arXiv subjects

Paul A. Wiggins

Publications and source records attributed to Paul A. Wiggins.

17 recordsLinked to original sources

arXiv2024

Protein overabundance is driven by growth robustness

Protein expression levels optimize cell fitness: Too low an expression level of essential proteins will slow growth by compromising essential processes; whereas overexpression slows growth by increasing the metabolic load. This trade-off naively predicts that cells maximize their fitness by sufficiency, expressing just enough of each essential protein for function. We test this prediction in the naturally-competent bacterium Acinetobacter baylyi by characterizing the proliferation dynamics of essential-gene knockouts at a single-cell scale (by imaging) as well as at a genome-wide scale (by TFNseq). In these experiments, cells proliferate for multiple generations as target protein levels are diluted from their endogenous levels. This approach facilitates a proteome-scale analysis of protein overabundance. As predicted by the Robustness-Load Trade-Off (RLTO) model, we find that roughly 70% of essential proteins are overabundant and that overabundance increases as the expression level decreases, the signature prediction of the model. These results reveal that robustness plays a fundamental role in determining the expression levels of essential genes and that overabundance is a key mechanism for ensuring robust growth.

physics.bio-ph↗

arXiv2024

Noise robustness and metabolic load determine the principles of central dogma regulation

The processes of gene expression are inherently stochastic, even for essential genes required for growth. How does the cell maximize fitness in light of noise? To answer this question, we build a mathematical model to explore the trade-off between metabolic load and growth robustness. The model predicts novel principles of central dogma regulation: Optimal protein expression levels for many genes are in vast overabundance. Essential genes are transcribed above a lower limit of one message per cell cycle. Gene expression is achieved by load balancing between transcription and translation. We present evidence that each of these novel regulatory principles is observed. These results reveal that robustness and metabolic load determine the global regulatory principles that govern gene expression processes, and these principles have broad implications for cellular function.

q-bio.MN↗

arXiv2024

Direct measure of DNA bending by quantum magnetic imaging of a nano-mechanical torque-balance

DNA flexibility is a key determinant of biological function, from nucleosome positioning to transcriptional regulation, motivating a direct measurement of the bend-torque response of individual DNA molecules. In this work, DNA bending is detected using a nano-mechanical torque balance formed by tethering a ferromagnetic nanoparticle probe by an individual DNA molecule to a diamond magnetic field imager. The torque exerted by the DNA in response to bending caused by an applied magnetic torque is measured using wide-field imaging of quantum defects near the surface of the diamond. Qualitative measurements of differences in DNA bio-mechanical binding configuration are demonstrated, and as a proof-of-principle, a quantitative measurement of the bend response is made for individual DNA molecules. This quantum-enabled measurement approach could be applied to characterize the bend response of biophysically relevant short DNA molecules as well as the sequence dependence of DNA bending energy.

physics.bio-ph↗

arXiv2023

The one-message-per-cell-cycle rule: A conserved minimum transcription level for essential genes

The inherent stochasticity of cellular processes leads to significant cell-to-cell variation in protein abundance. Although this noise has already been characterized and modeled, its broader implications and significance remain unclear. In this paper, we revisit the noise model and identify the number of messages transcribed per cell cycle as the critical determinant of noise. In yeast, we demonstrate that this quantity predicts the non-canonical scaling of noise with protein abundance, as well as quantitatively predicting its magnitude. We then hypothesize that growth robustness requires an upper ceiling on noise for the expression of essential genes, corresponding to a lower floor on the transcription level. We show that just such a floor exists: a minimum transcription level of one message per cell cycle is conserved between three model organisms: Escherichia coli, yeast, and human. Furthermore, all three organisms transcribe the same number of messages per gene, per cell cycle. This common transcriptional program reveals that robustness to noise plays a central role in determining the expression level of a large fraction of essential genes, and that this fundamental optimal strategy is conserved from E. coli to human cells.

physics.bio-ph↗

arXiv2022

The high-resolution in vivo measurement of replication fork velocity and pausing by lag-time analysis

An important step towards understanding the mechanistic basis of the central dogma is the quantitative characterization of the dynamics of nucleic-acid-bound molecular motors in the context of the living cell, where a crowded cytoplasm as well as competing and potentially antagonistic processes may significantly affect their rapidity and reliability. To capture these dynamics, we develop a novel method, lag-time analysis, for measuring in vivo dynamics. The approach uses exponential growth as the stopwatch to resolve dynamics in an asynchronous culture and therefore circumvents the difficulties and potential artifacts associated with synchronization or fluorescent labeling. Although lag-time analysis has the potential to be widely applicable to the quantitative analysis of in vivo dynamics, we focus on an important application: characterizing replication dynamics. To benchmark the approach, we analyze replication dynamics in three different species and a collection of mutants. We provide the first quantitative locus-specific measurements of fork velocity, in units of kb per second, as well as replisome-pause durations, some with the precision of seconds. The measured fork velocity is observed to be both locus and time dependent, even in wild-type cells. In addition to quantitatively characterizing known phenomena, we detect brief, locus-specific pauses at rDNA in wild-type cells for the first time. We also observe temporal fork velocity oscillations in three highly-divergent bacterial species. Lag-time analysis not only has great potential to offer new insights into replication, as demonstrated in the paper, but also has potential to provide quantitative insights into other important processes.

physics.bio-ph↗

arXiv2022

Characterizing stochastic cell cycle dynamics in exponential growth

Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing population, while the other captures cell cycle dynamics, either by time-lapse imaging of full cell cycles or in bulk experiments on synchronized populations. In this paper, we study the subtle relationship between observations in these two distinct experimental approaches. We begin with an existing model: a single-cell deterministic description of cell cycle dynamics where cell states (i.e. periods or phases) have precise lifetimes. We then generalize this description to a stochastic model in which the states have stochastic lifetimes, as described by arbitrary probability distribution functions. Our analyses of the demographics of an exponential culture reveal a simple and exact correspondence between the deterministic and stochastic models: The corresponding state lifetimes in the deterministic model are equal to the exponential mean of the lifetimes in the stochastic model. An important implication is therefore that the demographics of an exponential culture will be well-fit by a deterministic model even if the state timing is stochastic. Although we explore the implications of the models in the context of the Escherichia coli cell cycle, we expect both the models as well as the significance of the exponential-mean lifetimes to find many applications in the quantitative analysis of cell cycle dynamics in other biological systems.

physics.bio-ph↗

arXiv2021

Wide-field dynamic magnetic microscopy using double-double quantum driving of a diamond defect ensemble

Wide-field magnetometry can be realized by imaging the optically-detected magnetic resonance of diamond nitrogen vacancy (NV) center ensembles. However, NV ensemble inhomogeneities significantly limit the magnetic-field sensitivity of these measurements. We demonstrate a double-double quantum (DDQ) driving technique to facilitate wide-field magnetic imaging of dynamic magnetic fields at a micron scale. DDQ imaging employs four-tone radio frequency pulses to suppress inhomogeneity-induced variations of the NV resonant response. As a proof-of-principle, we use the DDQ technique to image the dc magnetic field produced by individual magnetic-nanoparticles tethered by single DNA molecules to a diamond sensor surface. This demonstrates the efficacy of the diamond NV ensemble system in high-frame-rate magnetic microscopy, as well as single-molecule biophysics applications.

physics.app-ph↗

arXiv2019

On the correspondence between thermodynamics and inference

We expand upon a natural analogy between Bayesian statistics and statistical physics in which sample size corresponds to inverse temperature. This analogy motivates the definition of two novel statistical quantities: a learning capacity and a Gibbs entropy. The analysis of the learning capacity, corresponding to the heat capacity in thermal physics, leads to new insight into the mechanism of learning and explains why some models have anomalously-high learning performance. We explore the properties of the learning capacity in a number of examples, including a sloppy model. Next, we propose that the Gibbs entropy provides a natural device for counting distinguishable distributions in the context of Bayesian inference. We use this device to define a generalized principle of indifference (GPI) in which every distinguishable model is assigned equal a priori probability. This principle results in a new solution to a long-standing problem in Bayesian inference: the definition of an objective or uninformative prior. A key characteristic of this new approach is that it can be applied to analyses where the model dimension is unknown and circumvents the automatic rejection of higher-dimensional models in Bayesian inference.

math.ST↗

arXiv2018

Information-based inference for singular models and finite sample sizes: A frequentist information criterion

In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the predictive complexity. In the large-sample-size limit of a regular model, the predictive performance is well estimated by the Akaike Information Criterion (AIC). However, this approximation can either significantly under or over-estimating the complexity in a wide range of important applications where models are either non-regular or finite-sample-size corrections are significant. We introduce an improved approximation for the complexity that is used to define a new information criterion: the Frequentist Information Criterion (QIC). QIC extends the applicability of information-based inference to the finite-sample-size regime of regular models and to singular models. We demonstrate the power and the comparative advantage of QIC in a number of example analyses.

stat.ML↗

arXiv2017

The Lindley paradox: The loss of resolution in Bayesian inference

There are three principle paradigms of statistics: Bayesian, frequentist and information-based inference. Although these paradigms are in agreement in some contexts, the Lindley paradox describes a class of problems, models of unknown dimension, where conflicting conclusions are generated by frequentist and Bayesian inference. This conflict can materially affect the scientific conclusions. Understanding the Lindley paradox---where it applies, why it occurs, and how it can be avoided---is therefore essential to the understanding of statistical analysis. In this paper, we revisit the Lindley paradox in the context of a simple biophysical application. We describe how predictive and postdictive measures of model performance provide a natural framework for understanding the Lindley paradox. We then identify methods which result in optimal experimental resolution for discovery.

math.ST↗

arXiv2015

An objective prior that unifies objective Bayes and information-based inference

There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and information-based inference. The $w$-prior is chosen to make the marginal probability an unbiased estimator of the predictive performance of the model. This definition has several other natural interpretations. From the perspective of the information content of the prior, the $w$-prior is both uniformly and maximally uninformative. The $w$-prior can also be understood to result in a uniform density of distinguishable models in parameter space. Finally we demonstrate the the $w$-prior is equivalent to the Akaike Information Criterion (AIC) for regular models in the asymptotic limit. The $w$-prior appears to be generically applicable to statistical inference and is free of {\it ad hoc} regularization. The mechanism for suppressing complexity is analogous to AIC: model complexity reduces model predictivity. We expect this new objective-Bayes approach to inference to be widely-applicable to machine-learning problems including singular models.

stat.ML↗

arXiv2015

A simple application of FIC to model selection

We have recently proposed a new information-based approach to model selection, the Frequentist Information Criterion (FIC), that reconciles information-based and frequentist inference. The purpose of this current paper is to provide a simple example of the application of this criterion and a demonstration of the natural emergence of model complexities with both AIC-like ($N^0$) and BIC-like ($\log N$) scaling with observation number $N$. The application developed is deliberately simplified to make the analysis analytically tractable.

physics.data-an↗

arXiv2015

The development of an information criterion for Change-Point Analysis

Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change-point algorithm is used to identify the time indices (change points) at which the system transitions between these discrete states. We present a unified information-based approach to testing for the existence of change points. This new approach reconciles two previously disparate approaches to Change-Point Analysis (frequentist and information-based) for testing transitions between states. The resulting method is statistically principled, parameter and prior free and widely applicable to a wide range of change-point problems.

physics.data-an↗

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↗

arXiv2005

A generalized theory of semiflexible polymers

DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biological length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific toy model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by the Renormalization Group. In particular, we show that either the WLC or our new model adequate describes force-extension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization J factors observed by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments.

cond-mat.soft↗

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↗