Investigation of stoichiometry of T4 bacteriophage helicase loader protein (gp59)

MaxCal can infer models from coupled stochastic trajectories of gene expression and cell division

Gene expression is inherently noisy due to small numbers of proteins and nucleic acids inside a cell. Likewise, cell division is stochastic, particularly when tracking at the level of a single cell. The two can be coupled when gene expression affects the rate of cell division. Single-cell time-lapse experiments can measure both fluctuations by simultaneously recording protein levels inside a cell and its stochastic division. These information-rich noisy trajectory data sets can be harnessed to learn about the underlying molecular and cellular details that are often not known a priori. A critical question is: How can we infer a model given data where fluctuations at two levels-gene expression and cell division-are intricately convoluted? We show the principle of maximum caliber (MaxCal)-integrated within a Bayesian framework-can be used to infer several cellular and molecular details (division rates, protein production, and degradation rates) from these coupled stochastic trajectories (CSTs). We demonstrate this proof of concept using synthetic data generated from a known model. An additional challenge in data analysis is that trajectories are often not in protein numbers, but in noisy fluorescence that depends on protein number in a probabilistic manner. We again show that MaxCal can infer important molecular and cellular rates even when data are in fluorescence, another example of CST with three confounding factors-gene expression noise, cell division noise, and fluorescence distortion-all coupled. Our approach will provide guidance to build models in synthetic biology experiments as well as general biological systems where examples of CSTs are abundant.

Modeling Non-additive Effects in Neighboring Chemically Identical Fluorophores

Quantitative fluorescence analysis is often used to derive chemical properties, including stoichiometries, of biomolecular complexes. One fundamental underlying assumption in the analysis of fluorescence data─whether it be the determination of protein complex stoichiometry by super-resolution, or step-counting by photobleaching, or the determination of RNA counts in diffraction-limited spots in RNA fluorescence in situ hybridization (RNA-FISH) experiments─is that fluorophores behave identically and do not interact. However, recent experiments on fluorophore-labeled DNA origami structures such as fluorocubes have shed light on the nature of the interactions between identical fluorophores as these are brought closer together, thereby raising questions on the validity of the modeling assumption that fluorophores do not interact. Here, we analyze photon arrival data under pulsed illumination from fluorocubes where distances between dyes range from 2 to 10 nm. We discuss the implications of non-additivity of brightness on quantitative fluorescence analysis.

From Bioorganic Models to Cells

I endeavor to share how various choices-some deliberate, some unconscious-and the unmistakable influence of many others shaped my scientific pursuits. I am fascinated by how two long-term, major streams of my research, DNA replication and purine biosynthesis, have merged with unexpected interconnections. If I have imparted to many of the talented individuals who have passed through my lab a degree of my passion for uncloaking the mysteries hidden in scientific research and an understanding of the honesty and rigor it demands and its impact on the world community, then my mentorship has been successful.

Maximum Caliber Can Build and Infer Models of Oscillation in a Three-Gene Feedback Network

Single-cell protein expression time trajectories provide rich temporal data quantifying cellular variability and its role in dictating fitness. However, theoretical models to analyze and fully extract information from these measurements remain limited for three reasons: (i) gene expression profiles are noisy, rendering models of averages inapplicable, (ii) experiments typically measure only a few protein species while leaving other molecular actors-necessary to build traditional bottom-up models-unnoticed, and (iii) measured data are in fluorescence, not particle number. We recently addressed these challenges in an alternate top-down approach using the principle of Maximum Caliber (MaxCal) to model genetic switches with one and two protein species. In the present work we address scalability and broader applicability of MaxCal by extending to a three-gene (A, B, C) feedback network that exhibits oscillation, commonly known as the repressilator. We test MaxCal's inferential power by using synthetic data of noisy protein number time traces-serving as a proxy for experimental data-generated from a known underlying model. We notice that the minimal MaxCal model-accounting for production, degradation, and only one type of symmetric coupling between all three species-reasonably infers several underlying features of the circuit such as the effective production rate, degradation rate, frequency of oscillation, and protein number distribution. Next, we build models of higher complexity including different levels of coupling between A, B, and C and rigorously assess their relative performance. While the minimal model (with four parameters) performs remarkably well, we note that the most complex model (with six parameters) allowing all possible forms of crosstalk between A, B, and C slightly improves prediction of rates, but avoids ad hoc assumption of all the other models. It is also the model of choice based on Bayesian information criteria. We further analyzed time trajectories in arbitrary fluorescence (using synthetic trajectories) to mimic realistic data. We conclude that even with a three-protein system including both fluorescence noise and intrinsic gene expression fluctuations, MaxCal can faithfully infer underlying details of the network, opening future directions to model other network motifs with many species.

Maximum Caliber Can Characterize Genetic Switches with Multiple Hidden Species

Gene networks with feedback often involve interactions between multiple species of biomolecules, much more than experiments can actually monitor. Coupled with this is the challenge that experiments often measure gene expression in noisy fluorescence instead of protein numbers. How do we infer biophysical information and characterize the underlying circuits from this limited and convoluted data? We address this by building stochastic models using the principle of Maximum Caliber (MaxCal). MaxCal uses the basic information on synthesis, degradation, and feedback-without invoking any other auxiliary species and ad hoc reactions-to generate stochastic trajectories similar to those typically measured in experiments. MaxCal in conjunction with Maximum Likelihood (ML) can infer parameters of the model using fluctuating trajectories of protein expression over time. We demonstrate the success of the MaxCal + ML methodology using synthetic data generated from known circuits of different genetic switches: (i) a single-gene autoactivating circuit involving five species (including mRNA), (ii) a mutually repressing two-gene circuit (toggle switch) with seven species (including mRNA) considering stochastic time traces of two proteins, and (iii) the same toggle switch circuit considering stochastic time traces of only one of the two proteins. To further challenge the MaxCal + ML inference scheme, we repeat our analysis for the second and third scenario with traces expressed in noisy fluorescence instead of protein number to closely mimic typical experiments. We show that, for all of these models with increasing complexity and obfuscation, the minimal model of MaxCal is still able to capture the fluctuations of the trajectory and infer basic underlying rate parameters when benchmarked against the known values used to generate the synthetic data. Importantly, the model also yields an effective feedback parameter that can be used to quantify interactions within these circuits. These applications show the promise of MaxCal's ability to characterize circuits with limited data, and its utility to better understand evolution and advance design strategies for specific functions.

Building Predictive Models of Genetic Circuits Using the Principle of Maximum Caliber

Learning the underlying details of a gene network is a major challenge in cellular and synthetic biology. We address this challenge by building a chemical kinetic model that utilizes information encoded in the stochastic protein expression trajectories typically measured in experiments. The applicability of the proposed method is demonstrated in an auto-activating genetic circuit, a common motif in natural and synthetic gene networks. Our approach is based on the principle of maximum caliber (MaxCal)-a dynamical analog of the principle of maximum entropy-and builds a minimal model using only three constraints: 1) protein synthesis, 2) protein degradation, and 3) positive feedback. The MaxCal-generated model (described with four parameters) was benchmarked against synthetic data generated using a Gillespie algorithm on a known reaction network (with seven parameters). MaxCal accurately predicts underlying rate parameters of protein synthesis and degradation as well as experimental observables such as protein number and dwell-time distributions. Furthermore, MaxCal yields an effective feedback parameter that can be useful for circuit design. We also extend our methodology and demonstrate how to analyze trajectories that are not in protein numbers but in arbitrary fluorescence units, a more typical condition in experiments. This "top-down" methodology based on minimal information-in contrast to traditional "bottom-up" approaches that require ad hoc knowledge of circuit details-provides a powerful tool to accurately infer underlying details of feedback circuits that are not otherwise visible in experiments and to help guide circuit design.

Understanding DNA replication by the bacteriophage T4 replisome

The T4 replisome has provided a unique opportunity to investigate the intricacies of DNA replication. We present a comprehensive review of this system focusing on the following: its 8-protein composition, their individual and synergistic activities, and assembly in vitro and in vivo into a replisome capable of coordinated leading/lagging strand DNA synthesis. We conclude with a brief comparison with other replisomes with emphasis on how coordinated DNA replication is achieved.

A novel method to accurately locate and count large numbers of steps by photobleaching

Photobleaching event counting is a single-molecule fluorescence technique that is increasingly being used to determine the stoichiometry of protein and RNA complexes composed of many subunits in vivo as well as in vitro. By tagging protein or RNA subunits with fluorophores, activating them, and subsequently observing as the fluorophores photobleach, one obtains information on the number of subunits in a complex. The noise properties in a photobleaching time trace depend on the number of active fluorescent subunits. Thus, as fluorophores stochastically photobleach, noise properties of the time trace change stochastically, and these varying noise properties have created a challenge in identifying photobleaching steps in a time trace. Although photobleaching steps are often detected by eye, this method only works for high individual fluorophore emission signal-to-noise ratios and small numbers of fluorophores. With filtering methods or currently available algorithms, it is possible to reliably identify photobleaching steps for up to 20-30 fluorophores and signal-to-noise ratios down to ∼1. Here we present a new Bayesian method of counting steps in photobleaching time traces that takes into account stochastic noise variation in addition to complications such as overlapping photobleaching events that may arise from fluorophore interactions, as well as on-off blinking. Our method is capable of detecting ≥50 photobleaching steps even for signal-to-noise ratios as low as 0.1, can find up to ≥500 steps for more favorable noise profiles, and is computationally inexpensive.

DNA replication at the single-molecule level

A cell can be thought of as a highly sophisticated micro factory: in a pool of billions of molecules - metabolites, structural proteins, enzymes, oligonucleotides - multi-subunit complexes assemble to perform a large number of basic cellular tasks, such as DNA replication, RNA/protein synthesis or intracellular transport. By purifying single components and using them to reconstitute molecular processes in a test tube, researchers have gathered crucial knowledge about mechanistic, dynamic and structural properties of biochemical pathways. However, to sort this information into an accurate cellular road map, we need to understand reactions in their relevant context within the cellular hierarchy, which is at the individual molecule level within a crowded, cellular environment. Reactions occur in a stochastic fashion, have short-lived and not necessarily well-defined intermediates, and dynamically form functional entities. With the use of single-molecule techniques these steps can be followed and detailed kinetic information that otherwise would be hidden in ensemble averaging can be obtained. One of the first complex cellular tasks that have been studied at the single-molecule level is the replication of DNA. The replisome, the multi-protein machinery responsible for copying DNA, is built from a large number of proteins that function together in an intricate and efficient fashion allowing the complex to tolerate DNA damage, roadblocks or fluctuations in subunit concentration. In this review, we summarize advances in single-molecule studies, both in vitro and in vivo, that have contributed to our current knowledge of the mechanistic principles underlying DNA replication.

Single molecule photobleaching (SMPB) technology for counting of RNA, DNA, protein and other molecules in nanoparticles and biological complexes by TIRF instrumentation

Direct counting of biomolecules within biological complexes or nanomachines is demanding. Single molecule counting using optical microscopy is challenging due to the diffraction limit. The single molecule photobleaching (SMPB) technology for direct counting developed by our team (Shu et al., 2007 [18]; Zhang et al., 2007 [19]) offers a simple and straightforward method to determine the stoichiometry of molecules or subunits within biocomplexes or nanomachines at nanometer scales. Stoichiometry is determined by real-time observation of the number of descending steps resulted from the photobleaching of individual fluorophore. This technology has now been used extensively for single molecule counting of protein, RNA, and other macromolecules in a variety of complexes or nanostructures. Here, we elucidate the SMPB technology, using the counting of RNA molecules within a bacteriophage phi29 DNA-packaging biomotor as an example. The method described here can be applied to the single molecule counting of other molecules in other systems. The construction of a concise, simple and economical single molecule total internal reflection fluorescence (TIRF) microscope combining prism-type and objective-type TIRF is described. The imaging system contains a deep-cooled sensitive EMCCD camera with single fluorophore detection sensitivity, a laser combiner for simultaneous dual-color excitation, and a Dual-View™ imager to split the multiple outcome signals to different detector channels based on their wavelengths. Methodology of the single molecule photobleaching assay used to elucidate the stoichiometry of RNA on phi29 DNA packaging motor and the mechanism of protein/RNA interaction are described. Different methods for single fluorophore labeling of RNA molecules are reviewed. The process of statistical modeling to reveal the true copy number of the biomolecules based on binomial distribution is also described.

Dark-field illumination on zero-mode waveguide/microfluidic hybrid chip reveals T4 replisomal protein interactions

The ability of zero-mode waveguides (ZMWs) to guide light energy into subwavelength-diameter cylindrical nanoapertures has been exploited for single-molecule fluorescence studies of biomolecules at micromolar concentrations, the typical dissociation constants for biomolecular interactions. Although epi-fluorescence microscopy is now adopted for ZMW-based imaging as an alternative to the commercialized ZMW imaging platform, its suitability and performance awaits rigorous examination. Here, we present conical lens-based dark-field fluorescence microscopy in combination with a ZMW/microfluidic chip for single-molecule fluorescence imaging. We demonstrate that compared to epi-illumination, the dark-field configuration displayed diminished background and noise and enhanced signal-to-noise ratios. This signal-to-noise ratio for imaging using the dark-field setup remains essentially unperturbed by the presence of background fluorescent molecules at micromolar concentration. Our design allowed single-molecule FRET studies that revealed weak DNA-protein and protein-protein interactions found with T4 replisomal proteins.

Inferring subunit stoichiometry from single molecule photobleaching

Single molecule photobleaching is a powerful tool for determining the stoichiometry of protein complexes. By attaching fluorophores to proteins of interest, the number of associated subunits in a complex can be deduced by imaging single molecules and counting fluorophore photobleaching steps. Because some bleaching steps might be unobserved, the ensemble of steps will be binomially distributed. In this work, it is shown that inferring the true composition of a complex from such data is nontrivial because binomially distributed observations present an ill-posed inference problem. That is, a unique and optimal estimate of the relevant parameters cannot be extracted from the observations. Because of this, a method has not been firmly established to quantify confidence when using this technique. This paper presents a general inference model for interpreting such data and provides methods for accurately estimating parameter confidence. The formalization and methods presented here provide a rigorous analytical basis for this pervasive experimental tool.

Insights into Okazaki fragment synthesis by the T4 replisome: the fate of lagging-strand holoenzyme components and their influence on Okazaki fragment size

In this study, we employed a circular replication substrate with a low priming site frequency (1 site/1.1 kb) to quantitatively examine the size distribution and formation pattern of Okazaki fragments. Replication reactions by the T4 replisome on this substrate yielded a patterned series of Okazaki fragments whose size distribution shifted through collision and signaling mechanisms as the gp44/62 clamp loader levels changed but was insensitive to changes in the gp43 polymerase concentration, as expected for a processive, recycled lagging-strand polymerase. In addition, we showed that only one gp45 clamp is continuously associated with the replisome and that no additional clamps accumulate on the DNA, providing further evidence that the clamp departs, whereas the polymerase is recycled upon completion of an Okazaki fragment synthesis cycle. We found no support for the participation of a third polymerase in Okazaki fragment synthesis.

Mutational analysis of the T4 gp59 helicase loader reveals its sites for interaction with helicase, single-stranded binding protein, and DNA

Efficient DNA replication involves coordinated interactions among DNA polymerase, multiple factors, and the DNA. From bacteriophage T4 to eukaryotes, these factors include a helicase to unwind the DNA ahead of the replication fork, a single-stranded binding protein (SSB) to bind to the ssDNA on the lagging strand, and a helicase loader that associates with the fork, helicase, and SSB. The previously reported structure of the helicase loader in the T4 system, gene product (gp)59, has revealed an N-terminal domain, which shares structural homology with the high mobility group (HMG) proteins from eukaryotic organisms. Modeling of this structure with fork DNA has suggested that the HMG-like domain could bind to the duplex DNA ahead of the fork, whereas the C-terminal portion of gp59 would provide the docking sites for helicase (T4 gp41), SSB (T4 gp32), and the ssDNA fork arms. To test this model, we have used random and targeted mutagenesis to generate mutations throughout gp59. We have assayed the ability of the mutant proteins to bind to fork, primed fork, and ssDNAs, to interact with SSB, to stimulate helicase activity, and to function in leading and lagging strand DNA synthesis. Our results provide strong biochemical support for the role of the N-terminal gp59 HMG motif in fork binding and the interaction of the C-terminal portion of gp59 with helicase and SSB. Our results also suggest that processive replication may involve the switching of gp59 between its interactions with helicase and SSB.

Assembly and dynamics of Gp59-Gp32-single-stranded DNA (ssDNA), a DNA helicase loading complex required for recombination-dependent replication in bacteriophage T4

The Gp59 protein of bacteriophage T4 plays critical roles in recombination-dependent DNA replication and repair by correctly loading the replicative helicase, Gp41, onto recombination intermediates. Previous work demonstrated that Gp59 is required to load helicase onto single-stranded DNA that is saturated with Gp32, the T4 single-stranded DNA (ssDNA)-binding protein. Gp59 and Gp32 bind simultaneously to ssDNA, forming a Gp59-Gp32-ssDNA complex that is a key intermediate in helicase loading. Here we characterize the assembly and dynamics of this helicase loading complex (HLC) through changes in the fluorescent states of Gp32F, a fluorescein-Gp32 conjugate. Results show that HLC formation requires a minimum Gp32-ssDNA cluster size and that Gp59 co-localizes with Gp32-ssDNA clusters in the presence of excess free ssDNA. These and other results indicate that Gp59 targets helicase assembly onto Gp32-ssDNA clusters that form on the displaced strand of D-loops, which suggests a mechanism for the rapid initiation of recombination-dependent DNA replication. Helicase loading at the HLC requires ATP binding (not hydrolysis) by Gp41 and results in local remodeling of Gp32 within the HLC. Subsequent ATPase-driven translocation of Gp41 progressively disrupts Gp32-ssDNA interactions. Evidence suggests that Gp59 from the HLC is recycled to promote multiple rounds of helicase assembly on Gp32-ssDNA, a capability that could be important for the restart of stalled replication forks.

Photophysics of fluorescent probes for single-molecule biophysics and super-resolution imaging

Single-molecule fluorescence spectroscopy and super-resolution microscopy are important elements of the ongoing technical revolution to reveal biochemical and cellular processes in unprecedented clarity and precision. Demands placed on the photophysical properties of the fluorophores are stringent and drive the choice of appropriate probes. Such fluorophores are not simple light bulbs of a certain color and brightness but instead have their own "personalities" regarding spectroscopic parameters, redox properties, size, water solubility, photostability, and several other factors. Here, we review the photophysics of fluorescent probes, both organic fluorophores and fluorescent proteins, used in applications such as particle tracking, single-molecule FRET, stoichiometry determination, and super-resolution imaging. Of particular interest is the thiol-induced blinking of Cy5, a curse for single-molecule biophysical studies that was later overcome using Trolox through a reducing/oxidizing system but a boon for super-resolution imaging owing to the controllable photoswitching. Understanding photophysics is critical in the design and interpretation of single-molecule experiments.

Detection and quantification of biomolecular association in living cells using single-molecule microscopy

During their random motion, biomolecules experience a manifold of interactions that transiently conjoin their paths. It is extremely difficult to measure such binding events directly in the context of a living cell: interactions may be short lived, they may affect only a minority fraction of molecules, or they may not lead to a macroscopically observable effect. We describe here a new single-molecule imaging method that allows for detecting and quantifying associations of mobile molecules. By "thinning out clusters while conserving the stoichiometry of labeling" (TOCCSL), we can virtually dilute the probe directly in the cell, without affecting the fluorescence labeling of single clusters. Essentially, an analysis region is created within the cell by photobleaching; this region is devoid of active probe. Brownian diffusion or other transport processes lead to reentry of active probe into the analysis region. At the onset of the recovery process, single spots can be resolved as well-separated, diffraction-limited signals. Standard single-molecule microscopy then allows for characterizing the spots in terms of their composition and mobility.

Recombination-dependent concatemeric viral DNA replication

The initiation of viral double stranded (ds) DNA replication involves proteins that recruit and load the replisome at the replication origin (ori). Any block in replication fork progression or a programmed barrier may act as a factor for ori-independent remodelling and assembly of a new replisome at the stalled fork. Then replication initiation becomes dependent on recombination proteins, a process called recombination-dependent replication (RDR). RDR, which is recognized as being important for replication restart and stability in all living organisms, plays an essential role in the replication cycle of many dsDNA viruses. The SPP1 virus, which infects Bacillus subtilis cells, serves as a paradigm to understand the links between replication and recombination in circular dsDNA viruses. SPP1-encoded initiator and replisome assembly proteins control the onset of viral replication and direct the recruitment of host-encoded replisomal components at viral oriL. SPP1 uses replication fork reactivation to switch from ori-dependent θ-type (circle-to-circle) replication to σ-type RDR. Replication fork arrest leads to a double strand break that is processed by viral-encoded factors to generate a D-loop into which a new replisome is assembled, leading to σ-type viral replication. SPP1 RDR proteins are compared with similar proteins encoded by other viruses and their possible in vivo roles are discussed.

Insight into helicase mechanism and function revealed through single-molecule approaches

Helicases are a class of nucleic acid (NA) motors that catalyze NTP-dependent unwinding of NA duplexes into single strands, a reaction essential to all areas of NA metabolism. In the last decade, single-molecule (sm) technology has proven to be highly useful in revealing mechanistic insight into helicase activity that is not always detectable via ensemble assays. A combination of methods based on fluorescence, optical and magnetic tweezers, and flow-induced DNA stretching has enabled the study of helicase conformational dynamics, force generation, step size, pausing, reversal and repetitive behaviors during translocation and unwinding by helicases working alone and as part of multiprotein complexes. The contributions of these sm investigations to our understanding of helicase mechanism and function will be discussed.