Erik G. Marklund

The lac Repressor Displays Facilitated Diffusion in Living Cells

Slide and Find Transcription factors rapidly find their specific binding sites on chromosomal DNA. It has been proposed that searching is facilitated by complementing three-dimensional diffusion with one-dimensional diffusion along DNA. Such sliding on DNA has been observed in vitro, but whether and how far transcription factors slide along chromosomes in vivo is unclear. Hammar et al. (p. 1595) used single-molecule imaging to demonstrate that the lac repressor slides into its chromosomal operators in living cells. The average sliding distance was about 45 base pairs, and the repressor frequently slid over its operator before binding. The lac repressor slides along DNA in living cells, frequently passing its operator before binding. Transcription factors (TFs) are proteins that regulate the expression of genes by binding sequence-specific sites on the chromosome. It has been proposed that to find these sites fast and accurately, TFs combine one-dimensional (1D) sliding on DNA with 3D diffusion in the cytoplasm. This facilitated diffusion mechanism has been demonstrated in vitro, but it has not been shown experimentally to be exploited in living cells. We have developed a single-molecule assay that allows us to investigate the sliding process in living bacteria. Here we show that the lac repressor slides 45 ± 10 base pairs on chromosomal DNA and that sliding can be obstructed by other DNA-bound proteins near the operator. Furthermore, the repressor frequently (>90%) slides over its natural lacO1 operator several times before binding. This suggests a trade-off between rapid search on nonspecific sequences and fast binding at the specific sequence.

Bayesian Deconvolution of Mass and Ion Mobility Spectra: From Binary Interactions to Polydisperse Ensembles

Interpretation of mass spectra is challenging because they report a ratio of two physical quantities, mass and charge, which may each have multiple components that overlap in m/z. Previous approaches to disentangling the two have focused on peak assignment or fitting. However, the former struggle with complex spectra, and the latter are generally computationally intensive and may require substantial manual intervention. We propose a new data analysis approach that employs a Bayesian framework to separate the mass and charge dimensions. On the basis of this approach, we developed UniDec (Universal Deconvolution), software that provides a rapid, robust, and flexible deconvolution of mass spectra and ion mobility-mass spectra with minimal user intervention. Incorporation of the charge-state distribution in the Bayesian prior probabilities provides separation of the m/z spectrum into its physical mass and charge components. We have evaluated our approach using systems of increasing complexity, enabling us to deduce lipid binding to membrane proteins, to probe the dynamics of subunit exchange reactions, and to characterize polydispersity in both protein assemblies and lipoprotein Nanodiscs. The general utility of our approach will greatly facilitate analysis of ion mobility and mass spectra.

Collision Cross Sections for Structural Proteomics

Ion mobility mass spectrometry (IM-MS) allows the structural interrogation of biomolecules by reporting their collision cross sections (CCSs). The major bottleneck for exploiting IM-MS in structural proteomics lies in the lack of speed at which structures and models can be related to experimental data. Here we present IMPACT (Ion Mobility Projection Approximation Calculation Tool), which overcomes these twin challenges, providing accurate CCSs up to 10(6) times faster than alternative methods. This allows us to assess the CCS space presented by the entire structural proteome, interrogate ensembles of protein conformers, and monitor molecular dynamics trajectories. Our data demonstrate that the CCS is a highly informative parameter and that IM-MS is of considerable practical value to structural biologists.

High-throughput gene expression analysis at the level of single proteins using a microfluidic turbidostat and automated cell tracking

We have developed a method combining microfluidics, time-lapsed single-molecule microscopy and automated image analysis allowing for the observation of an excess of 3000 complete cell cycles of exponentially growing Escherichia coli cells per experiment. The method makes it possible to analyse the rate of gene expression at the level of single proteins over the bacterial cell cycle. We also demonstrate that it is possible to count the number of non-specifically DNA binding LacI–Venus molecules using short excitation light pulses. The transcription factors are localized on the nucleoids in the cell and appear to be uniformly distributed on chromosomal DNA. An increase in the expression of LacI is observed at the beginning of the cell cycle, possibly because some gene copies are de-repressed as a result of partitioning inequalities at cell division. Finally, a size–growth rate uncertainty relation is observed where cells living in rich media vary more in the length at birth than in generation time, and the opposite is true for cells living in poorer media.

Transcription-factor binding and sliding on DNA studied using micro- and macroscopic models.

Significance Transcription factors (TFs) are the major regulators of gene expression. We have used a combination of computer simulations and theoretical methods to explore the atomic details for how a model TF, the lac repressor, moves on DNA in search for its specific binding site. We find that it slides along the DNA along a helical path, which allows it to probe for specific binding in a major groove. The uniqueness in the study lies in that the fully atomistic molecular dynamics model allows us to estimate the microscopic interaction energies from the TF-DNA structure and that we have developed a theoretical tool to derive macroscopic, experimentally testable, predictions for DNA residence time and sliding lengths from the microscopic interaction energies. Transcription factors search for specific operator sequences by alternating rounds of 3D diffusion with rounds of 1D diffusion (sliding) along the DNA. The details of such sliding have largely been beyond direct experimental observation. For this purpose we devised an analytical formulation of umbrella sampling along a helical coordinate, and from extensive and fully atomistic simulations we quantified the free-energy landscapes that underlie the sliding dynamics and dissociation kinetics for the LacI dimer. The resulting potential of mean force distributions show a fine structure with an amplitude of 1 kBT for sliding and 12 kBT for dissociation. Based on the free-energy calculations the repressor slides in close contact with DNA for 8 bp on average before making a microscopic dissociation. By combining the microscopic molecular-dynamics calculations with Brownian simulation including rotational diffusion from the microscopically dissociated state we estimate a macroscopic residence time of 48 ms at the same DNA segment and an in vitro sliding distance of 240 bp. The sliding distance is in agreement with previous in vitro sliding-length estimates. The in vitro prediction for the macroscopic residence time also compares favorably to what we measure by single-molecule imaging of nonspecifically bound fluorescently labeled LacI in living cells. The investigation adds to our understanding of transcription-factor search kinetics and connects the macro-/mesoscopic rate constants to the microscopic dynamics.

Structural stability of electrosprayed proteins: temperature and hydration effects

Electrospray ionization is a gentle method for sample delivery, routinely used in gas-phase studies of proteins. It is crucial for structural investigations that the protein structure is preserved, and a good understanding of how structure is affected by the transition to the gas phase is needed for the tuning of experiments to meet that requirement. Small amounts of residual solvent have been shown to protect the protein, but temperature is important too, although it is not well understood how the latter affects structural details. Using molecular dynamics we have simulated four sparingly hydrated globular proteins (Trp-cage; Ctf, a C-terminal fragment of a bacterial ribosomal protein; ubiquitin; and lysozyme) in vacuum starting at temperatures ranging from 225 K to 425 K. For three of the proteins, our simulations show that a water layer corresponding to 3 A preserves the protein structure in vacuum, up to starting temperatures of 425 K. Only Ctf shows minor secondary structural changes at lower starting temperatures. The structural conservation stems mainly from interactions with the surrounding water. Temperature scales in simulations are not directly translatable into experiments, but the wide temperature range in which we find the proteins to be stable is reassuring for the success of future single particle imaging experiments. The water molecules aggregate in clusters and form patterns on the protein surface, maintaining a reproducible hydrogen bonding network. The simulations were performed mainly using OPLS-AA/L, with cross checks using AMBER03 and GROMOS96 53a6. Only minor differences between the results from the three different force fields were observed.

Radiation damage in biological material : electronic properties and electron impact ionization in urea

Radiation damage is an unavoidable process when performing structural investigations of biological macromolecules with X-rays. In crystallography this process can be limited through damage distribution in a crystal, while for single molecular imaging it can be outrun by employing short intense pulses. Secondary electron generation is crucial during damage formation and we present a study of urea, as model for biomaterial. From first principles we calculate the band structure and energy loss function, and subsequently the inelastic electron cross-section in urea. Using Molecular Dynamics simulations, we quantify the damage and study the magnitude and spatial extent of the electron cloud coming from an incident electron, as well as the dependence with initial energy.

Formation of secondary electron cascades in single-crystalline plasma-deposited diamond upon exposure to femtosecond x-ray pulses

Secondary electron cascades were measured in high purity single-crystalline chemical vapor deposition (CVD) diamond, following exposure to ultrashort hard x-ray pulses (140 fs full width at half ma ...

A Hydrodynamic Comparison of Solution and Gas Phase Proteins and Their Complexes

The extent to which protein structures are preserved on transfer from solution to gas phase is a central question for native mass spectrometry. Here we compare the collision cross sections (Ω) of a wide range of different proteins and protein complexes (15-500 kDa) with their corresponding Stokes radii (RS). Using these methods, we find that Ω and RS are well correlated, implying overall preservation of protein structure in the gas phase. Accounting for protein hydration, a scaling term is required to bring Ω and RS into parity. Interestingly, the magnitude of this scaling term agrees almost entirely with the drag factor proposed by Millikan. RS were then compared with various different predicted values of Ω taken from their atomic coordinates. We find that many of the approaches used to obtained Ω from atomic coordinates miscalculate the physical sizes of the proteins in solution by as much as 20%. Rescaling of Ω estimated from atomic coordinates may therefore seem appropriate as a general method to bring theoretical values in line with those observed in solution.

Integrating mass spectrometry with MD simulations reveals the role of lipids in Na+/H+ antiporters

Na+/H+ antiporters are found in all kingdoms of life and exhibit catalysis rates that are among the fastest of all known secondary-active transporters. Here we combine ion mobility mass spectrometry and molecular dynamics simulations to study the conformational stability and lipid-binding properties of the Na+/H+ exchanger NapA from Thermus thermophilus and compare this to the prototypical antiporter NhaA from Escherichia coli and the human homologue NHA2. We find that NapA and NHA2, but not NhaA, form stable dimers and do not selectively retain membrane lipids. By comparing wild-type NapA with engineered variants, we show that the unfolding of the protein in the gas phase involves the disruption of inter-domain contacts. Lipids around the domain interface protect the native fold in the gas phase by mediating contacts between the mobile protein segments. We speculate that elevator-type antiporters such as NapA, and likely NHA2, use a subset of annular lipids as structural support to facilitate large-scale conformational changes within the membrane.