arXiv subjects

Rob Phillips

Publications and source records attributed to Rob Phillips.

At least 73 records · Page 4Linked to original sources

arXiv2010

Ion-dependent dynamics of DNA ejections for bacteriophage lambda

We study the control parameters that govern the dynamics of in vitro DNA ejection in bacteriophage lambda. Past work has demonstrated that bacteriophage DNA is highly pressurized; this pressure has been hypothesized to help drive DNA ejection. Ions influence this process by screening charges on DNA; however, a systematic variation of salt concentrations to explore these effects has not been undertaken. To study the nature of the forces driving DNA ejection, we performed in vitro measurements of DNA ejection in bulk and at the single-phage level. We present measurements on the dynamics of ejection and on the self-repulsion force driving ejection. We examine the role of ion concentration and identity in both measurements, and show that the charge of counter-ions is an important control parameter. These measurements show that the frictional force acting on the ejecting DNA is subtly dependent on ionic concentrations for a given amount of DNA in the capsid. We also present evidence that phage DNA forms loops during ejection; we confirm that this effect occurs using optical tweezers. We speculate this facilitates circularization of the genome in the cytoplasm.

q-bio.BM↗

arXiv2009

Lipid Domain Order and the Algebra of Morphology

Lipid membranes regulate the flow of materials and information between cells and their organelles. Further, lipid composition and morphology can play a key role in regulating a variety of biological processes. For example, viral uptake, plasma membrane tension regulation, and the formation of caveolae all require the creation and control of groups of lipids that adopt specific morphologies. In this paper, we use a simplified model mixture of lipids and cholesterol to examine the interplay between lipid phase-separation and bilayer morphology. We observe and theoretically analyze three main features of phase-separated giant unilamellar vesicles. First, by tracking the motion of `dimpled' domains, we measure repulsive, elastic interactions that create short--range translational and orientational order, leading to a stable distribution of domain sizes, and hence maintaining lateral heterogeneity on relatively short length scales and long time scales. Second, we examine the transition to `budded' domain morphologies, showing that the transition is size-selective, and has two kinetic regimes, as revealed by a calculated phase diagram. Finally, using observations of the interactions between dimpled and budded domains, we build a theoretical framework with an elastic model that maps the free energies and allowed transitions in domain morphology upon coalescence, to serve as an interpretive tool for understanding the algebra of domain morphology. In all three cases, the two major factors that regulate domain morphology and morphological transitions are the domain size and membrane tension.

q-bio.BM↗

arXiv2009

Morphology and Interaction between Lipid Domains

Cellular membranes are a heterogeneous mix of lipids, proteins and small molecules. Special groupings of saturated lipids and cholesterol form a liquid-ordered phase, known as `lipid rafts,' serving as platforms for signaling, trafficking and material transport throughout the secretory pathway. Questions remain as to how the cell maintains heterogeneity of a fluid membrane with multiple phases, through time, on a length-scale consistent with the fact that no large-scale phase separation is observed. We have utilized a combination of mechanical modeling and in vitro experiments to show that membrane morphology can be a key player in maintaining this heterogeneity and organizing such domains in the membrane. We demonstrate that lipid domains can adopt a flat or dimpled morphology, where the latter facilitates a repulsive interaction that slows coalescence and tends to organize domains. These forces, that depend on domain morphology, play an important role in regulating lipid domain size and in the lateral organization of lipids in the membrane.

q-bio.QM↗

arXiv2008

First-principles calculation of DNA looping in tethered particle experiments

We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in Tethered Particle Motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. [...] We show how to compute both the "looping J factor" (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on tethered particle motion, and then compare to our model's predictions. [...] Our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical "open" conformation of the LacI tetramer.

q-bio.BM↗

arXiv2008

Concentration and Length Dependence of DNA Looping in Transcriptional Regulation

In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the J-factor for looping.

q-bio.BM↗

arXiv2008

A trajectory approach to two-state kinetics of single particles on sculpted energy landscapes

We study the trajectories of a single colloidal particle as it hops between two energy wells A and B, which are sculpted using adjacent optical traps by controlling their respective power levels and separation. Whereas the dynamical behaviors of such systems are often treated by master-equation methods that focus on particles as actors, we analyze them here instead using a trajectory-based variational method called Maximum Caliber, which utilizes a dynamical partition function. We show that the Caliber strategy accurately predicts the full dynamics that we observe in the experiments: from the observed averages, it predicts second and third moments and covariances, with no free parameters. The covariances are the dynamical equivalents of Maxwell-like equilibrium reciprocal relations and Onsager-like dynamical relations. In short, this work describes an experimental model system for exploring full trajectory distributions in one-particle two-state systems, and it validates the Caliber approach as a useful way to understand trajectory-based dynamical distribution functions in this system.

physics.data-an↗

arXiv2007

A First Exposure to Statistical Mechanics for Life Scientists

Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a clue that it might have some bearing on the analysis of the molecules of living matter. As a result of data on biological systems becoming increasingly quantitative, there is a concomitant demand that the models set forth to describe biological systems be themselves quantitative. We describe how statistical mechanics is part of the quantitative toolkit that is needed to respond to such data. The power of statistical mechanics is not limited to traditional physical and chemical problems and there are a host of interesting ways in which these ideas can be applied in biology. This article reports on our efforts to teach statistical mechanics to life science students and provides a framework for others interested in bringing these tools to a nontraditional audience in the life sciences.

q-bio.QM↗

arXiv2007

Cooperative Gating and Spatial Organization of Membrane Proteins through Elastic Interactions

Biological membranes are elastic media in which the presence of a transmembrane protein leads to local bilayer deformation. The energetics of deformation allow two membrane proteins in close proximity to influence each other's equilibrium conformation via their local deformations, and spatially organize the proteins based on their geometry. We use the mechanosensitive channel of large conductance (MscL) as a case study to examine the implications of bilayer-mediated elastic interactions on protein conformational statistics and clustering. The deformations around MscL cost energy on the order of 10 kT and extend ~3nm from the protein edge, as such elastic forces induce cooperative gating and we propose experiments to measure these effects. Additionally, since elastic interactions are coupled to protein conformation, we find that conformational changes can severely alter the average separation between two proteins. This has important implications for how conformational changes organize membrane proteins into functional groups within membranes.

q-bio.SC↗

arXiv2007

The Role of Lipid Bilayer Mechanics in Mechanosensation

Mechanosensation is a key part of the sensory repertoire of a vast array of different cells and organisms. The molecular dissection of the origins of mechanosensation is rapidly advancing as a result of both structural and functional studies. One intriguing mode of mechanosensation results from tension in the membrane of the cell (or vesicle) of interest. The aim of this review is to catalogue recent work that uses a mix of continuum and statistical mechanics to explore the role of the lipid bilayer in the function of mechanosensitive channels that respond to membrane tension. The role of bilayer deformation will be explored in the context of the well known mechanosensitive channel MscL. Additionally, we make suggestions for bridging gaps between our current theoretical understanding and common experimental techniques.

q-bio.SC↗

arXiv2006

Biological Consequences of Tightly Bent DNA: The Other Life of a Macromolecular Celebrity

The mechanical properties of DNA play a critical role in many biological functions. For example, DNA packing in viruses involves confining the viral genome in a volume (the viral capsid) with dimensions that are comparable to the DNA persistence length. Similarly, eukaryotic DNA is packed in DNA-protein complexes (nucleosomes) in which DNA is tightly bent around protein spools. DNA is also tightly bent by many proteins that regulate transcription, resulting in a variation in gene expression that is amenable to quantitative analysis. In these cases, DNA loops are formed with lengths that are comparable to or smaller than the DNA persistence length. The aim of this review is to describe the physical forces associated with tightly bent DNA in all of these settings and to explore the biological consequences of such bending, as increasingly accessible by single-molecule techniques.

q-bio.BM↗

arXiv2006

Measurement of FLux Fluctuations in Diffusion in the Small-Numbers Limit

Using a microfluidics device filled with a colloidal suspension of microspheres, we test the laws of diffusion in the limit of small particle numbers. Our focus is not just on average properties such as the mean flux, but rather on the features of the entire distribution of allowed microscopic trajectories that are possible during diffusive dynamics. The experiments show that: (1) the flux distribution is Gaussian; (2) Fick's Law --- that the average flux is proportional to the particle gradient --- holds even for particle gradients down to one or zero particles; (3) the variance in the flux is proportional to the sum of the particle numbers; and (4) there are backwards flows, where particles flow up a concentration gradient, rather than down it, and their numbers are well-predicted by theory and consistent with a new Flux Fluctuation Theorem.

cond-mat.stat-mech↗

arXiv2005

Excluded-Volume Effects in Tethered-Particle Experiments: Bead Size Matters

The tethered-particle method is a single-molecule technique that has been used to explore the dynamics of a variety of macromolecules of biological interest. We give a theoretical analysis of the particle motions in such experiments. Our analysis reveals that the proximity of the tethered bead to a nearby surface (the microscope slide) gives rise to a volume-exclusion effect, resulting in an entropic force on the molecule. This force stretches the molecule, changing its statistical properties. In particular, the proximity of bead and surface brings about intriguing scaling relations between key observables (statistical moments of the bead) and parameters such as the bead size and contour length of the molecule. We present both approximate analytic solutions and numerical results for these effects in both flexible and semiflexible tethers. Finally, our results give a precise, experimentally-testable prediction for the probability distribution of the distance between the polymer attachment point and the center of the mobile bead.

q-bio.BM↗

arXiv2005

Teaching the Principles of Statistical Dynamics

We describe a simple framework for teaching the principles that underlie the dynamical laws of transport: Fick's law of diffusion, Fourier's law of heat flow, the Newtonian viscosity law, and mass-action laws of chemical kinetics. In analogy with the way that the maximization of entropy over microstates leads to the Boltzmann law and predictions about equilibria, maximizing a quantity that E. T. Jaynes called "Caliber" over all the possible microtrajectories leads to these dynamical laws. The principle of Maximum Caliber also leads to dynamical distribution functions which characterize the relative probabilities of different microtrajectories. A great source of recent interest in statistical dynamics has resulted from a new generation of single-particle and single-molecule experiments which make it possible to observe dynamics one trajectory at a time.

cond-mat.stat-mech↗

arXiv2005

Dynamics of DNA Ejection From Bacteriophage

The ejection of DNA from a bacterial virus (``phage'') into its host cell is a biologically important example of the translocation of a macromolecular chain along its length through a membrane. The simplest mechanism for this motion is diffusion, but in the case of phage ejection a significant driving force derives from the high degree of stress to which the DNA is subjected in the viral capsid. The translocation is further sped up by the ratcheting and entropic forces associated with proteins that bind to the viral DNA in the host cell cytoplasm. We formulate a generalized diffusion equation that includes these various pushing and pulling effects and make estimates of the corresponding speed-ups in the overall translocation process. Stress in the capsid is the dominant factor throughout early ejection, with the pull due to binding particles taking over at later stages. Confinement effects are also investigated, in the case where the phage injects its DNA into a volume comparable to the capsid size. Our results suggest a series of in vitro experiments involving the ejection of DNA into vesicles filled with varying amounts of binding proteins from phage whose state of stress is controlled by ambient salt conditions or by tuning genome length.

q-bio.BM↗

arXiv2005

The effect of genome length on ejection forces in bacteriophage lambda

A variety of viruses tightly pack their genetic material into protein capsids that are barely large enough to enclose the genome. In particular, in bacteriophages, forces as high as 60 pN are encountered during packaging and ejection, produced by DNA bending elasticity and self-interactions. The high forces are believed to be important for the ejection process, though the extent of their involvement is not yet clear. As a result, there is a need for quantitative models and experiments that reveal the nature of the forces relevant to DNA ejection. Here we report measurements of the ejection forces for two different mutants of bacteriophage lambda, lambda b221cI26 and lambda cI60, which differ in genome length by ~30%. As expected for a force-driven ejection mechanism, the osmotic pressure at which DNA release is completely inhibited varies with the genome length: we find inhibition pressures of 15 atm and 25 atm, respectively, values that are in agreement with our theoretical calculations.

q-bio.BM↗

arXiv2004

Transcriptional Regulation by the Numbers 1: Models

The study of gene regulation and expression is often discussed in quantitative terms. In particular, the expression of genes is regularly characterized with respect to how much, how fast, when and where. Whether discussing the level of gene expression in a bacterium or its precise location within a developing embryo, the natural language for these experiments is that of numbers. Such quantitative data demands quantitative models. We review a class of models ("thermodynamic models") which exploit statistical mechanics to compute the probability that RNA polymerase is at the appropriate promoter. This provides a mathematically precise elaboration of the idea that activators are agents of recruitment which increase the probability that RNA polymerase will be found at the promoter of interest. We discuss a framework which describes the interactions of repressors, activators, helper molecules and RNA polymerase using the concept of effective concentrations, expressed in terms of a function we call the "regulation factor". This analysis culminates in an expression for the probability of RNA polymerase binding at the promoter of interest as a function of the number of regulatory proteins in the cell. In a companion paper [1], these ideas are applied to several case studies which illustrate the use of the general formalism.

q-bio.MN↗

arXiv2004

Transcriptional Regulation by the Numbers 2: Applications

With the increasing amount of experimental data on gene expression and regulation, there is a growing need for quantitative models to describe the data and relate them to the different contexts. The thermodynamic models reviewed in the preceding paper provide a useful framework for the quantitative analysis of bacterial transcription regulation. We review a number of well-characterized bacterial promoters that are regulated by one or two species of transcription factors, and apply the thermodynamic framework to these promoters. We show that the framework allows one to quantify vastly different forms of gene expression using a few parameters. As such, it provides a compact description useful for higher-level studies, e.g., of genetic networks, without the need to invoke the biochemical details of every component. Moreover, it can be used to generate hypotheses on the likely mechanisms of transcriptional control.

q-bio.MN↗

arXiv2004

Exact theory of kinkable elastic polymers

The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the Wormlike Chain model, as well as the high-curvature softening observed in recent cyclization experiments.

cond-mat.soft↗