fluctuations are sensitive to tension is related to the persistence length l<sub>p</sub> by f<sub>c</sub> = k<sub>B</sub>T/l<sub>p</sub> = 80 fN, which is generally considered small for a crowded cellular environment. We are studying the dynamics of single DNA molecules under tension under equilibrium conditions using a modified scanning-line laser trap. This technique allows us to apply a constant force between 20 fN and 3 pN to a λ-DNA molecule while we measure fluctuations of its extension with sub-millisecond time resolution. We compute the time-correlation functions of these fluctuations to determine their time constants, and model them with a simple bead-and-spring model. We observe a decrease of the fundamental time constant with increasing extension of the molecule. This suggests that the change in spring constant dominates changes in the intra-chain hydrodynamic coupling between segments as the Gaussian coil unravels into an extended conformation.
Protein-mediated DNA looping, which occurs when a linker protein binds to two operator sites on the same DNA molecule, is an important regulatory element of many biological processes such as transcription and DNA replication. In physiologic conditions, the conformation of DNA undergoes thermal fluctuations which enable the operators to align for looping. The likelihood for the operator sites to align can be significantly altered by mechanically constraining the substrate DNA. For instance, tension extends DNA and increases the free energy of operator alignment. By modeling DNA as a wormlike chain, we use statistical mechanics to show that when the loop size is greater than 100bp a tension of 500 femtonewtons can increase the time required for loop closure by two orders of magnitude. This force is small compared to the piconewton forces that are associated with RNA polymerases and other molecular motors, indicating that intracellular mechanical forces might affect transcriptional regulation. We propose that supercoiling of DNA may help to stabilize the looping process against the disruptive effective of tension. Since DNA looping is important in gene regulation and genetic transformation, our theory suggests that thermal fluctuations and response to mechanical constraints play an important role in a living cell. Indeed, recent micromechanical measurements on DNA looping have verified the importance of mechanical constraints. Besides providing perspective on these experiments we offer suggestions for future micromechanical studies.
Optical tweezers are widely used to manipulate individual biomolecules. Conventionally, they hold a molecule at a constant extension while the restoring force of the molecule is measured. Many applications, however, require that the molecule be held under constant force while its extension is measured. We developed two all-optical trapping techniques that provide such constant-force conditions together with a fast extension measurement scheme. Our techniques are based on a scanning-line optical trap, which provides a one-dimensional flat optical potential well. A position-independent lateral force is generated either by a synchronous modulation of the laser intensity during the scan or the use of an asymmetrically shaped beam profile in the back focal plane of the microscope objective. The position of the trapped particle as a measure of the extension of an attached molecule is measured by monitoring the diffraction pattern of the forward-scattered laser light. The performance of these techniques, along with consideration for the design and calibration of the instrument is discussed.