arXiv subjects

John Bechhoefer

Publications and source records attributed to John Bechhoefer.

51 records · Page 3Linked to original sources

arXiv2011

Kramers-Kronig, Bode, and the meaning of zero

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.

physics.class-ph↗

arXiv2008

How Xenopus laevis embryos replicate reliably: investigating the random-completion problem

DNA synthesis in \textit{Xenopus} frog embryos initiates stochastically in time at many sites (origins) along the chromosome. Stochastic initiation implies fluctuations in the time to complete and may lead to cell death if replication takes longer than the cell cycle time ($\approx 25$ min). Surprisingly, although the typical replication time is about 20 min, \textit{in vivo} experiments show that replication fails to complete only about 1 in 300 times. How is replication timing accurately controlled despite the stochasticity? Biologists have proposed two solutions to this "random-completion problem." The first solution uses randomly located origins but increases their rate of initiation as S phase proceeds, while the second uses regularly spaced origins. In this paper, we investigate the random-completion problem using a type of model first developed to describe the kinetics of first-order phase transitions. Using methods from the field of extreme-value statistics, we derive the distribution of replication-completion times for a finite genome. We then argue that the biologists' first solution to the problem is not only consistent with experiment but also nearly optimizes the use of replicative proteins. We also show that spatial regularity in origin placement does not alter significantly the distribution of replication times and, thus, is not needed for the control of replication timing.

q-bio.CB↗

arXiv2006

How Xenopus laevis replicates DNA reliably even though its origins of replication are located and initiated stochastically

DNA replication in Xenopus laevis is extremely reliable, failing to complete before cell division no more than once in 10,000 times; yet replication origins sites are located and initiated stochastically. Using a model based on 1d theories of nucleation and growth and using concepts from extreme-value statistics, we derive the distribution of replication times given a particular initiation function. We show that the experimentally observed initiation strategy for Xenopus laevis meets the reliability constraint and is close to the one that requires the fewest resources of a cell.

q-bio.CB↗

arXiv2004

Nucleation and growth in one dimension, part I: The generalized Kolmogorov-Johnson-Mehl-Avrami model

Motivated by a recent application of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model to the study of DNA replication, we consider the one-dimensional version of this model. We generalize previous work to the case where the nucleation rate is an arbitrary function $I(t)$ and obtain analytical results for the time-dependent distributions of various quantities (such as the island distribution). We also present improved computer simulation algorithms to study the 1D KJMA model. The analytical results and simulations are in excellent agreement.

cond-mat.soft↗

arXiv2004

Nucleation and growth in one dimension, part II: Application to DNA replication kinetics

Inspired by recent experiments on DNA replication, we apply a one-dimensional nucleation-and-growth model to DNA-replication kinetics, focusing on how to extract the time-dependent nucleation rate I(t) and growth speed v from data. We discuss generic experimental problems, namely spatial inhomogeneity, measurement noise, and finite-size effects. After evaluating how each of these affects the measurements of I(t) and v, we give guidelines for the design of experiments. These ideas are then discussed in the context of the DNA-replication experiments.

cond-mat.soft↗

arXiv2003

Persistence length of chromatin determines origin spacing in Xenopus early-embryo DNA replication: Quantitative comparisons between theory and experiment

In Xenopus early embryos, replication origins neither require specific DNA sequences nor is there an efficient S/M checkpoint, even though the whole genome (3 billion bases) is completely duplicated within 10-20 minutes. This leads to the"random-completion problem" of DNA replication in embryos, where one needs to find a mechanism that ensures complete, faithful, timely reproduction of the genome without any sequence dependence of replication origins. We analyze recent DNA replication data in Xenopus laevis egg extracts and find discrepancies with models where replication origins are distributed independently of chromatin structure. Motivated by these discrepancies, we have investigated the role that chromatin looping may play in DNA replication. We find that the loop-size distribution predicted from a wormlike-chain model of chromatin can account for the spatial distribution of replication origins in this system quantitatively. Together with earlier findings of increasing frequency of origin firings, our results can explain the random-completion problem. The agreement between experimental data (molecular combing) and theoretical predictions suggests that the intrinsic stiffness of chromatin loops plays a fundamental biological role in DNA replication in early-embryo Xenopus in regulating the origin spacing.

q-bio.QM↗

arXiv2003

Role of Polymer Loops in DNA Replication

Loop formation in long molecules occurs many places in nature, from solutions of carbon nanotubes to polymers inside a cell. In this article, we review theoretical studies of the static and dynamic properties of polymer loops. For example, long polymers must search many configurations to find a "target" binding site, while short polymers are stiff and resist bending. In between, there is an optimal loop size, which balances the entropy of long loops against the energetic cost of short loops. We show that such simple pictures of loop formation can explain several long-standing observations in DNA replication, quantitatively.

physics.bio-ph↗

arXiv2003

Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing

We show that Kramers rate theory gives a straightforward, accurate estimate of the closing time $τ_c$ of a semiflexible polymer that is valid in cases of physical interest. The calculation also reveals how the time scales of chain relaxation and closing are intertwined, illuminating an apparent conflict between two ways of calculating $τ_c$ in the flexible limit.

cond-mat.soft↗

arXiv2003

Kinetic model of DNA replication in eukaryotic organisms

We formulate a kinetic model of DNA replication that quantitatively describes recent results on DNA replication in the in vitro system of Xenopus laevis prior to the mid-blastula transition. The model describes well a large amount of different data within a simple theoretical framework. This allows one, for the first time, to determine the parameters governing the DNA replication program in a eukaryote on a genome-wide basis. In particular, we have determined the frequency of origin activation in time and space during the cell cycle. Although we focus on a specific stage of development, this model can easily be adapted to describe replication in many other organisms, including budding yeast.

physics.bio-ph↗

arXiv2000

Effect of order-parameter fluctuations on the Halperin-Lubensky-Ma first-order transition in superconductors and liquid crystals

We show that order-parameter fluctuations in a good type-I superconductor or a liquid crystal always increase the size of the first-order transition. This behavior is eventually changed when the system crosses over to inverted-XY critical behavior, with the size of the first-order transition vanishing as a power law with a crossover exponent. We find a good agreement between our theory and a recent experiment on the nematic-smectic-A first-order transition in 8CB-10CB mixtures of liquid crystals.

cond-mat.soft↗

arXiv1999

Two Experimental Tests of the Halperin-Lubensky-Ma Effect at the Nematic-Smectic-A Phase Transition

We have conducted two quantitative tests of predictions based on the Halperin-Lubensky-Ma (HLM) theory of fluctuation-induced first-order phase transitions. First, we explore the effect of an external magnetic field on the nematic-smectic-A (NA) transition in a liquid crystal. Second, we examine the dependence of the first-order discontinuity as a function of mixture concentration in pure 8CB and three 8CB-10CB mixtures. We find the first quantitative evidence for deviations from the HLM theory.

cond-mat.soft↗

arXiv1999

External-field-induced tricritical point in a fluctuation-driven nematic-smectic-A transition

We study theoretically the effect of an external field on the nematic-smectic-A (NA) transition close to the tricritical point, where fluctuation effects govern the qualitative behavior of the transition. An external field suppresses nematic director fluctuations, by making them massive. For a fluctuation-driven first-order transition, we show that an external field can drive the transition second-order. In an appropriate liquid crystal system, we predict the required magnetic field to be of order 10 T. The equivalent electric field is of order $1 V/μm$.

cond-mat.soft↗

arXiv1996

A Simple Model for Faraday Waves

We show that the linear-stability analysis of the birth of Faraday waves on the surface of a fluid is simplified considerably when the fluid container is driven by a triangle waveform rather than by a sine wave. The calculation is simple enough to use in an undergraduate course on fluid dynamics or nonlinear dynamics. It is also an attractive starting point for a nonlinear analysis.

patt-sol↗

arXiv1995

Secondary Instabilities of Surface Waves on Viscous Fluids in the Faraday Instability

Secondary instabilities of Faraday waves show three regimes: (1) As seen previously, low-viscosity (nu) fluids destabilize first into squares. At higher driving accelerations a, squares show low-frequency modulations corresponding to the motion of phase defects, while theory predicts a stationary transverse amplitude modulation (TAM). (2) High-nu fluids destabilize first to stripes. Stripes then show an oscillatory TAM whose frequency is incommensurate with the driving frequency. At higher a, the TAM undergoes a phase instability. At still higher a, edge dislocations form and fluid droplets are ejected. (3) Intermediate-nu fluids show a complex coexistence of squares and stripes, as well as stationary and oscillatory TAM instabilities of the stripes.

patt-sol↗

arXiv1993

Nonequilibrium Phenomena in Liquid Crystals

This paper summarizes a talk presented at the April NATO ASI on Spatiotemporal Chaos in Complex Fluids, in Santa Fe, NM. The paper gives reasons that make complex fluids good material systems for conducting experiments on pattern formation and other nonequilibrium phenomena. Much of the discussion focuses on the different phenomena observed in solidification and how the increasing complexity of fluid systems decreases the velocity scale for achieving "rapid" solidification. Five systems are compared to illustrate this point: simple fluids, simple alloys, thermotropic liquid crystals, lyotropic liquid crystals, and diblock copolymers. Finally, an example is given of the kinds of transitions that may be observed in rapid solidification.

patt-sol↗