How to connect time-lapse recorded trajectories of motile microorganisms with dynamical models in continuous time.

We provide a tool for data-driven modeling of motility, data being time-lapse recorded trajectories. Several mathematical properties of a model to be found can be gleaned from appropriate model-independent experimental statistics, if one understands how such statistics are distorted by the finite sampling frequency of time-lapse recording, by experimental errors on recorded positions, and by conditional averaging. We give exact analytical expressions for these effects in the simplest possible model for persistent random motion, the Ornstein-Uhlenbeck process. Then we describe those aspects of these effects that are valid for any reasonable model for persistent random motion. Our findings are illustrated with experimental data and Monte Carlo simulations.

Ratchets in hydrodynamic flow: more than waterwheels.

The transport of objects in microfluidic arrays of obstacles is a surprisingly rich area of physics and statistical mechanics. Tom Duke's mastery of these areas had a major impact in the development of biotechnology which uses these ideas at an increasing scale. We first review how biological objects are transported in fluids at low Reynolds numbers, including a discussion of electrophoresis, then concentrate on the separation of objects in asymmetric arrays, sometimes called Brownian ratchets when diffusional symmetry is broken by the structures. We move beyond this to what are called deterministic arrays where non-hydrodynamic forces in asymmetric arrays allow for extraordinary separation, and we look to the future of using these unusual arrays at the nanoscale and at the hundreds of micrometre scale. The emphasis is on how the original ideas of Tom Duke drove this work forward.

DNA-binding-protein inhomogeneity in E. coli modeled as biphasic facilitated diffusion.

We have recently shown that nonspecifically bound lac repressors are spatially inhomogeneous in E. coli cells and depends upon the location of its encoding gene and the DNA compaction state [Kuhlman and Cox, Mol. Syst. Biol. 8, 610 (2012)]. Here we model this inhomogeneity as a consequence of diffusion within and exchange between two distinct intracellular phases: the condensed chromosomal DNA and an extrachromosomal compartment, the cytoplasm. We discuss the consequences of this model for the target search process.

Gene location and DNA density determine transcription factor distributions in Escherichia coli.

The diffusion coefficient of the transcription factor LacI within living Escherichia coli has been measured directly by in vivo tracking to be D = 0.4 µm(2)/s. At this rate, simple models of diffusion lead to the expectation that LacI and other proteins will rapidly homogenize throughout the cell. Here, we test this expectation of spatial homogeneity by single-molecule visualization of LacI molecules non-specifically bound to DNA in fixed cells. Contrary to expectation, we find that the distribution depends on the spatial location of its encoding gene. We demonstrate that the spatial distribution of LacI is also determined by the local state of DNA compaction, and that E. coli can dynamically redistribute proteins by modifying the state of its nucleoid. Finally, we show that LacI inhomogeneity increases the strength with which targets located proximally to the LacI gene are regulated. We propose a model for intranucleoid diffusion that can reconcile these results with previous measurements of LacI diffusion, and we discuss the implications of these findings for gene regulation in bacteria and eukaryotes.

An excitable cortex and memory model successfully predicts new pseudopod dynamics.

Motile eukaryotic cells migrate with directional persistence by alternating left and right turns, even in the absence of external cues. For example, Dictyostelium discoideum cells crawl by extending distinct pseudopods in an alternating right-left pattern. The mechanisms underlying this zig-zag behavior, however, remain unknown. Here we propose a new Excitable Cortex and Memory (EC&M) model for understanding the alternating, zig-zag extension of pseudopods. Incorporating elements of previous models, we consider the cell cortex as an excitable system and include global inhibition of new pseudopods while a pseudopod is active. With the novel hypothesis that pseudopod activity makes the local cortex temporarily more excitable--thus creating a memory of previous pseudopod locations--the model reproduces experimentally observed zig-zag behavior. Furthermore, the EC&M model makes four new predictions concerning pseudopod dynamics. To test these predictions we develop an algorithm that detects pseudopods via hierarchical clustering of individual membrane extensions. Data from cell-tracking experiments agrees with all four predictions of the model, revealing that pseudopod placement is a non-Markovian process affected by the dynamics of previous pseudopods. The model is also compatible with known limits of chemotactic sensitivity. In addition to providing a predictive approach to studying eukaryotic cell motion, the EC&M model provides a general framework for future models, and suggests directions for new research regarding the molecular mechanisms underlying directional persistence.

'Dicty dynamics': Dictyostelium motility as persistent random motion.

We model the motility of Dictyostelium cells in a systematic data-driven manner. We deduce a minimal dynamical model that reproduces the statistical features of experimental trajectories. These are trajectories of the centroid of the cell perimeter, which is more sensitive to pseudopod activity than the usual tracking by centroid or nucleus. Our data account for cell individuality and dictate a model that extends the cell-type specific models recently derived for mammalian cells. Two generalized Langevin equations model stochastic periodic pseudopod motion parallel and orthogonal to the amoeba's direction of motion. This motion propels the amoeba with a random periodic left-right waddle in a direction that has a long persistence time. The model fully accounts for the statistics of the experimental trajectories, including velocity power spectra and auto-correlations, non-Gaussian velocity distributions, and multiplicative noise. Thus, we find neither need nor place in our data for an interpretation in terms of anomalous diffusion. The model faithfully captures cell individuality as different parameter values in the model, and serves as a basis for integrating the local mechanics of cell motion with our observed long-term behavior.

Using deep sequencing to characterize the biophysical mechanism of a transcriptional regulatory sequence.

Cells use protein-DNA and protein-protein interactions to regulate transcription. A biophysical understanding of this process has, however, been limited by the lack of methods for quantitatively characterizing the interactions that occur at specific promoters and enhancers in living cells. Here we show how such biophysical information can be revealed by a simple experiment in which a library of partially mutated regulatory sequences are partitioned according to their in vivo transcriptional activities and then sequenced en masse. Computational analysis of the sequence data produced by this experiment can provide precise quantitative information about how the regulatory proteins at a specific arrangement of binding sites work together to regulate transcription. This ability to reliably extract precise information about regulatory biophysics in the face of experimental noise is made possible by a recently identified relationship between likelihood and mutual information. Applying our experimental and computational techniques to the Escherichia coli lac promoter, we demonstrate the ability to identify regulatory protein binding sites de novo, determine the sequence-dependent binding energy of the proteins that bind these sites, and, importantly, measure the in vivo interaction energy between RNA polymerase and a DNA-bound transcription factor. Our approach provides a generally applicable method for characterizing the biophysical basis of transcriptional regulation by a specified regulatory sequence. The principles of our method can also be applied to a wide range of other problems in molecular biology.

Site-specific chromosomal integration of large synthetic constructs.

We have developed an effective, easy-to-use two-step system for the site-directed insertion of large genetic constructs into arbitrary positions in the Escherichia coli chromosome. The system uses lambda-Red mediated recombineering accompanied by the introduction of double-strand DNA breaks in the chromosome and a donor plasmid bearing the desired insertion fragment. Our method, in contrast to existing recombineering or phage-derived insertion methods, allows for the insertion of very large fragments into any desired location and in any orientation. We demonstrate this method by inserting a 7-kb fragment consisting of a venus-tagged lac repressor gene along with a target lacZ reporter into six unique sites distributed symmetrically about the chromosome. We also demonstrate the universality and repeatability of the method by separately inserting the lac repressor gene and the lacZ target into the chromosome at separate locations around the chromosome via repeated application of the protocol.

A place for everything: chromosomal integration of large constructs.

We have developed an easy, reliable two-step method for the insertion of large DNA fragments into any desired location in the E. coli chromosome. The method is based on the recombineering of a small (∼1.3 kbp) "Landing Pad" into the chromosome at the insertion site, to which the large construct is subsequently delivered via I-SceI endonuclease excision from a donor plasmid. To demonstrate the power of this method, we here show the insertion of a fragment containing the entire lac operon (∼9 kbp) into four predefined novel locations in the E. coli chromosome, a feat not possible with existing technologies. In addition, the chromosomal breaks induced by landing pad excision provide sufficient selective pressure that positive selection by antibiotics is unnecessary, making precise, exact insertion without extraneous sequence possible.

Quantitative transcription factor binding kinetics at the single-molecule level.

We investigated the binding interaction between the bacteriophage lambda-repressor CI and its target DNA using total internal reflection fluorescence microscopy. Large stepwise changes in the intensity of the red fluorescent protein fused to CI were observed as it associated with and dissociated from individually labeled single-molecule DNA targets. The stochastic association and dissociation were characterized by Poisson statistics. Dark and bright intervals were measured for thousands of individual events. The exponential distribution of the intervals allowed direct determination of the association and dissociation rate constants (k(a) and k(d), respectively). We resolved in detail how k(a) and k(d) varied as a function of three control parameters: the DNA length L, the CI dimer concentration, and the binding affinity. Our results show that although interactions with nonoperator DNA sequences are observable, CI binding to the operator site is not dependent on the length of flanking nonoperator DNA.

Persistent cell motion in the absence of external signals: a search strategy for eukaryotic cells.

BACKGROUND: Eukaryotic cells are large enough to detect signals and then orient to them by differentiating the signal strength across the length and breadth of the cell. Amoebae, fibroblasts, neutrophils and growth cones all behave in this way. Little is known however about cell motion and searching behavior in the absence of a signal. Is individual cell motion best characterized as a random walk? Do individual cells have a search strategy when they are beyond the range of the signal they would otherwise move toward? Here we ask if single, isolated, Dictyostelium and Polysphondylium amoebae bias their motion in the absence of external cues. METHODOLOGY: We placed single well-isolated Dictyostelium and Polysphondylium cells on a nutrient-free agar surface and followed them at 10 sec intervals for approximately 10 hr, then analyzed their motion with respect to velocity, turning angle, persistence length, and persistence time, comparing the results to the expectation for a variety of different types of random motion. CONCLUSIONS: We find that amoeboid behavior is well described by a special kind of random motion: Amoebae show a long persistence time ( approximately 10 min) beyond which they start to lose their direction; they move forward in a zig-zag manner; and they make turns every 1-2 min on average. They bias their motion by remembering the last turn and turning away from it. Interpreting the motion as consisting of runs and turns, the duration of a run and the amplitude of a turn are both found to be exponentially distributed. We show that this behavior greatly improves their chances of finding a target relative to performing a random walk. We believe that other eukaryotic cells may employ a strategy similar to Dictyostelium when seeking conditions or signal sources not yet within range of their detection system.

Chapter 8: Spatiotemporal dynamics in bacterial cells: real-time studies with single-event resolution.

To produce a quantitative picture of cellular life, one has to study the processes comprising it in individual living cells, quantifying intracellular dynamics with sufficient resolution to describe individual events in space and time. To perform such studies, we have recently developed a novel measurement approach, based on quantitative fluorescence microscopy, and applied it to the study of transcription in Escherichia coli and of the spatiotemporal dynamics of individual mRNA molecules in the cell (Golding and Cox, 2004, 2006a; Golding et al., 2005). The ability to detect individual events in real time depends on the engineering of an endogenous cellular process for amplifying the biological signal, in a way which allows signal detection to be independent of slow and highly stochastic cellular processes (Golding and Cox, 2006a). In this chapter, we describe the ingredients of our system and the way data is acquired and analyzed. We attempt to give general lessons for researchers who wish to implement a similar approach for the study of transcription in other organisms and, more generally, for the study of cellular processes with single-event resolution.

Isoprenylcysteine carboxy methylation is essential for development in Dictyostelium discoideum.

Members of the Ras superfamily of small GTPases and the heterotrimeric G protein gamma subunit are methylated on their carboxy-terminal cysteine residues by isoprenylcysteine methyltransferase. In Dictyostelium discoideum, small GTPase methylation occurs seconds after stimulation of starving cells by cAMP and returns quickly to basal levels, suggesting an important role in cAMP-dependent signaling. Deleting the isoprenylcysteine methyltransferase-encoding gene causes dramatic defects. Starving mutant cells do not propagate cAMP waves in a sustained manner, and they do not aggregate. Motility is rescued when cells are pulsed with exogenous cAMP, or coplated with wild-type cells, but the rescued cells exhibit altered polarity. cAMP-pulsed methyltransferase-deficient cells that have aggregated fail to differentiate, but mutant cells plated in a wild-type background are able to do so. Localization of and signaling by RasG is altered in the mutant. Localization of the heterotrimeric Ggamma protein subunit was normal, but signaling was altered in mutant cells. These data indicate that isoprenylcysteine methylation is required for intercellular signaling and development in Dictyostelium.

High-throughput analysis of spatio-temporal dynamics in Dictyostelium.

We demonstrate a time-lapse video approach that allows rapid examination of the spatio-temporal dynamics of Dictyostelium cell populations. Quantitative information was gathered by sampling life histories of more than 2,000 mutant clones from a large mutagenesis collection. Approximately 4% of the clonal lines showed a mutant phenotype at one stage. Many of these could be ordered by clustering into functional groups. The dataset allows one to search and retrieve movies on a gene-by-gene and phenotype-by-phenotype basis.

Regulation of G protein-coupled cAMP receptor activation by a hydrophobic residue in transmembrane helix 3.

cAR1, a G protein-coupled cAMP receptor, is essential for multicellular development of Dictyostelium. We previously identified a cAR1-Ile(104) mutant that appeared to be constitutively activated based on its constitutive phosphorylation, elevated affinity for cAMP, and dominant-negative effects on development as well as specific cAR1 pathways that are subject to adaptation. To investigate how Ile(104) might regulate cAR1 activation, we assessed the consequences of substituting it with all other amino acids. Constitutive phosphorylation of these Ile(104) mutants varied broadly, suggesting that they are activated to varying extents, and was correlated with polarity of the substituting amino acid residue. Remarkably, all Ile(104) substitutions, except for the most conservative, dramatically elevated the receptor's cAMP affinity. However, only a third of the mutants (those with the most polar substitutions) blocked development. These findings are consistent with a model in which polar Ile(104) substitutions perturb the equilibrium between inactive and active cAR1 conformations in favour of the latter. Based on homology with rhodopsin, Ile(104) is likely buried within inactive cAR1 and exposed to the cytoplasm upon activation. We propose that the hydrophobic effect normally promotes burial of Ile(104) and hence cAR1 inactivation, while polar substitution of Ile(104) mitigates this effect, resulting in activation.

Single molecule measurements of repressor protein 1D diffusion on DNA.

We used single-molecule imaging techniques and measured the one-dimensional diffusion of LacI repressor proteins along elongated DNA to address the long-standing puzzle of why some proteins find their targets faster than allowed by 3D diffusion. Our analysis of the LacI transcription factor's diffusion yielded four main results: (1) LacI diffuses along nonspecific sequences of DNA in the form of 1D Brownian motion; (2) the observed 1D diffusion coefficients D1vary over an unexpectedly large range, from 2.3x10(-12) cm2/s to 1.3x10(-9) cm2/s; (3) the lengths of DNA covered by these 1D diffusions vary from 120 nm to 2920 nm; and (4) the mean values of D1 and the diffusional lengths indeed predict a LacI target binding rate 90 times faster than the 3D diffusion limit.

Protein synthesis molecule by molecule.

Since the earliest days of molecular biology it has been known that even a seemingly uniform culture of bacteria is made up of cells very different from each other in terms of their levels of a given protein. This individuality has now finally been quantified at single-molecule resolution, as reported in two recent papers.

A series of Dictyostelium expression vectors for recombination cloning.

We describe a series of Dictyostelium expression vectors for recombination cloning using the Gateway technology. DNA fragments generated by high fidelity polymerase chain reaction are cloned by topoisomerase-mediated ligation, then recombined into any of several Dictyostelium expression vectors using phage lambda LR recombinase. No restriction enzymes are used in this procedure. Coding regions can be expressed from their own promoters, or from a strong actin 15 promoter as a native protein, or with an amino or carboxyl-terminal GFP fusion. Gene promoters of interest can be analyzed by controlled expression of GFP and beta-galactosidase. These vectors allow for rapid and simple characterization of novel DNA, and are ideal for high-throughput studies.

Eukaryotic transcription: what does it mean for a gene to be 'on'?

Until recently, transcription could only be observed by measuring mRNA production of cell populations, thus obscuring the kinetics at the level of individual transcription events. A new study now shows that eukaryotic transcription, visualised in individual living cells, occurs in bursts -- much as it does in prokaryotes.

Physical nature of bacterial cytoplasm.

We track the motion of individual fluorescently labeled mRNA molecules inside live E. coli cells. We find that the motion is subdiffusive, with an exponent that is robust to physiological changes, including the disruption of cytoskeletal elements. By modifying the parameters of the RNA molecule and the bacterial cell, we are able to examine the possible mechanisms that can lead to this unique type of motion, especially the effect of macromolecular crowding. We also examine the implications of anomalous diffusion on the kinetics of bacterial gene regulation, in particular, how transcription factors find their DNA targets.