RESUMEN EJECUTIVO DE LA ESTRATEGIA DE NEGOCIO

The purpose of DHMM is to enhance the ability of tethered particle experiments to study DNA looping kinetics in vitro. For illustration, a simplified 2-state model that includes the

one looped and one unlooped tether state is used, i.e., the various possible occupancies of the repressor protein on the DNA binding sites is ignored, but the method can readily be extended to include such details. Since publication, DHMM has been used to study the kinetics of DNA looping by the Type II restriction enzyme SfiI [101].

Previously, threshold methods were applied to the data to quantify the kinetic rates be- tween various looped and unlooped states. This method involves filtering the data to extract the transitions from the noisy diffusive motion of the bead, then fitting a (single or double) exponential to the tail of a histogram of the dwell times. Both filtering and histogramming discard potentially useful information; moreover, at least in the lambdaphage system stud- ied here, the choice of filter window can influence the reported results. The DHMM method avoids any such steps.

Hidden Markov modeling is a useful tool to learn about the hidden conformation of the DNA tether from the observed motion of the bead, because the observed motion can be statis- tically quantified and simple models used to describe the unobserved state of the tether. The uninteresting diffusive motion is determined empirically from control experiments, and then the looping is assumed to follow exponential kinetics with unknown parameters corresponding to the loop formation and breakdown lifetimes. Then the likelihood that the experimental data (or a simulation) came from the proposed model is maximized. The method is implemented in a computationally efficient code inMathematica. Since there is no filtering and no binning of the data in DHMM, the kinetic parameters can be determined unambiguously. If desired, the most-likely transition state sequence can also be determined.

pressor protein during the experiment; however looped control data can be more challenging. For the lambda system considered here, infrequent yet long-lived looped states made this a relatively simple task. In other systems alternatives exist, including separate experiments on constructs with shorter length tethers corresponding to the expected looped length or, if available, mutant repressor proteins with stronger affinity for DNA that result in permanently looped tethers. In the lambdasystem, the robustness of DHMM to the model of the looped state is verified by varying the fit parameters in Eq. (2.4.3) by±10%and noting thatτLB and τLF remained unchanged (data not shown).

Another advantage of DHMM is its ability to, at least partially, compensate an experi- mental bias inherent in the tethered particle method: Loops cannot form between successive measurements if the DNA is in an extended conformation due to the time for the bead to dif- fuse to a location closer to the anchor point. This effect inflates the observed loop formation times relative to the case of interest (free DNA in solution); indeed, in simulations where the lifetimes are knowna priori, this effect inflatesτLF by∼ 30%. The DHMM model compen- sates for this by allowing loops to form only whenρ<ρmax.

The recent incorporation of single–particle tracking into the TPM method was essen- tial, because it allows rapid and precise measurements of bead position that are required for DHMM. In particular, the ability to simultaneously trackmultipletethered beads is helpful for removing instrumental drift [76]. Future experiments could in principle remove drift from the data entirely by simultaneously tracking a fixed, fiducial marker object.

DHMM is applied to one illustrative experimental dataset of lambdaDNA with 200 nM

One surprisingly biologically relevant application of this work is that, at physiological [cI] corresponding to the lysogenic state, the loop is not permanently closed. It is interesting that these lifetimes are neither representative of all the beads that were observed in [86] (data not shown), nor even for the entire observation time of any single bead (see Fig. 2.2). Prior to adding cI, most beads have nearly identical tethered diffusive motion; however, after addition of cI, the kinetics of looping varied widely. Some beads were mostly unlooped with occasional looping events, some beads were the inverse of this, others showed long periods of dynamic looping, and some like Fig. 2.2 seemed to show very sharply-defined changes between long- lived (often > 10min) regimes of homogeneous behavior. One hypothesis to explain these long-time looping trends is that the occupancy of cI protein among the 6lambdabinding sites changes, resulting in periods with more or less stable loops. For example, when all 6 sites are occupied a very stable loop might form, whereas 4-sites occupancy could result in a less stable, but still detectable, loop. Future experiments with fewer operators, or perhaps fluorescent cI protein, could be used to test this hypothesis directly.

One technique for considering such complex kinetic scenarios is to use a more elaborate state diagram; however, a different approach might be appropriate if cI proteins are binding and unbinding on a time scale much slower than loop formation, as observed. In this case, DNA looping data could be adequately represented by a concatenation of 2-state models, each with different kinetics, rather than by a far more elaborate model with many states. There appear to be three such regions in the data shown in Fig. 2.2. First, the mostly unlooped region was removed to focus on the faster dynamics of the later region, which was split in all possible ways into two subregions. Each subregion was analyzed separately using DHMM,

and the partition that resulted in the highest total likelihood, which was also much higher than if the two regions were assumed to be one homogeneous kinetic regime, was chosen. The sharp peak in Fig. 2.13 indicates that DHMM is a sensitive tool to localize such subtle transitions in time.

Chapter 3

Twirling of actin by myosin II observed

via polarized TIRF in a modified gliding

assay

3.1 Introduction

The swinging lever arm model [102, 103] explains force production and movement between actin and myosin II in muscle contraction [104] and also applies to non-muscle myosins [105]. Separate crystal structures of myosin and actin docked into cyro-EM maps of actomyosin [106] indicate that the lever arm swing is nearly parallel to the axis of the actin filament, thereby efficiently converting the free energy released from ATP hydrolysis into motion along the filament. Even small torque components around the filament axis, however, may have biological roles in muscle contraction (Ref. [107], and references therein) or regulation [108].

For processive non-muscle motors, a torque may be desirable for navigating cargo around obstacles present in the crowded environment of the cell [109–111].

Several studies have suggested off-axis components to the relative motion between actin and myosin. For example, decreased lateral spacing of the filaments of frog skeletal muscle in rigor compared with relaxation was attributed to radial forces between the thick and thin filaments [112]. In a modified gliding assay, actin filaments that were selectively immobi- lized onto the slide at their pointed ends formed superhelices that suggested a right-handed component of torque generated by myosin II [113]. In standard gliding assays where the filaments are free to translocate, a torque component of the cross-bridge force could result in rotation of the filament about its longitudinal axis, i.e., “twirling.” Actin filaments with marker beads attached at their ends showed no twirling on HMM-coated slides [114] while gliding, but when the filaments were marked sparsely with fluorescently labeled actin monomers, si- multaneous twirling and gliding of the filaments was observed by polarized fluorescence mi- croscopy [59, 65]. Symmetries in the fluorescence polarization technique prevented both of those studies from determining the handedness of the twirling motion.

A separate way of gauging sideways motions and possible components of torque between actin and processive myosins is to suspend the actin filament above the surface of the micro- scope slide and record the path of a bead being transported by myosin along the suspended filament [115,116]. Off-axis force causes the bead to travel in a helical path. In the suspended filament assay, myosins V [115] and VI [116] exhibited left-handed and right-handed helical paths, respectively.

cence (polTIRF) microscopy [62, 63, 65] typically use incident and/or detected light polarized along the x, y and z axes of the microscope. In such configurations, rotation of the fluo- rophore, but not the handedness of its helical motion, can be observed because orientations of the fluorophore reflected across any of the Cartesian planes give the same fluorescence inten- sities and thus are not distinguishable. Intermediate excitation or emission polarizations that break these symmetries enable the handedness to be recovered [117].

In the present work, extra linear polarizations are added to the previously reported polTIRF technique [2,61–63,65] that are intermediate between those aligned along the Cartesian direc- tions. As a result, there is a four-fold increase in the range of unambiguously detected probe orientations. The orientation is then estimated within a hemisphere, the remaining two-fold ambiguity being an unavoidable property of dipolar absorption and emission of light.

This chapter reports on twirling and its handedness from gliding actin filaments that are translocated by whole myosin II. The twirling motion is nearly always left-handed with an average pitch, i.e. the distance that the filament translocates during one complete rotation, of approximately 0.5 µm that is not strongly influenced by myosin concentration, Mg·ATP concentration or filament length in the range studied here. These values for the twirling pitch are much longer and opposite in handedness to the intrinsic pitch of the actin filament. Several mechanical effects are discussed that could give rise to filament twirling.