Session V40: Focus Session: Single Molecule Biological Physics - Proteins

From single molecule to single tubules

Biological systems often make decisions upon conformational changes and assembly of single molecules. \textit{In vivo}, epithelial cells (such as the mammary gland cells) can respond to extracellular matrix (ECM) molecules, type I collagen (COL), and switch their morphology from a lobular lumen (100-200 micron) to a tubular lumen (1mm-1cm). However, how cells make such a morphogenetic decision through interactions with each other and with COL is unclear. Using a temporal control of cell-ECM interaction, we find that epithelial cells, in response to a fine-tuned percentage of type I collagen (COL) in ECM, develop various linear patterns. Remarkably, these patterns allow cells to self-assemble into a tubule of length $\sim $ 1cm and diameter $\sim $ 400 micron in the liquid phase (i.e., scaffold-free conditions). In contrast with conventional thought, the linear patterns arise through bi-directional transmission of traction force, but not through diffusible biochemical factors secreted by cells. In turn, the transmission of force evokes a long-range ($\sim $ 600 micron) intercellular mechanical interaction. A feedback effect is encountered when the mechanical interaction modifies cell positioning and COL alignment. Micro-patterning experiments further reveal that such a feedback is a novel cell-number-dependent, rich-get-richer process, which allows cells to integrate mechanical interactions into long-range ($>$ 1mm) linear coordination. Our results suggest a mechanism cells can use to form and coordinate long-range tubular patterns, independent of those controlled by diffusible biochemical factors, and provide a new strategy to engineer/regenerate epithelial organs using scaffold-free self-assembly methods.   

Studying spatial gradients of signaling proteins in mitotic spindles with time-integrated multipoint moment analysis

The organization of the mitotic spindle is orchestrated by the activities of multiple signaling proteins, such as the GTPase Ran.~ It has been proposed that the Ran pathway produces a cascade of events which gives rise to spatial gradients in the behavior of soluble proteins, which in turn produce spatial gradients in microtubule behaviors important for spindle assembly.~ Previous experiments have directly demonstrated the existence of gradients around the spindle in the upstream components of the Ran pathway, but it is still unclear if there are significant gradients in the downstream soluble components in this pathway.~ We recently developed a method, TIMMA, time-integrated multipoint moment analysis, a multipoint form of fluorescence fluctuation spectroscopy capable of quantitatively measuring the concentration, diffusion coefficient, and molecular brightness of soluble proteins throughout live cells.~ We are using TIMMA to characterize the behaviors of the upstream and downstream components of the Ran pathway in live mitotic cell to test the validity of the Ran gradient model.   

New chemical kinetics for description of chemical noise in small, heterogeneous biological systems: Beyond the paradigm of the rate constant concept

We introduce a novel chemical kinetics for quantitative description of chemical fluctuations in a small, heterogeneous biological reaction system. At first, we discuss the recently proposed renewal chemical kinetics, and its application to quantitative interpretation of the randomness in fluctuating enzymatic turnover times of a-galactosidase. From the analysis of the randomness parameter data of the single enzyme reaction, one can extract valuable quantitative information about the enzyme reaction system, beyond the reach of the conventional Michaelis-Menten analysis. Next, we discuss a new universal behavior in the time dependence of the chemical fluctuation of product density for a small, heterogeneous reaction system, which is predicted from an exact analytic study for a general reaction model and confirmed by stochastic simulation results. We also discuss the dependence of the chemical noise on substrate concentrations for a heterogeneous enzyme reaction system, which turns out qualitatively different from that for a homogeneous enzyme reaction system.   

Generalized Michaelis-Menten equation for conformation-modulated monomeric enzyme catalysis

The conformational fluctuations induce complex enzymatic catalytic behaviors, which can be investigated by single-molecule experiments. We introduce a kinetic network model to describe conformation-modulated monomeric enzyme catalysis and formulate a generalized Michaelis-Menten (MM) rate equation for non-equilibrium steady-state turnover reactions. Using the flux balance method, we map the original kinetic network to a flux network with unbalanced population currents and derive the general substrate concentration dependence for the average turnover rate of non-equilibrium steady-state enzymatic reactions. In addition to the standard MM term, the generalized MM equation includes non-MM correction terms, which share the same functional form of substrate-dependence. Each non-MM correction term corresponds to a non-equilibrium unbalanced population current induced by conformational fluctuations. Under detailed balance conditions without population currents, non-MM terms vanish and the classical MM equation is recovered. With non-MM terms, the generalized MM equation provides a systematic approach to investigate non-MM behavior and predicts cooperativity, inhibition, and multiple-stability.   

Conformational-Modulated Enzyme Catalysis: Generalized Michaelis-Menten Equation and Single Molecule Measurements

The Michaelis-Menten (MM) equation is a basic rate equation to describe the substrate-dependence of enzymatic reactions; therefore, it is important to establish the validity of the MM-equation for complex enzymatic reactions and derive the correction terms when the MM equation fails. Indeed, single molecule experiments reveal complex catalytic behaviors induced by conformational dynamics and possible deviations from the MM rate equation. To model such complex catalytic reactions, we construct a generic kinetic network model characterized by multiple intermediates and multiple conformational sub-states and, by solving for the turnover rate of this network, we extend the MM equation into a general form. The generalized MM equation predicts that (i) the MM equation holds under detailed balance and (ii) the correction to the MM expression depends on the unbalanced conformational currents. Using these predictions, we can establish a relationship between the substrate-dependence of the turnover rate and the connectivity of the enzymatic network. To confirm these predictions, we propose several single molecule indicators to test the violations of detailed balance. However, these single molecule indicators may be difficult to resolve from noisy single molecule data. To address these issues, we propose information theory based data analysis methods to process single molecule time series, and apply the Baysian technique to analyze a single protein fluctuation experiment. \\[4pt] [1] Jianlan Wu and Jianshu Cao, ``Generalized Michaelis-Menten equation for conformation modulated monomeric enzymes,'' in Adv. Chem. Phys. (2011) \\[0pt] [2] Jianshu Cao, ``Michaelis-Menten Equation and Detailed Balance in Enzymatic Networks,'' JPC B, P5493 (2001) \\[0pt] [3] Jianshu Cao and Rob Silbey, ``Generic models of single molecule kinetics: self-consistent solutions,'' JPC B, 112, p12876 (2008) feature article \\[0pt] [4] Jim Witkoskie and Jianshu Cao, ``Analysis of the entire sequence of a single photon experiment on a Flavin Protein,'' JPC B, 112, p5988-5991 (2008)   

Probing short-lived protein ligand interactions with single-molecule force spectroscopy

Hydrogen bonding plays an important role in stabilizing biomolecular complexes. Although life time of individual bonds can be extremely short, cooperativity among many interactions increase the overall life time of the complex. To probe short-lived individual interactions, we have employed a recently developed atomic force microscopy technique that can carry out single-molecule force spectroscopy experiments on the microsecond timescale. Our loading-rate dependent measurements provide experimental evidence for an additional energy barrier in the biotin-streptavidin complex. The width of this barrier, estimated from the measurements, is both close to theoretical predictions based on steered molecular dynamics simulations and to the characteristic width of individual hydrogen bonds. We will present our experimental methodology and analysis of the results on biotin-streptavidin complex.   

Using Surface Curvature to Control the Dimerization of a Surface-Active Protein

Understanding the influence of surface geometry on adsorbed proteins promises new possibilities in biophysics, such as topographical catalysis, molecular recognition of geometric cues, and modulations of oligomerization or ligand binding. We have created nano-textured hydrophobic surfaces that are stable in buffer by spin coating polystyrene (PS) nanoparticles (NPs) to form patchy NP monolayers on a PS substrate, yielding flat and highly curved areas on the same sample. Moreover, we have separated surface chemistry from texture by floating a 10 nm thick film of monodisperse PS onto the NP-functionalized surface. Using Single Molecule Force Spectroscopy we have compared \textit{in situ} the distribution of detachment lengths for proteins on curved surfaces to that measured on flat surfaces. We have shown that $\beta $-Lactoglobulin ($\beta $-LG), a surface-active protein which helps to stabilize oil droplets in milk, forms dimers on both flat PS surfaces and surfaces with a radius of curvature of 100 nm, whereas $\beta $-LG monomers exist for more highly curved surfaces with radii of curvature of 25 and 40 nm. It is surprising that rather large radii of curvature have such a strong influence on proteins whose radius is only $\sim $2 nm. Furthermore, the transition from dimer to monomer with changes in surface curvature offers promising applications for proteins whose function can be modified by their oligomerization state.   

Ligand Binding Stability and Site Specific Chemical Potentials in the Anisotropic Network Model

Anisotropic network model (ANM) is a quadratic elastic model based on local force balance around each constituent material point. In ANM the potential energy functional is system specific and is built up from the connectivity and spatial distribution of elastic contacts (Atilgan et al., Biophysical J 2001, 80, 505). Because the potential energy functional is readily available in closed form, it becomes possible to derive exact expressions for energetics of the system. Recently, a simple analytical identity has been derived for free energy change associated with bond addition/removal for the Gaussian Network Model (GNM), which is one dimensional analog of ANM (Hamacher, Phys. Rev. E 2011, 84, 016703). In the current work, we generalize this formulation to ANM, and for an arbitrary potential functional which might have an acting force distribution on its constituents. Our formulation gives a complete characterization of site specific chemical potential under an arbitrary time independent force distribution. We correlate the chemical potentials with bond orientational order parameters evaluated at each site. Our results are validated on all-heavy atom networks for 15 ligand bound/unbound protein pairs, and show the decisive role of coordination geometry around each node. We show that local chemical potential is predominantly governed by changes in the bond orientational order.   

Watching Single Enzymes and Fluorescent Proteins in Action in Solution Using a Microfluidic Trap

Observation of dynamics of single biomolecules over a prolonged time without altering the biomolecule via immobilization is achieved with a specialized microfluidic device. This device, the Anti-Brownian ELectrokinetic (ABEL) Trap, uses real-time electrokinetic feedback to cancel Brownian motion of single objects in solution. First, we use the ABEL Trap to study Allophycocyanin (APC), a photosynthetic antenna-protein and popular fluorescent probe. A complex relationship between fluorescence intensity and lifetime is observed, suggesting light-induced conformational changes and radiative and non-radiative rate fluctuations. Second, we apply the ABEL Trap to single molecules of the multi-copper enzyme blue Nitrite Reductase where a fluorescent label reports on the oxidation state of the Type I Copper. Redox cycling is observed and kinetic analysis allows extraction of the microscopic rate constants in the kinetic scheme. Evidence of a substrate-induced shift of the intramolecular electron transfer rate is seen. Taken together, these observations provide windows of unprecedented detail into the dynamics of solution-phase biomolecules.