Jane Kondev

Forces during Bacteriophage DNA Packaging and Ejection

The conjunction of insights from structural biology, solution biochemistry, genetics, and single-molecule biophysics has provided a renewed impetus for the construction of quantitative models of biological processes. One area that has been a beneficiary of these experimental techniques is the study of viruses. In this article we describe how the insights obtained from such experiments can be utilized to construct physical models of processes in the viral life cycle. We focus on dsDNA bacteriophages and show that the bending elasticity of DNA and its electrostatics in solution can be combined to determine the forces experienced during packaging and ejection of the viral genome. Furthermore, we quantitatively analyze the effect of fluid viscosity and capsid expansion on the forces experienced during packaging. Finally, we present a model for DNA ejection from bacteriophages based on the hypothesis that the energy stored in the tightly packed genome within the capsid leads to its forceful ejection. The predictions of our model can be tested through experiments in vitro where DNA ejection is inhibited by the application of external osmotic pressure.

Mechanics of DNA packaging in viruses

A new generation of single-molecule experiments has opened up the possibility of reexamining many of the fundamental processes of biochemistry and molecular biology from a unique and quantitative perspective. One technique producing a host of intriguing results is the use of optical tweezers to measure the mechanical forces exerted by molecular motors during key processes such as the transcription of DNA or the packing of a viral genome into its capsid. The objective of the current article is to respond to such measurements on viruses and to use the theory of elasticity and a simple model of charge and hydration forces to derive the force required to pack DNA into a viral capsid as a function of the fraction of the viral genome that has been packed. The results are found to be in excellent accord with recent measurements and complement previous theoretical work. Because the packing of DNA in viral capsids occurs under circumstances of high internal pressure, we also compute how much pressure a capsid can sustain without rupture.

Strong intranucleoid interactions organize the Escherichia coli chromosome into a nucleoid filament

The stochasticity of chromosome organization was investigated by fluorescently labeling genetic loci in live Escherichia coli cells. In spite of the common assumption that the chromosome is well modeled by an unstructured polymer, measurements of the locus distributions reveal that the E. coli chromosome is precisely organized into a nucleoid filament with a linear order. Loci in the body of the nucleoid show a precision of positioning within the cell of better than 10% of the cell length. The precision of interlocus distance of genomically-proximate loci was better than 4% of the cell length. The measured dependence of the precision of interlocus distance on genomic distance singles out intranucleoid interactions as the mechanism responsible for chromosome organization. From the magnitude of the variance, we infer the existence of an as-yet uncharacterized higher-order DNA organization in bacteria. We demonstrate that both the stochastic and average structure of the nucleoid is captured by a fluctuating elastic filament model.

Transcriptional control of noise in gene expression

Cis-regulatory control of transcription is the dominant form of regulation of gene expression. Recent experimental results suggest that, in addition to the mean expression level, cell-to-cell variability might also be transcriptionally regulated. Here, we develop a stochastic model of transcriptional regulation that allows us to calculate closed-form analytical expressions for the mean and variance of the protein and mRNA distributions for an arbitrarily complex cis-regulatory motif. Our model allows us to investigate how noise may be transcriptionally regulated independently from the mean expression. We show that our approach is in excellent agreement with stochastic simulations and experiment, and leads to an experimentally testable formula for the noise in gene expression as a function of inducer-molecule concentrations.

Regulation of Noise in Gene Expression

The biochemical processes leading to the synthesis of new proteins are random, as they typically involve a small number of diffusing molecules. They lead to fluctuations in the number of proteins in a single cell as a function of time and to cell-to-cell variability of protein abundances. These in turn can lead to phenotypic heterogeneity in a population of genetically identical cells. Phenotypic heterogeneity may have important consequences for the development of multicellular organisms and the fitness of bacterial colonies, raising the question of how it is regulated. Here we review the experimental evidence that transcriptional regulation affects noise in gene expression, and discuss how the noise strength is encoded in the architecture of the promoter region. We discuss how models based on specific molecular mechanisms of gene regulation can make experimentally testable predictions for how changes to the promoter architecture are reflected in gene expression noise.

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

According to recent experimental evidence, promoter architecture, defined by the number, strength and regulatory role of the operators that control transcription, 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 variability in gene expression in a systematic rather than case-by-case fashion. In this article we make such a systematic investigation, based on a 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 transcriptional output 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 be used to test kinetic models of gene regulation. The emphasis of the discussion is on prokaryotic gene regulation, but our analysis can be extended to eukaryotic cells as well.

Thermodynamics of Biological Processes

There is a long and rich tradition of using ideas from both equilibrium thermodynamics and its microscopic partner theory of equilibrium statistical mechanics. In this chapter, we provide some background on the origins of the seemingly unreasonable effectiveness of ideas from both thermodynamics and statistical mechanics in biology. After making a description of these foundational issues, we turn to a series of case studies primarily focused on binding that are intended to illustrate the broad biological reach of equilibrium thinking in biology. These case studies include ligand-gated ion channels, thermodynamic models of transcription, and recent applications to the problem of bacterial chemotaxis. As part of the description of these case studies, we explore a number of different uses of the famed Monod-Wyman-Changeux (MWC) model as a generic tool for providing a mathematical characterization of two-state systems. These case studies should provide a template for tailoring equilibrium ideas to other problems of biological interest.

Transcription by the Numbers Redux: Experiments and Calculations that Surprise

The study of transcription has witnessed an explosion of quantitative effort both experimentally and theoretically. In this article we highlight some of the exciting recent experimental efforts in the study of transcription with an eye to the demands that such experiments put on theoretical models of transcription. From a modeling perspective, we focus on two broad classes of models: the so-called thermodynamic models that use statistical mechanics to reckon the level of gene expression as probabilities of promoter occupancy, and rate-equation treatments that focus on the temporal evolution of the activity of a given promoter and that make it possible to compute the distributions of messenger RNA and proteins. We consider several appealing case studies to illustrate how quantitative models have been used to dissect transcriptional regulation.

Stochastic models of transcription: From single molecules to single cells

Genes in prokaryotic and eukaryotic cells are typically regulated by complex promoters containing multiple binding sites for a variety of transcription factors leading to a specific functional dependence between regulatory inputs and transcriptional outputs. With increasing regularity, the transcriptional outputs from different promoters are being measured in quantitative detail in single-cell experiments thus providing the impetus for the development of quantitative models of transcription. We describe recent progress in developing models of transcriptional regulation that incorporate, to different degrees, the complexity of multi-state promoter dynamics, and its effect on the transcriptional outputs of single cells. The goal of these models is to predict the statistical properties of transcriptional outputs and characterize their variability in time and across a population of cells, as a function of the input concentrations of transcription factors. The interplay between mathematical models of different regulatory mechanisms and quantitative biophysical experiments holds the promise of elucidating the molecular-scale mechanisms of transcriptional regulation in cells, from bacteria to higher eukaryotes.

Reduced amino acid alphabets exhibit an improved sensitivity and selectivity in fold assignment

MOTIVATION Many proteins with vastly dissimilar sequences are found to share a common fold, as evidenced in the wealth of structures now available in the Protein Data Bank. One idea that has found success in various applications is the concept of a reduced amino acid alphabet, wherein similar amino acids are clustered together. Given the structural similarity exhibited by many apparently dissimilar sequences, we undertook this study looking for improvements in fold recognition by comparing protein sequences written in a reduced alphabet. RESULTS We tested over 150 of the amino acid clustering schemes proposed in the literature with all-versus-all pairwise sequence alignments of sequences in the Distance mAtrix aLIgnment database. We combined several metrics from information retrieval popular in the literature: mean precision, area under the Receiver Operating Characteristic curve and recall at a fixed error rate and found that, in contrast to previous work, reduced alphabets in many cases outperform full alphabets. We find that reduced alphabets can perform at a level comparable to full alphabets in correct pairwise alignment of sequences and can show increased sensitivity to pairs of sequences with structural similarity but low-sequence identity. Based on these results, we hypothesize that reduced alphabets may also show performance gains with more sophisticated methods such as profile and pattern searches. AVAILABILITY A table of results as well as the substitution matrices and residue groupings from this study can be downloaded from (http://www.rpgroup.caltech.edu/publications/supplements/alphabets).