Session W40: Single Molecule Biophysics

Crowding Effects on the Unfolding of Ubiquitin

Using a coarse-grained representation of polypeptide chains, we probed the mechanical stability of Ubiquitin (Ub) monomers and trimers ((Ub)$_3$) in the presence of monodisperse spherical crowding agents. Our findings indicate that crowding increases the volume fraction ($\Phi_c$)-dependent average force ($\langle f_u(\Phi_c) \rangle$), relative to the value at $\Phi_c = 0$, needed to unfold Ub and the polyprotein. Furthermore, we found that average unfolding forces increase with decreasing crowder diameter ($\sigma_c$). The average unfolding force $\langle f_u(\Phi_c) \rangle$ depends on the ratio $\frac{D}{R_g}$, where $D \approx \sigma_c (\frac{\pi}{6 \Phi_c})^{\frac{1}{3}}$ with $R_g$ being the radius of gyration of Ub (or (Ub)$_3$) in the unfolded state. Examination of the unfolding pathways shows that, relative to $\Phi_c = 0$, crowding promotes reassociation of ruptured secondary structural elements. Both the nature of the unfolding pathways and $\langle f_u(\Phi_c) \rangle$ for (Ub)$_3$ are altered in the presence of crowding particles with the effect being most dramatic for the subunit that unfolds last. We predict that $\langle f_u(\Phi_c) \rangle$ scales in a simple manner with $\Phi_c$.   

Electron Transfer in Myoglobin-based Single-Electron Transistors

The mechanism of electron transfer by myoglobin was investigated using nanometer-gap platinum electrodes fabricated by breaking a small junction by electromigration at cryogenic temperatures. The experimental results suggest single electron transport behavior is mediated by resonance of the electronic levels of the heme group in a single myoglobin protein. Evidence for a two-step electron tunneling process, resulting from the structural relaxation of the protein with the addition of a single electron, was observed. Our experimental results show that the slow protein relaxation may result in resonant tunneling and the fast protein relaxation is the condition of two-step resonant tunneling behavior. The conformation and orientation of myoglobin in the gap of electrodes may significantly affect the conductance of these devices. The calculation for the conductance graph as a function of gate voltage and bias voltage was performed with the rate equations for electron tunneling via discrete quantum states and considering the two-step process. The results of calculation match those of our experiment.   

Surface-enhanced photocycle studied in a single photoreceptor protein molecule

Photoactive yellow protein (PYP) functions as a blue light sensor for bacterial vision (phototaxis). The photocycle of PYP is initiated by the absorption of a blue photon (absorption peak at 446 nm) by its para-coumaric acid (pCA) chromophore. The photon energy is stored in the pCA through photoisomerization which is subsequently transferred to the rest of the protein through a series of conformational states, finally leading to its partial unfolding (signaling). The present work captures the distinct conformational changes of PYP at the single molecule level, during the execution of its photocycle. In particular, the present work employs surface-enhanced Raman scattering (SERS) active substrates and non-resonant excitation at 514 nm. As we confirm with regular Raman spectroscopy, the photocycle of PYP cannot be excited under 514 nm irradiation. On the contrary, 514 nm photons can excite the photocycle when PYP is adsorbed on silver, as we evidence from single molecule as well as ensemble-averaged SERS. In this case, the optical absorption of PYP shows a dramatic broadening (full width at half maximum shifting from 0.4 to 0.9 eV) such that electronic excitation can occur significantly at 514 nm. Therefore, the origin of the observed ``surface-enhanced photocycle'' is understood to be of the same as ``chemical enhancement'' in SERS in view of the ``adsorbate-induced resonance states'' model (Persson, 1993).   

Rigidity effects and mechanical unfolding of proteins

We describe a new method that shows promise for evaluating the partition function for a protein under an applied external force within a Distance Constraint Model (DCM). This approach is based on an approximate account for the rigidity effects due to hydrogen bond crosslinking using Maxwell constraint counting. Within a mean-field treatment, the free energy is estimated accurately over an ensemble of accessible conformations conditional upon the breaking of various weakest-link distance constraints, as they successively break due to a series of mini structural transitions. These calculations are performed using an exact transfer matrix approach combined with a combinatorial partitioning of the structure into different parts based on separating lines of unfolding pathways. The various shortest paths over an ensemble of structures that ``crack'' open in different ways are used to obtain the appropriate Boltzmann weight, related to the work done by the external pulling force. For structures with beta-hairpin geometry, all permutations of unfolding pathways are enumerated exactly. For a simple minimal DCM, results for extension-force curves agree markedly well with experiment. Using computational methods, this approach can be used to describe single-molecule experiments on mechanical protein unfolding under different settings, such as fixed extension, or constant force conditions. This work is supported by NIH R01 GM073082.   

Physical Principles of Virus Templating through Single Molecule Dynamic Force Spectroscopy

The use of macromolecular scaffolds for hierarchical organization of molecules and materials is a common strategy in living systems that leads to emergent behavior. One characteristic of this strategy is that it generates micron-scale structures from nm-scale building blocks, possessing high-density functionality, defined at angstrom-scales by active sites; a typical example being viral capsids. We are systematically determining the physical variables necessary to consistently pattern virus particles on to nanoscale templates. This presentation will focus on our theoretical and experimental findings regarding our Dynamic force spectroscopy (DFS) measurements; a technique in which fundamental parameters related to interaction potentials can be determined. Here we present a novel theory for determining kinetic desorption rates and equilibrium free energies using DFS in which two well-defined states exist. We compare the results with force spectra measured between individual MS2 virions and chemically modified AFM tips. We also investigate the effects of solution additives, such as PEG, on microscopic kinetics and free energies. Finally, we discuss the relation of single-molecule measurements with the ensemble, and show a connection between the two in the case of bimolecular dissociation.   

Probing Protein Folding Kinetics with High-resolution, Stabilized Optical Tweezers

Single-molecule techniques provide a powerful means of exploring molecular transitions such as the unfolding and refolding of a protein. However, the quantification of bi-directional transitions and near-equilibrium phenomena poses unique challenges, and is often limited by the detection resolution and long-term stability of the instrument. We have developed unique optical tweezers methods that address these problems, including an interference-based method for high-resolution 3D bead tracking ($\sim$1 nm laterally, $\sim$0.3 nm vertically, at $>$ 100 Hz), and a continuous autofocus system that stabilizes the trap height to within 1-2 nm longterm [1,2]. We have used our instruments to quantify the force-dependent unfolding and refolding kinetics of single protein domains (e.g. spectrin in collaboration with E. Evans). These single-molecule studies are presented, together with the accompanying probabilistic analysis that we have developed. References: 1. W.P. Wong, V. Heinrich, E. Evans, Mat. Res. Soc. Symp. Proc., 790, P5.1-P5.10 (2004). 2. V. Heinrich, W.P. Wong, K. Halvorsen, E. Evans, Langmuir, 24, 1194-1203 (2008).   

Electrostatic signatures of single protein dynamics for detection with carbon nanotube sensors

Observing single molecule dynamics in real time at atomic resolution is crucial to study enzyme function, which is closely linked to the intrinsic dynamics of the enzyme and molecular interactions between enzyme and substrate. At present, techniques such as nuclear magnetic resonance (NMR) and single molecule fluorescence energy transfer (FRET) are used together with computer simulations to study single molecule dynamics. Recent progress in point-functionalization of single wall carbon nanotubes\footnote{B. R. Goldsmith et al, Science 315, 77-81 (2007).} (CNT) opens up the possibility of electronic detection of single molecule dynamics.\footnote{B. R. Goldsmith et al, Nano Lett 8, 189-194 (2008).} CNTs are ideal candidates for electronic sensing of single protein dynamics. Typical CNT diameters are 1-2 nm, comparable to both the size of proteins in solution and the electrostatic screening length in physiological solutions. CNT sensors based on point defects have potential advantages over FRET including better time resolution. We report results for the electrostatic signature of several proteins in solution, both in substrate free and bound forms, and discuss the potential for electronic detection of biologically relevant single protein dynamics using functionalized carbon nanotubes.   

Experimental Investigation of the Velocity Convergence of Jarzynski's Equality Using Single-Molecule AFM Pulling of Titin I27

Single molecule atomic force microscopy (AFM) of individual biomolecules allows one to observe high energy conformations and transitions between equilibrium states that are not otherwise observable. Jarzynski's equality has been used to extract important equilibrium information, such as free energy surfaces, from these nonequilibrium AFM measurements. However, the convergence behavior of Jarzynski's equality, i.e. the number of AFM trajectories required to adequately sample the nonequilibrium work distribution of a process, depends nontrivially on the AFM pulling schedule. Here we study the velocity dependent nature of Jarzynski's equality in AFM experiments. We reconstructed the free energy surfaces for the forced unfolding of the I27 domain of human cardiac titin via AFM using different pulling velocities. We found that the number of experimental trajectories required for convergence of Jarzynski's equality increases roughly exponentially as experimental pulling velocity is increased. We suggest optimal pulling velocities for pulling titin I27 and discuss the obstacles involved with using extreme pulling velocities.   

Real Time Single Molecule Imaging of Protein-Surface Interactions

We study the dynamics of the adsorption of protein to surfaces using real time Total Internal Reflection Fluorescence microscopy (TIRF). We have observed two mechanisms responsible for protein adsorption on surfaces: Reversible and Irreversible binding. The irreversible binding occurs on the deposition step induced by the initial deposition flow, and the reversible binding is the equilibrium binding between the proteins and the surfaces. Our study has shown that the irreversible binding is the main contribution to the surface adsorption of proteins. We will discuss the energy for GFP and fused-silica surface interaction, and also a method to prevent protein adsorption onto surfaces.   

Single molecule image deconvolution. I. Standard deviation analysis of immobile fluorescent molecules

Single molecule fluorescence imaging has been a powerful technique in studying individual processes not accessible by bulk, ensemble-averaged measurements [1]. Improvements in image analysis are required for high temporal and spatial precision in the localization of single fluorescent molecules. We present the first thorough standard deviation analysis for point spread functions (PSFs) of single immobile fluorescent molecules. Using this new single molecule image deconvolution (SMID) method, we show that 3D localization of individual molecules with sub-nanometer precision can be achieved. We have derived an expression estimating the standard error of the PSF's standard deviation, incorporating experimental effects of the number of collected photons, finite pixel size, and background noise. The localization precision obtained via this expression is approximately 1.5 times better than the current available methods. The use of SMID to extract subexposure dynamics of mobile molecules will also be discussed.\\ $[1]$. Wang, Y. M, R. H, Austin, \& Cox, E. C. 2006 \textit{Physical Review Letters} \textbf{97}, 048302(1-4).   

Monte Carlo simulation of single-molecule trapping via electrophoresis

For many biophysical studies, there is a need to observe a molecule for an extended duration without immobilizing it on a surface. The problem of trapping a single fluorescent molecule in solution is examined here via Monte Carlo numerical simulation.~ Optical forces are insufficient for trapping small molecules. Instead, trapping is executed by sensing the position and applying real-time feedback of flow to compensate diffusional displacement. Using a nanochannel as the volume of interest reduces the problem to one dimension, and with such a configuration the position of the molecule can be measured from its fluorescence in the presence of a two-focus irradiance pattern.~ The collected photons are analyzed by an algorithm developed for a field-programmable gate array controller for experimental implementation, and an electrophoretic flow provides the trapping mechanism.~ Trapping is also possible in three dimensions with two-photon excitation of the molecule from a four-focus irradiance pattern arranged as a tetrahedron or with a single focus scanning over a three-dimensional volume.   

Sub-diffraction limit differentiation of single fluorophores using Single Molecule Image Deconvolution (SMID)

In order to better understand biological systems, researchers demand new techniques and improvements in single molecule differentiation. We present a unique approach utilizing an analysis of the standard deviation of the Gaussian point spread function of single immobile fluorescent molecules. This technique, Single Molecule Image Deconvolution (SMID), is applicable to standard TIRF instrumentation and standard fluorophores. We demonstrate the method by measuring the separation of two Cy3 molecules attached to the ends of short double-stranded DNA immobilized on a surface without photobleaching. Preliminary results and further applications will be presented.   

Selection of optimal variants of Go-like models of proteins through studies of stretching

The Go-like models of proteins are constructed based on the knowledge of the native conformation. However, there are many possible choices of a Hamiltonian for which the ground state coincides with the native state. Here, we propose to use experimental data on protein stretching to determine what choices are most adequate physically. This criterion is motivated by the fact that stretching processes usually start with the native structure, in the vicinity of which the Go-like models should work the best. Our selection procedure is applied to 62 different versions of the Go model and is based on 28 proteins. We consider different potentials, contact maps, local stiffness energies, and energy scales -- uniform and non-uniform. In the latter case, the strength of the nonuniformity was governed either by specificity or by properties related to positioning of the side groups. Among them there is the simplest variant: uniform couplings and no$ i,i+2 $contacts. This choice also leads to good folding properties in most cases. We elucidate relationship between the local stiffness described by a potential which involves local chirality and the one which involves dihedral and bond angles. The latter stiffness improves folding but there is little difference between them when it comes to stretching.   

Discontinuities at the DNA supercoiling transition

While slowly turning the ends of a single molecule of DNA at constant applied force, a discontinuity was recently observed at the supercoiling transition, when a small plectoneme is suddenly formed. This can be understood as an abrupt transition into a phase in which stretched and plectonemic DNA coexist. We argue that there should be discontinuities in both the extension and the torque at the transition, and provide experimental evidence for both. To predict the sizes of these discontinuities and how they change with the overall length of DNA, we organize a theory for the coexisting plectonemic state in terms of four length-independent parameters. We also test plectoneme theories, including our own elastic rod simulation, finding discrepancies with experiment that can be understood in terms of the four coexisting state parameters.   

Pressure-driven single-file transport of DNA molecules along linear arrays of nanopits embedded in a slit-like nanochannel.

Due to the growth in nanobiofluidic technology for DNA manipulation and analysis there is growing interest in understanding the physics of DNA in nanoconfined environments. Using fluorescence video microscopy we study the transport of DNA in slit-like nanochannels with an embedded nanotopology consisting of linear arrays of nanopit structures. The nanopit structures are made via a two level fabrication process: (1) An ebeam lithography and etching step to make the nanopits followed by (2) a photolithography step to fabricate the slit. Under an applied pressure drop the DNA molecules are observed to move single-file down the nanopit array undergoing sequential pit-to-pit hops. We make systematic measurements of pressure dependent nanopit velocity. We observe two distinct transport regimes depending on whether the molecule configuration can occupy a single pit or must subtend multiple pits. We interpret our results in terms of a simple scaling picture of the free energy of chains in the linear array.