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Rob Phillips

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Biological Physics Biomolecules cond-mat.soft Molecular Networks Subcellular Processes Other Quantitative Biology Populations and Evolution cond-mat.stat-mech Genomics Quantitative Methods Cell Behavior physics.data-an physics.hist-ph physics.soc-ph q-bio.MN

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preprint2026arXiv

Conditioning as a route to stereotyped behavior in growing populations

Biological systems perform complex multi-step processes in a reproducible way despite underlying stochasticity. The standard explanation is micromanagement by molecular machinery that recognizes and corrects specific errors. Here we study conditioning, a qualitatively different strategy in which attempts failing a coarse criterion are destroyed and do not leave a physical record. The surviving, i.e., conditioned, ensemble is narrower and therefore more ordered. We model conditioning through stochastic resets in a ''socks-before-shoes'' model of a growing population, where $n$ actions must be completed in any order to replicate and any replication attempt not finished by a threshold time is discarded. We find that resets impose hierarchical temporal ordering of the $n$ actions without microscopic control over which action happens when. When disorder carries a sufficient time penalty, this ordering is free: the fastest-growing population is automatically the most ordered, with no direct selection for order required. Save points, at which verified progress is preserved across resets, allow conditioning to scale to complex multi-step processes. Conditioning provides a minimal route to reliable behavior, requiring only a clock rather than molecular machinery that recognizes specific errors. For the right class of processes, it pays for itself.

preprint2026arXiv

Informational blueprints reveal condition-dependent gene regulatory architectures

While coding regions in the genome have a direct interpretation in terms of protein products, significant fractions are non-coding and yet control essential biological functions. Unlike the genetic code, there is no "lookup table" that identifies where regulatory proteins, known as transcription factors (TFs), bind. Here, we extract these binding sites by distilling sequences of nucleotide letters into collective coordinates (hyperletters) representing the binding sites that are active under specific environmental conditions. Going beyond local information footprints between individual bases and expression levels, our $\textit{information blueprint}$ algorithm compresses the global information by optimising filters that simultaneously scan an entire promoter sequence. Inspired by renormalisation-group techniques, we identify TF binding sites as coarse-grained variables combining groups of correlated mutations with the highest collective impact on gene expression. We validate our approach on experimental data for $\textit{E. coli}$ and discover novel regulatory elements illustrating its deployment at scale across growth conditions.

preprint2022arXiv

Modeling and mechanical perturbations reveal how spatially regulated anchorage gives rise to spatially distinct mechanics across the mammalian spindle

During cell division, the spindle generates force to move chromosomes. In mammals, microtubule bundles called kinetochore-fibers (k-fibers) attach to and segregate chromosomes. To do so, k-fibers must be robustly anchored to the dynamic spindle. We previously developed microneedle manipulation to mechanically challenge k-fiber anchorage, and observed spatially distinct response features revealing the presence of heterogeneous anchorage (Suresh et al. 2020). How anchorage is precisely spatially regulated, and what forces are necessary and sufficient to recapitulate the k-fiber's response to force remain unclear. Here, we develop a coarse-grained k-fiber model and combine with manipulation experiments to infer underlying anchorage using shape analysis. By systematically testing different anchorage schemes, we find that forces solely at k-fiber ends are sufficient to recapitulate unmanipulated k-fiber shapes, but not manipulated ones for which lateral anchorage over a 3 $μ$m length scale near chromosomes is also essential. Such anchorage robustly preserves k-fiber orientation near chromosomes while allowing pivoting around poles. Anchorage over a shorter length scale cannot robustly restrict pivoting near chromosomes, while anchorage throughout the spindle obstructs pivoting at poles. Together, this work reveals how spatially regulated anchorage gives rise to spatially distinct mechanics in the mammalian spindle, which we propose are key for function.

preprint2021arXiv

Programming Boundary Deformation Patterns in Active Networks

Active materials take advantage of their internal sources of energy to self-organize in an automated manner. This feature provides a novel opportunity to design micron-scale machines with minimal required control. However, self-organization goes hand in hand with predetermined dynamics that are hardly susceptible to environmental perturbations. Therefore utilizing this feature of active systems requires harnessing and directing the macroscopic dynamics to achieve specific functions; which in turn necessitates understanding the underlying mechanisms of active forces. Here we devise an optical control protocol to engineer the dynamics of active networks composed of microtubules and light-activatable motor proteins. The protocol enables carving activated networks of different shapes, and isolating them from the embedding solution. Studying a large set of shapes, we observe that the active networks contract in a shape-preserving manner that persists over the course of contraction. We formulate a coarse-grained theory and demonstrate that self-similarity of contraction is associated with viscous-like active stresses. These findings help us program the dynamics of the network through manipulating the light intensity in space and time, and maneuver the network into bending in specific directions, as well as temporally alternating directions. Our work improves understanding the active dynamics in contractile networks, and paves a new path towards engineering the dynamics of a large class of active materials.

preprint2021arXiv

Schrödinger's "What is Life?" at 75

2019 marked the 75th anniversary of the publication of Erwin Schrödinger's "What is Life?", a short book described by Roger Penrose in his preface to a reprint of this classic as "among the most influential scientific writings of the 20th century." In this article, I review the long argument made by Schrödinger as he mused on how the laws of physics could help us understand "the events in space and time which take place within the spatial boundary of a living organism." Though Schrödinger's book is often hailed for its influence on some of the titans who founded molecular biology, this article takes a different tack. Instead of exploring the way the book touched biologists such as James Watson and Francis Crick, as well as its critical reception by others such as Linus Pauling and Max Perutz, I argue that Schrödinger's classic is a timeless manifesto, rather than a dated historical curiosity. "What is Life?" is full of timely outlooks and approaches to understanding the mysterious living world that includes and surrounds us and can instead be viewed as a call to arms to tackle the great unanswered challenges in the study of living matter that remain for 21$^{st}$ century science.

preprint2021arXiv

The Anthropocene by the Numbers: A Quantitative Snapshot of Humanity's Influence on the Planet

The presence and action of humans on Earth has exerted a strong influence on the evolution of the planet over the past $\approx$ 10,000 years, the consequences of which are now becoming broadly evident. Despite a deluge of tightly-focused and necessarily technical studies exploring each facet of "human impacts" on the planet, their integration into a complete picture of the human-Earth system lags far behind. Here, we quantify twelve dimensionless ratios which put the magnitude of human impacts in context, comparing the magnitude of anthropogenic processes to their natural analogues. These ratios capture the extent to which humans alter the terrestrial surface, hydrosphere, biosphere, atmosphere, and biogeochemistry of Earth. In almost all twelve cases, the impact of human processes rivals or exceeds their natural counterparts. The values and corresponding uncertainties for these impacts at global and regional resolution are drawn from the primary scientific literature, governmental and international databases, and industry reports. We present this synthesis of the current "state of affairs" as a graphical snapshot designed to be used as a reference. Furthermore, we establish a searchable database termed the Human Impacts Database (www.anthroponumbers.org) which houses all quantities reported here and many others with extensive curation and annotation. While necessarily incomplete, this work collates and contextualizes a set of essential numbers summarizing the broad impacts of human activities on Earth's atmosphere, land, water, and biota.

preprint2020arXiv

A quantitative compendium of COVID-19 epidemiology

Accurate numbers are needed to understand and predict viral dynamics. Curation of high-quality literature values for the infectious period duration or household secondary attack rate, for example, is especially pressing currently because these numbers inform decisions about how and when to lockdown or reopen societies. We aim to provide a curated source for the key numbers that help us understand the virus driving our current global crisis. This compendium focuses solely on COVID-19 epidemiology. The numbers reported in summary format are substantiated by annotated references. For each property, we provide a concise definition, description of measurement and inference methods, and associated caveats. We hope this compendium will make essential numbers more accessible and avoid common sources of confusion for the many newcomers to the field such as using the incubation period to denote and quantify the latent period or using the hospitalization duration for the infectiousness period duration. This document will be repeatedly updated and the community is invited to participate in improving it.

preprint2020arXiv

Allostery and Kinetic Proofreading

Kinetic proofreading is an error correction mechanism present in the processes of the central dogma and beyond, and typically requires the free energy of nucleotide hydrolysis for its operation. Though the molecular players of many biological proofreading schemes are known, our understanding of how energy consumption is managed to promote fidelity remains incomplete. In our work, we introduce an alternative conceptual scheme called 'the piston model of proofreading' where enzyme activation through hydrolysis is replaced with allosteric activation achieved through mechanical work performed by a piston on regulatory ligands. Inspired by Feynman's ratchet and pawl mechanism, we consider a mechanical engine designed to drive the piston actions powered by a lowering weight, whose function is analogous to that of ATP synthase in cells. Thanks to its mechanical design, the piston model allows us to tune the 'knobs' of the driving engine and probe the graded changes and trade-offs between speed, fidelity and energy dissipation. It provides an intuitive explanation of the conditions necessary for optimal proofreading and reveals the unexpected capability of allosteric molecules to beat the Hopfield limit of fidelity by leveraging the diversity of states available to them. The framework that we built for the piston model can also serve as a basis for additional studies of driven biochemical systems.

preprint2020arXiv

Deciphering the regulatory genome of $\textit{Escherichia coli}$, one hundred promoters at a time

Advances in DNA sequencing have revolutionized our ability to read genomes. However, even in the most well-studied of organisms, the bacterium ${\it Escherichia coli}$, for $\approx$ 65$\%$ of the promoters we remain completely ignorant of their regulation. Until we have cracked this regulatory Rosetta Stone, efforts to read and write genomes will remain haphazard. We introduce a new method (Reg-Seq) linking a massively-parallel reporter assay and mass spectrometry to produce a base pair resolution dissection of more than 100 promoters in ${\it E. coli}$ in 12 different growth conditions. First, we show that our method recapitulates regulatory information from known sequences. Then, we examine the regulatory architectures for more than 80 promoters in the ${\it E. coli}$ genome which previously had no known regulation. In many cases, we also identify which transcription factors mediate their regulation. The method introduced here clears a path for fully characterizing the regulatory genome of model organisms, with the potential of moving on to an array of other microbes of ecological and medical relevance.

preprint2020arXiv

First-principles prediction of the information processing capacity of a simple genetic circuit

Given the stochastic nature of gene expression, genetically identical cells exposed to the same environmental inputs will produce different outputs. This heterogeneity has been hypothesized to have consequences for how cells are able to survive in changing environments. Recent work has explored the use of information theory as a framework to understand the accuracy with which cells can ascertain the state of their surroundings. Yet the predictive power of these approaches is limited and has not been rigorously tested using precision measurements. To that end, we generate a minimal model for a simple genetic circuit in which all parameter values for the model come from independently published data sets. We then predict the information processing capacity of the genetic circuit for a suite of biophysical parameters such as protein copy number and protein-DNA affinity. We compare these parameter-free predictions with an experimental determination of protein expression distributions and the resulting information processing capacity of E. coli cells. We find that our minimal model captures the scaling of the cell-to-cell variability in the data and the inferred information processing capacity of our simple genetic circuit up to a systematic deviation.

preprint2020arXiv

Proofreading through spatial gradients

Key enzymatic processes in biology use the nonequilibrium error correction mechanism called kinetic proofreading to enhance their specificity. Kinetic proofreading typically requires several dedicated structural features in the enzyme, such as a nucleotide hydrolysis site and multiple enzyme-substrate conformations that delay product formation. Such requirements limit the applicability and the adaptability of traditional proofreading schemes. Here, we explore an alternative conceptual mechanism of error correction that achieves delays between substrate binding and subsequent product formation by having these events occur at distinct physical locations. The time taken by the enzyme-substrate complex to diffuse from one location to another is leveraged to discard wrong substrates. This mechanism does not require dedicated structural elements on the enzyme, making it easier to overlook in experiments but also making proofreading tunable on the fly. We discuss how tuning the length scales of enzyme or substrate concentration gradients changes the fidelity, speed and energy dissipation, and quantify the performance limitations imposed by realistic diffusion and reaction rates in the cell. Our work broadens the applicability of kinetic proofreading, and sets the stage for the study of spatial gradients as a possible route to specificity.

preprint2020arXiv

Quantitative clarification of key questions about COVID-19 epidemiology

Modeling the spread of COVID-19 is crucial for informing public health policy. All models for COVID-19 epidemiology rely on parameters describing the dynamics of the infection process. The meanings of epidemiological parameters like R_0, R_t, the "serial interval" and "generation interval" can be challenging to understand, especially as these and other parameters are conceptually overlapping and sometimes confusingly named. Moreover, the procedures used to estimate these parameters make various assumptions and use different mathematical approaches that should be understood and accounted for when relying on parameter values and reporting them to the public. Here, we offer several insights regarding the derivation of commonly-reported epidemiological parameters, and describe how mitigation measures like lockdown are expected to affect their values. We aim to present these quantitative relationships in a manner that is accessible to the widest audience possible. We hope that better communicating the intricacies of epidemiological models will improve our collective understanding of their strengths and weaknesses, and will help avoid possible pitfalls when using them.

preprint2020arXiv

SARS-CoV-2 (COVID-19) by the numbers

The current SARS-CoV-2 pandemic is a harsh reminder of the fact that, whether in a single human host or a wave of infection across continents, viral dynamics is often a story about the numbers. In this snapshot, our aim is to provide a one-stop, curated graphical source for the key numbers that help us understand the virus driving our current global crisis. The discussion is framed around two broad themes: 1) the biology of the virus itself and 2) the characteristics of the infection of a single human host. Our one-page summary provides the key numbers pertaining to SARS-CoV-2, based mostly on peer-reviewed literature. The numbers reported in summary format are substantiated by the annotated references below. Readers are urged to remember that much uncertainty remains and knowledge of this pandemic and the virus driving it is rapidly evolving. In the paragraphs below we provide "back of the envelope" calculations that exemplify the insights that can be gained from knowing some key numbers and using quantitative logic. These calculations serve to improve our intuition through sanity checks, but do not replace detailed epidemiological analysis.

preprint2019arXiv

Harnessing Avidity: Quantifying Entropic and Energetic Effects of Linker Length and Rigidity Required for Multivalent Binding of Antibodies to HIV-1 Spikes

Due to the low density of envelope (Env) spikes on the surface of HIV-1, neutralizing IgG antibodies rarely bind bivalently using both antigen-binding arms (Fabs) to crosslink between spikes (inter-spike crosslinking), instead resorting to weaker monovalent binding that is more sensitive to Env mutations. Synthetic antibodies designed to bivalently bind a single Env trimer (intra-spike crosslinking) were previously shown to exhibit increased neutralization potencies. In initial work, diFabs joined by varying lengths of rigid double-stranded DNA (dsDNA) were considered. Anticipating future experiments to improve synthetic antibodies, we investigate whether linkers with different rigidities could enhance diFab potency by modeling DNA-Fabs containing different combinations of rigid dsDNA and flexible single-stranded DNA (ssDNA) and characterizing their neutralization potential. Model predictions suggest that while a long flexible polymer may be capable of bivalent binding, it exhibits weak neutralization due to the large loss in entropic degrees of freedom when both Fabs are bound. In contrast, the strongest neutralization potencies are predicted to require a rigid linker that optimally spans the distance between two Fab binding sites on an Env trimer, and avidity can be further boosted by incorporating more Fabs into these constructs. These results inform the design of multivalent anti-HIV-1 therapeutics that utilize avidity effects to remain potent against HIV-1 in the face of the rapid mutation of Env spikes.

preprint2019arXiv

The Energetics of Molecular Adaptation in Transcriptional Regulation

Mutation is a critical mechanism by which evolution explores the functional landscape of proteins. Despite our ability to experimentally inflict mutations at will, it remains difficult to link sequence-level perturbations to systems-level responses. Here, we present a framework centered on measuring changes in the free energy of the system to link individual mutations in an allosteric transcriptional repressor to the parameters which govern its response. We find the energetic effects of the mutations can be categorized into several classes which have characteristic curves as a function of the inducer concentration. We experimentally test these diagnostic predictions using the well-characterized LacI repressor of Escherichia coli, probing several mutations in the DNA binding and inducer binding domains. We find that the change in gene expression due to a point mutation can be captured by modifying only a subset of the model parameters that describe the respective domain of the wild-type protein. These parameters appear to be insulated, with mutations in the DNA binding domain altering only the DNA affinity and those in the inducer binding domain altering only the allosteric parameters. Changing these subsets of parameters tunes the free energy of the system in a way that is concordant with theoretical expectations. Finally, we show that the induction profiles and resulting free energies associated with pairwise double mutants can be predicted with quantitative accuracy given knowledge of the single mutants, providing an avenue for identifying and quantifying epistatic interactions.

preprint2017arXiv

The Energetic Cost of Building a Virus

Viruses are incapable of autonomous energy production. Although many experimental studies make it clear that viruses are parasitic entities that hijack the host's molecular resources, a detailed estimate for the energetic cost of viral synthesis is largely lacking. To quantify the energetic cost of viruses to their hosts, we enumerated the costs associated with two very distinct but representative DNA and RNA viruses, namely T4 and influenza. We found that for these viruses, translation of viral proteins is the most energetically expensive process. Interestingly, the cost of building a T4 phage and a single influenza virus are nearly the same. Due to influenza's higher burst size, however, the overall cost of a T4 phage infection is only 2-3% of the cost of an influenza infection. The costs of these infections relative to their host's estimated energy budget during the infection reveal that a T4 infection consumes about a third of its host's energy budget, where as an influenza infection consumes only 1%. Building on our estimates for T4, we show how the energetic costs of double-stranded DNA viruses scale with virus size, revealing that the dominant cost of building a virus can switch from translation to genome replication above a critical virus size. Lastly, using our predictions for the energetic cost of viruses, we provide estimates for the strengths of selection and genetic drift acting on newly incorporated genetic elements in viral genomes, under conditions of energy limitation.

preprint2015arXiv

Modulation of DNA loop lifetimes by the free energy of loop formation

Storage and retrieval of the genetic information in cells is a dynamic process that requires the DNA to undergo dramatic structural rearrangements. DNA looping is a prominent example of such a structural rearrangement that is essential for transcriptional regulation in both prokaryotes and eukaryotes, and the speed of such regulations affects the fitness of individuals. Here, we examine the in vitro looping dynamics of the classic Lac repressor gene-regulatory motif. We show that both loop association and loop dissociation at the DNA-repressor junctions depend on the elastic deformation of the DNA and protein, and that both looping and unlooping rates approximately scale with the looping J factor, which reflects the system's deformation free energy. We explain this observation by transition state theory and model the DNA-protein complex as an effective worm-like chain with twist. We introduce a finite protein-DNA binding interaction length, in competition with the characteristic DNA deformation length scale, as the physical origin of the previously unidentified loop dissociation dynamics observed here, and discuss the robustness of this behavior to perturbations in several polymer parameters.

preprint2014arXiv

Multiple Lac-mediated loops revealed by Bayesian statistics and tethered particle motion

The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple co-existing loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly-used in vitro single-molecule technique. Our method, vbTPM, performs variational Bayesian inference in hidden Markov models. It learns the number of distinct states (i.e., DNA-protein conformations) directly from tethered particle motion data with better resolution than existing methods, while easily correcting for common experimental artifacts. Studying short (roughly 100 bp) LacI-mediated loops, we provide evidence for three distinct loop structures, more than previously reported in single-molecule studies. Moreover, our results confirm that changes in LacI conformation and DNA binding topology both contribute to the repertoire of LacI-mediated loops formed in vitro, and provide qualitatively new input for models of looping and transcriptional regulation. We expect vbTPM to be broadly useful for probing complex protein-nucleic acid interactions.

preprint2013arXiv

Directional interactions and cooperativity between mechanosensitive membrane proteins

While modern structural biology has provided us with a rich and diverse picture of membrane proteins, the biological function of membrane proteins is often influenced by the mechanical properties of the surrounding lipid bilayer. Here we explore the relation between the shape of membrane proteins and the cooperative function of membrane proteins induced by membrane-mediated elastic interactions. For the experimental model system of mechanosensitive ion channels we find that the sign and strength of elastic interactions depend on the protein shape, yielding distinct cooperative gating curves for distinct protein orientations. Our approach predicts how directional elastic interactions affect the molecular structure, organization, and biological function of proteins in crowded membranes.

preprint2013arXiv

DNA sequence-dependent mechanics and protein-assisted bending in repressor-mediated loop formation

As the chief informational molecule of life, DNA is subject to extensive physical manipulations. The energy required to deform double-helical DNA depends on sequence, and this mechanical code of DNA influences gene regulation, such as through nucleosome positioning. Here we examine the sequence-dependent flexibility of DNA in bacterial transcription factor-mediated looping, a context for which the role of sequence remains poorly understood. Using a suite of synthetic constructs repressed by the Lac repressor and two well-known sequences that show large flexibility differences in vitro, we make precise statistical mechanical predictions as to how DNA sequence influences loop formation and test these predictions using in vivo transcription and in vitro single-molecule assays. Surprisingly, sequence-dependent flexibility does not affect in vivo gene regulation. By theoretically and experimentally quantifying the relative contributions of sequence and the DNA-bending protein HU to DNA mechanical properties, we reveal that bending by HU dominates DNA mechanics and masks intrinsic sequence-dependent flexibility. Such a quantitative understanding of how mechanical regulatory information is encoded in the genome will be a key step towards a predictive understanding of gene regulation at single-base pair resolution.

preprint2013arXiv

Poly(dA:dT)-rich DNAs are highly flexible in the context of DNA looping

Large-scale DNA deformation is ubiquitous in transcriptional regulation in prokaryotes and eukaryotes alike. Though much is known about how transcription factors and constellations of binding sites dictate where and how gene regulation will occur, less is known about the role played by the intervening DNA. In this work we explore the effect of sequence flexibility on transcription factor-mediated DNA looping, by drawing on sequences identified in nucleosome formation and ligase-mediated cyclization assays as being especially favorable for or resistant to large deformations. We examine a poly(dA:dT)-rich, nucleosome-repelling sequence that is often thought to belong to a class of highly inflexible DNAs; two strong nucleosome positioning sequences that share a set of particular sequence features common to nucleosome-preferring DNAs; and a CG-rich sequence representative of high G+C-content genomic regions that correlate with high nucleosome occupancy in vivo. To measure the flexibility of these sequences in the context of DNA looping, we combine the in vitro single-molecule tethered particle motion assay, a canonical looping protein, and a statistical mechan- ical model that allows us to quantitatively relate the looping probability to the looping free energy. We show that, in contrast to the case of nucleosome occupancy, G+C content does not positively correlate with looping probability, and that despite sharing sequence features that are thought to determine nucleosome affinity, the two strong nucleosome positioning sequences behave markedly dissimilarly in the context of looping. Most surprisingly, the poly(dA:dT)-rich DNA that is often characterized as highly inflexible in fact exhibits one of the highest propensities for looping that we have measured.

preprint2012arXiv

A Single-Molecule Hershey-Chase Experiment

Ever since Hershey and Chase used phages to establish DNA as the carrier of genetic information in 1952, the precise mechanisms of phage DNA translocation have been a mystery. While bulk measurements have set a time scale for in vivo DNA translocation during bacteriophage infection, measurements of DNA ejection by single bacteriophages have only been made in vitro. Here, we present direct visualization of single bacteriophages infecting individual Escherichia coli cells. For bacteriophage lambda, we establish a mean ejection time of roughly 5 minutes with significant cell-to-cell variability, including pausing events. In contrast, corresponding in vitro single-molecule ejections take only 10 seconds to reach completion and do not exhibit significant variability. Our data reveal that the velocity of ejection for two different genome lengths collapses onto a single curve. This suggests that in vivo ejections are controlled by the amount of DNA ejected, in contrast with in vitro DNA ejections, which are governed by the amount of DNA left inside the capsid. This analysis provides evidence against a purely intrastrand repulsion based mechanism, and suggests that cell-internal processes dominate. This provides a picture of the early stages of phage infection and sheds light on the problem of polymer translocation.

preprint2012arXiv

Sequence Dependence of Transcription Factor-Mediated DNA Looping

DNA is subject to large deformations in a wide range of biological processes. Two key examples illustrate how such deformations influence the readout of the genetic information: the sequestering of eukaryotic genes by nucleosomes, and DNA looping in transcriptional regulation in both prokaryotes and eukaryotes. These kinds of regulatory problems are now becoming amenable to systematic quantitative dissection with a powerful dialogue between theory and experiment. Here we use a single-molecule experiment in conjunction with a statistical mechanical model to test quantitative predictions for the behavior of DNA looping at short length scales, and to determine how DNA sequence affects looping at these lengths. We calculate and measure how such looping depends upon four key biological parameters: the strength of the transcription factor binding sites, the concentration of the transcription factor, and the length and sequence of the DNA loop. Our studies lead to the surprising insight that sequences that are thought to be especially favorable for nucleosome formation because of high flexibility lead to no systematically detectable effect of sequence on looping, and begin to provide a picture of the distinctions between the short length scale mechanics of nucleosome formation and looping.

preprint2011arXiv

Elastic energy of polyhedral bilayer vesicles

In recent experiments [M. Dubois, B. Demé, T. Gulik-Krzywicki, J.-C. Dedieu, C. Vautrin, S. Désert, E. Perez, and T. Zemb, Nature (London) Vol. 411, 672 (2001)] the spontaneous formation of hollow bilayer vesicles with polyhedral symmetry has been observed. On the basis of the experimental phenomenology it was suggested [M. Dubois, V. Lizunov, A. Meister, T. Gulik-Krzywicki, J. M. Verbavatz, E. Perez, J. Zimmerberg, and T. Zemb, Proc. Natl. Acad. Sci. U.S.A. Vol. 101, 15082 (2004)] that the mechanism for the formation of bilayer polyhedra is minimization of elastic bending energy. Motivated by these experiments, we study the elastic bending energy of polyhedral bilayer vesicles. In agreement with experiments, and provided that excess amphiphiles exhibiting spontaneous curvature are present in sufficient quantity, we find that polyhedral bilayer vesicles can indeed be energetically favorable compared to spherical bilayer vesicles. Consistent with experimental observations we also find that the bending energy associated with the vertices of bilayer polyhedra can be locally reduced through the formation of pores. However, the stabilization of polyhedral bilayer vesicles over spherical bilayer vesicles relies crucially on molecular segregation of excess amphiphiles along the ridges rather than the vertices of bilayer polyhedra. Furthermore, our analysis implies that, contrary to what has been suggested on the basis of experiments, the icosahedron does not minimize elastic bending energy among arbitrary polyhedral shapes and sizes. Instead, we find that, for large polyhedron sizes, the snub dodecahedron and the snub cube both have lower total bending energies than the icosahedron.

preprint2011arXiv

Minimal Bending Energies of Bilayer Polyhedra

Motivated by recent experiments on bilayer polyhedra composed of amphiphilic molecules, we study the elastic bending energies of bilayer vesicles forming polyhedral shapes. Allowing for segregation of excess amphiphiles along the ridges of polyhedra, we find that bilayer polyhedra can indeed have lower bending energies than spherical bilayer vesicles. However, our analysis also implies that, contrary to what has been suggested on the basis of experiments, the snub dodecahedron, rather than the icosahedron, generally represents the energetically favorable shape of bilayer polyhedra.

preprint2010arXiv

An equivalence between a Maximum Caliber analysis of two-state kinetics and the Ising model

Application of the information-theoretic Maximum Caliber principle to the microtrajectories of a two-state system shows that the determination of key dynamical quantities can be mapped onto the evaluation of properties of the 1-D Ising model. The strategy described here is equivalent to an earlier Maximum Caliber formulation of the two-state problem, but reveals a different way of imposing the constraints which determine the probability distribution of allowed microtrajectories. The theoretical calculations of second moments, covariances, and correlation times that are obtained from Maximum Caliber agree well with simulated data of a particle diffusing on a double Gaussian surface, as well as with recent experiments on a particle trapped by a dual-well optical trap. The formalism reveals a new relationship between the average occupancy of the two states of the system, the average number of transitions between the two states that the system undergoes, Markov transition probabilities, and the discretization time step. In addition, Maxwell-like relations imply how measurements on one potential landscape can be used to make predictions about the dynamics on a different potential landscape, independent of further experiment.

preprint2010arXiv

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, the architecture of a promoter, defined as the number, strength and regulatory role of the operators that control the promoter, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect noise in gene expression in a systematic rather than case-by-case fashion. In this article, we make such a systematic investigation, based on a simple microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcription product from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can discriminate between different kinetic models of gene regulation.

preprint2010arXiv

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.

preprint2009arXiv

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.

preprint2008arXiv

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.

preprint2007arXiv

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.

preprint2005arXiv

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.

Rob Phillips

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32 published item(s)

Conditioning as a route to stereotyped behavior in growing populations

Informational blueprints reveal condition-dependent gene regulatory architectures

Modeling and mechanical perturbations reveal how spatially regulated anchorage gives rise to spatially distinct mechanics across the mammalian spindle

Programming Boundary Deformation Patterns in Active Networks

Schrödinger's "What is Life?" at 75

The Anthropocene by the Numbers: A Quantitative Snapshot of Humanity's Influence on the Planet

A quantitative compendium of COVID-19 epidemiology

Allostery and Kinetic Proofreading

Deciphering the regulatory genome of $\textit{Escherichia coli}$, one hundred promoters at a time

First-principles prediction of the information processing capacity of a simple genetic circuit

Proofreading through spatial gradients

Quantitative clarification of key questions about COVID-19 epidemiology

SARS-CoV-2 (COVID-19) by the numbers

Harnessing Avidity: Quantifying Entropic and Energetic Effects of Linker Length and Rigidity Required for Multivalent Binding of Antibodies to HIV-1 Spikes

The Energetics of Molecular Adaptation in Transcriptional Regulation

The Energetic Cost of Building a Virus

Modulation of DNA loop lifetimes by the free energy of loop formation

Multiple Lac-mediated loops revealed by Bayesian statistics and tethered particle motion

Directional interactions and cooperativity between mechanosensitive membrane proteins

DNA sequence-dependent mechanics and protein-assisted bending in repressor-mediated loop formation

Poly(dA:dT)-rich DNAs are highly flexible in the context of DNA looping

A Single-Molecule Hershey-Chase Experiment

Sequence Dependence of Transcription Factor-Mediated DNA Looping

Elastic energy of polyhedral bilayer vesicles

Minimal Bending Energies of Bilayer Polyhedra

An equivalence between a Maximum Caliber analysis of two-state kinetics and the Ising model

Effect of promoter architecture on the cell-to-cell variability in gene expression

Ion-dependent dynamics of DNA ejections for bacteriophage lambda

Morphology and Interaction between Lipid Domains

Concentration and Length Dependence of DNA Looping in Transcriptional Regulation

Cooperative Gating and Spatial Organization of Membrane Proteins through Elastic Interactions

Teaching the Principles of Statistical Dynamics