The readings listed below are the foundation of this course. Where available, journal article abstracts from PubMed (an online database providing access to citations from biomedical literature) are included.

Recommended Textbooks

Alberts, B. et al. Molecular biology of the cell. 3rd edition. Garland, 1995.

Edelstein-Keshet, L. Mathematical models in biology. McGraw-Hill, 1988.

Fell, D. Understanding the control of metabolism. Portland Press, 1997.

Goldbeter, A. Biochemical oscillations and cellular rhythms. Cambridge Univ., 1996.

Heinrich, R., and S. Schuster. The regulation of cellular systems. Chapman & Hall, 1996.

Murray, J. D. Mathematical biology. 2nd edition. Springer, 1993.

Ptashne, M. A genetic switch. 2nd edition. Cell Press, 1992.

Reading List by Lecture

Introduction and Overview

The Problem of Understanding Nonlinearity and Feedback in Biological Networks

"From Molecules to the First Cell." Chap 1. in Molecular Biology of the cell. Pp. 4-11.

Gold, L, et al. "From Oligonucleotide Shapes to Genomic SELEX: Novel Biological Regulatory Loops." Proc. Natl. Acad. Sci. USA 94 (1997): 59-64.

PubMed abstract: The SELEX method and oligonucleotide combinatorial chemistry discovery process yields high-affinity/high-specificity ligands for virtually any molecular target. Typically, the enormous starting libraries used in the SELEX process contain 10(14)-10(15) sequences. We now ask if the smaller sequences, complexity of extant organisms, and evolutionary history provide useful interactions between oligonucleotides and at least some unexpected targets. That is, do organisms contain a robust "linkage map" between their oligonucleotides and proteins and/or small molecules that enriches life?


Spiegelman, S. "An Approach to the Experimental Analysis of Precellular Evolution." Q. Rev. Biophys. 4 (1971): 213-53.

"Viruses, Plasmids, and Transposable Genetic Elements." Chap 6. in Molecular Biology of the cell. Pp. 273-8.

DNA Computing and Self-Assembly

Adleman, L. M. "Molecular Computation of Solutions to Combinatorial Problems." Science 266(5187) (11 Nov 1994): 1021-4.

PubMed abstract: The tools of molecular biology were used to solve an instance of the directed Hamiltonian path problem. A small graph was encoded in molecules of DNA, and the "operations" of the computation were performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying out computations at the molecular level.

E, Winfree, Liu F, Wenzler LA, and Seeman NC. "Design and Self-Assembly of Two Dimensional DNA Crystals." Nature 394(6693) (6 Aug 1998): 539-44.

PubMed abstract: Molecular self-assembly presents a 'bottom-up' approach to the fabrication of objects specified with nanometre precision. DNA molecular structures and intermolecular interactions are particularly amenable to the design and synthesis of complex molecular objects. We report the design and observation of two-dimensional crystalline forms of DNA that self-assemble from synthetic DNA double-crossover molecules. Intermolecular interactions between the structural units are programmed by the design of 'sticky ends' that associate according to Watson-Crick complementarity, enabling us to create specific periodic patterns on the nanometre scale. The patterned crystals have been visualized by atomic force microscopy.

Enzyme Kinetics. Michaelis-Menten Theory

Cooperative BehaviorHeinrich and Schuster. This resource may not render correctly in a screen reader.The Regulation of Cellular Systems (PDF - 8.2 MB). Pp. 16-24.

Stryer. Pp. 192-9.

Metabolic Control Analysis

Fell, D. A. "Metabolic Control Analysis: A Survey of its Theoretical and Experimental Development." Biochem. J. 286 (1992): 313-30.

Heinrich and Schuster. This resource may not render correctly in a screen reader.The Regulation of Cellular Systems. Pp. 160-2.

General Formalism for Chemical Reaction Networks

Metabolic Flux AnalysisHeinrich and Schuster. The regulation of cellular systems. Pp. 9-15.

Theory of Chemical Computation

Magnasco, M. O. "Chemical Kinetics is Turing Universal." Phys. Rev. Lett. 78 (1997): 1190-3.

Overview of Transcriptional Regulation - Lambda Phage

Spiegelman, S. "An Approach to the Experimental Analysis of Precellular Evolution." Q. Rev. Biophys. 4 (1971): 213-53.

Molecular biology of the cell. Chap 6 (Pp. 223-7), Chap 8 (Pp. 365-71), Chap 9 (Pp. 401-453).

Student Presentations Synthetic Genetic Networks

Elowitz, M., and S. Leibler. "A Synthetic Oscillatory Network of Transcriptional Regulators." Nature 403 (2000): 335-338.

PubMed abstract: Networks of interacting biomolecules carry out many essential functions in living cells, but the 'design principles' underlying the functioning of such intracellular networks remain poorly understood, despite intensive efforts including quantitative analysis of relatively simple systems. Here we present a complementary approach to this problem: the design and construction of a synthetic network to implement a particular function. We used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli. The network periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells. The resulting oscillations, with typical periods of hours, are slower than the cell-division cycle, so the state of the oscillator has to be transmitted from generation to generation. This artificial clock displays noisy behaviour, possibly because of stochastic fluctuations of its components. Such 'rational network design may lead both to the engineering of new cellular behaviours and to an improved understanding of naturally occurring networks.

Gardner, T. S., C. R. Cantor, and J. J. Collins. "Construction of a Genetic Toggle Switch In Escherichia Coli." Nature 403 (2000): 339-342.

PubMed abstract: It has been proposed' that gene-regulatory circuits with virtually any desired property can be constructed from networks of simple regulatory elements. These properties, which include multistability and oscillations, have been found in specialized gene circuits such as the bacteriophage lambda switch and the Cyanobacteria circadian oscillator. However, these behaviours have not been demonstrated in networks of non-specialized regulatory components. Here we present the construction of a genetic toggle switch-a synthetic, bistable gene-regulatory network-in Escherichia coli and provide a simple theory that predicts the conditions necessary for bistability. The toggle is constructed from any two repressible promoters arranged in a mutually inhibitory network. It is flipped between stable states using transient chemical or thermal induction and exhibits a nearly ideal switching threshold. As a practical device, the toggle switch forms a synthetic, addressable cellular memory unit and has implications for biotechnology, biocomputing and gene therapy.

Additional readings

Lutz, R., and H. Bujard. "Independent and Tight Regulation of Transcriptional Units in Escherichia Coli via the LacR/O, the TetR/O and AraC/I1-I2 Regulatory Elements." Nucleic Acids Res. 25 (1997): 1203-10.

PubMed abstract: Based on parameters governing promoter activity and using regulatory elements of the lac, ara and tet operon transcription control sequences were composed which permit the regulation in Escherichia coli of several gene activities independently and quantitatively. The novel promoter PLtetO-1 allows the regulation of gene expression over an up to 5000-fold range with anhydrotetracycline (aTc) whereas with IPTG and arabinose the activity of Plac/ara-1 may be controlled 1800-fold. Escherichia coli host strains which produce defined amounts of the regulatory proteins, Lac and Tet repressor as well as AraC from chromosomally located expression units provide highly reproducible in vivo conditions. Controlling the expression of the genes encoding luciferase, the low abundance E.coli protein DnaJ and restriction endonuclease Cfr9I not only demonstrates that high levels of expression can be achieved but also suggests that under conditions of optimal repression only around one mRNA every 3rd generation is produced. This potential of quantitative control will open up new approaches in the study of gene function in vivo, in particular with low abundance regulatory gene products. The system will also provide new opportunities for the controlled expression of heterologous genes.

Oscillations in an Activator-Inhibitor System - Phase Plane Analysis

Stochastic simulations of chemical reactions.

Additional reading:

Gillespie, D. T. "Exact Stochastic Simulation of Coupled Chemical Reactions." J. Phys. Chem. 81 (1977): 2341-61.

Edelstein-Keshet, L. Mathematical models in biology.

Strogatz, S. Nonlinear Dynamics and Chaos.

Hodgkin-Huxley Model of the Action Potential

Koch, C. Chap. 6 in Biophysics of Computation.

Spike Frequency Adaptation and Negative Feedback Linearization

Ermentrout, B. "Linearization of F-I Curves by Adaptation." Neural Comput. 10 (1998): 1721-9.


Detwiler P., S. Ramanathan, A. Sengupta, and B. I. Shraiman. Engineering Aspects of Enzymatic Signal Transduction: Photo-receptors in the Retina. (Preprint).

Gray-Keller M., W. Denk, B. Shraiman, and P. B. Detwiler. "Longitudinal Spread of Second Messenger Signals in Isolated Rod Outer Segments of Lizards." J. Physiol. 519.3 (1999): 679-92.

Rodieck, R. W. The First Steps in Seeing. Sinauer. 1998.

Stryer. Chap. 13.


Alon, U., M. G. Surette, N. Barkai, and S. Leibler. "Robustness in Bacterial Chemotaxis." Nature 397 (1999): 168-71.

PubMed abstract: Networks of interacting proteins orchestrate the responses of living cells to a variety of external stimuli, but how sensitive is the functioning of these protein networks to variations in their biochemical parameters? One possibility is that to achieve appropriate function, the reaction rate constants and enzyme concentrations need to be adjusted in a precise manner, and any deviation from these 'fine-tuned' values ruins the network's performance. An alternative possibility is that key properties of biochemical networks are robust; that is, they are insensitive to the precise values of the biochemical parameters. Here we address this issue in experiments using chemotaxis of Escherichia coli, one of the best-characterized sensory systems. We focus on how response and adaptation to attractant signals vary with systematic changes in the intracellular concentration of the components of the chemotaxis network. We find that some properties, such as steady-state behaviour and adaptation time, show strong variations in response to varying protein concentrations. In contrast, the precision of adaptation is robust and does not vary with the protein concentrations. This is consistent with a recently proposed molecular mechanism for exact adaptation, where robustness is a direct consequence of the network's architecture.

Barkai, N., and S. Leibler. "Robustness in Simple Biochemical Networks." Nature 387 (1997): 913-7.

PubMed abstract: Cells use complex networks of interacting molecular components to transfer and process information. These "computational devices of living cells" are responsible for many important cellular processes, including cell-cycle regulation and signal transduction. Here we address the issue of the sensitivity of the networks to variations in their biochemical parameters. We propose a mechanism for robust adaptation in simple signal transduction networks. We show that this mechanism applies in particular to bacterial chemotaxis. This is demonstrated within a quantitative model which explains, in a unified way, many aspects of chemotaxis, including proper responses to chemical gradients. The adaptation property is a consequence of the network's connectivity and does not require the 'fine-tuning' of parameters. We argue that the key properties of biochemical networks should be robust in order to ensure their proper functioning.

Berg, H. C. Random walks in biology. Princeton, 1983.

Bray, D., M. D. Levin, and C. J. Morton-Firth. "Receptor Clustering as a Cellular Mechanism to Control Sensitivity." Nature 393 (1998): 85-8.

PubMed abstract: Chemotactic bacteria such as Escherichia coli can detect and respond to extremely low concentrations of attractants, concentrations of less than 5 nM in the case of aspartate. They also sense gradients of attractants extending over five orders of magnitude in concentration (up to 1 mM aspartate). Here we consider the possibility that this combination of sensitivity and range of response depends on the clustering of chemotactic receptors on the surface of the bacterium. We examine what will happen if ligand binding changes the activity of a receptor, propagating this change in activity to neighbouring receptors in a cluster. Calculations based on these assumptions show that sensitivity to extracellular ligands increases with the extent of spread of activity through an array of receptors, but that the range of concentrations over which the array works is severely diminished. However, a combination of low threshold of response and wide dynamic range can be attained if the cell has both clusters and single receptors on its surface, particularly if the extent of activity spread can adapt to external conditions. A mechanism of this kind can account quantitatively for the sensitivity and response range of E. coli to aspartate.

Bray, D., R. B. Bourret, and M. I. Simon. "Computer Simulation of the Phosphorylation Cascade Controlling Bacterial Chemotaxis." Mol. Biol. Cell. 4 (1993): 469-82.

PubMed abstract: We have developed a computer program that simulates the intracellular reactions mediating the rapid (nonadaptive) chemotactic response of Escherichia coli bacteria to the attractant aspartate and the repellent Ni2+ ions. The model is built from modular units representing the molecular components involved, which are each assigned a known value of intracellular concentration and enzymatic rate constant wherever possible. The components are linked into a network of coupled biochemical reactions based on a compilation of widely accepted mechanisms but incorporating several novel features. The computer motor shows the same pattern of runs, tumbles and pauses seen in actual bacteria and responds in the same way as living bacteria to sudden changes in concentration of aspartate or Ni2+. The simulated network accurately reproduces the phenotype of more than 30 mutants in which components of the chemotactic pathway are deleted and/or expressed in excess amounts and shows a rapidity of response to a step change in aspartate concentration similar to living bacteria. Discrepancies between the simulation and real bacteria in the phenotype of certain mutants and in the gain of the chemotactic response to aspartate suggest the existence of additional as yet unidentified interactions in the in vivo signal processing pathway.

Stryer. Chap. 13.

Long-term Potentiation


Dubnau, J., and T. Tully. "Gene Discovery in Drosophila: New Insights For Learning and Memory." Annu. Rev. Neurosci. 21 (1998): 407-44.

PubMed abstract: Genetic approaches have been used to investigate increasingly complex biological systems. Here we review the current state of genetic analysis of learning and memory in the fruitfly, Drosophila melanogaster. Emerging findings support two main themes. First, discovery and manipulation of genes involved with behavioral plasticity in genetically accessible systems such as D. melanogaster enables dissection of the biochemical, cellular, anatomical, and behavioral pathways of learning and memory. Second, because core cellular mechanisms of simple forms of learning are evolutionarily conserved, biological pathways discovered in invertebrates are likely to be conserved in vertebrate systems as well.

Malenka, R. C., and R. A. Nicoll. "Long-term Potentiation---A Decade of Progress?" Science 285 (1999): 1870-74.

PubMed abstract: Long-term potentiation of synaptic transmission in the hippocampus is the leading experimental model for the synaptic changes that may underlie learning and memory. This review presents a current understanding of the molecular mechanisms of this long-lasting increase in synaptic strength and describes a simple model that unifies much of the data that previously were viewed as contradictory.


Lisman, J. "A Mechanism for the Hebb and the Anti-Hebb Processes Underlying Learning and Memory." Proc. Natl. Acad. Sci. USA 86 (1989): 9574-78.

PubMed abstract: In a previous paper, a model was presented showing how the group of Ca2+/calmodulin-dependent protein kinase II molecules contained within a postsynaptic density could stably store a graded synaptic weight. This paper completes the model by showing how bidirectional control of synaptic weight could be achieved. It is proposed that the quantitative level of the activity-dependent rise in postsynaptic Ca2+ determines whether the synaptic weight will increase or decrease. It is further proposed that reduction of synaptic weight is governed by protein phosphatase 1, an enzyme indirectly controlled by Ca2+ through reactions involving phosphatase inhibitor 1, cAMP-dependent protein kinase, calcineurin, and adenylate cyclase. Modeling of this biochemical system shows that it can function as an analog computer that can store a synaptic weight and modify it in accord with the Hebb and anti-Hebb learning rules.

---. "A Mechanism for Memory Storage Insensitive to Molecular Turnover: A Bistable Autophosphorylating Kinase." Proc. Natl. Acad. Sci. USA 82 (1985): 3055-7.

PubMed abstract: A mechanism is proposed for a molecular switch that can store information indefinitely, despite the complete turnover of the molecules that make up the switch. The design of the switch is based on known types of biochemical reactions. Central to the mechanism is a kinase that is activated by phosphorylation and capable of intermolecular autophosphorylation. It is shown that such a kinase and an associated phosphatase form a bistable chemical switch that can be turned on by an external stimulus and that is not reset by protein turnover.

---. "The CaM kinase II Hypothesis for the Storage of Synaptic Memory." Trends Neurosci. 17 (1994): 406-12.

PubMed abstract: Much has been learned about the activity-dependent synaptic modifications (long-term potentiation and long-term depression) that are thought to underlie memory storage, but the mechanism by which these modifications are stored remains unclear. A good candidate for the storage mechanism is Ca2+/calmodulin-dependent protein kinase II (CaM kinase II) because it is localized at synapses, and its known autophosphorylation properties enable it to undergo long-term modification. In this review, John Lisman describes recent tests of the role of CaM kinase II in long-term potentiation. Experiments show that activity of CaM kinase II is increased for long periods of time after induction of long-term potentiation, that enhanced activity mimics long-term potentiation, and that enzyme activity is necessary for induction of long-term potentiation. The crucial question remaining is whether persistent enzyme activity is necessary to maintain stored information. Related issues concerning the mechanism by which synapses are weakened and the role of gene expression and structural changes are also discussed.

Lisman, J., and M. A. Goldring. "Feasibility of Long-term Storage of Graded Information by the Ca2+/calmodulin-dependent Protein Kinase Molecules of the Postsynaptic Density." Proc. Natl. Acad. Sci. USA 85 (1988): 5320-4.

PubMed abstract: The feasibility of long-term information storage by brain type II Ca2+/calmodulin-dependent protein kinase molecules is explored. Recent evidence indicates that this protein has switch-like properties. Equations are derived showing that a single kinase holoenzyme could form a bistable switch having the stability necessary to encode long-term memory, and that a group of kinase molecules, such as that contained within the postsynaptic density, could form a device capable of storing graded information.


Bhalla, U. S., and R. Iyengar. "Emergent Properties of Networks of Biological Signaling Pathways." Science 283 (1999): 381-7.

PubMed abstract: Many distinct signaling pathways allow the cell to receive, process, and respond to information. Often, components of different pathways interact, resulting in signaling networks. Biochemical signaling networks were constructed with experimentally obtained constants and analyzed by computational methods to understand their role in complex biological processes. These networks exhibit emergent properties such as integration of signals across multiple time scales, generation of distinct outputs depending on input strength and duration, and self-sustaining feedback loops. Feedback can result in bistable behavior with discrete steady-state activities, well-defined input thresholds for transition between states and prolonged signal output, and signal modulation in response to transient stimuli. These properties of signaling networks raise the possibility that information for "learned behavior" of biological systems may be stored within intracellular biochemical reactions that comprise signaling pathways.

Squire and Kandel. Memory: From Mind to Molecules. Scientific American Library. 1999, chap.7.

Circadian Rhythms

Barkai, N. and S. Leibler. "Circadian Clocks Limited by Noise." Nature 403 (2000): 267-8.

Dunlap, J. C. "Molecular Bases for Circadian Clocks." Cell. 96 (1999): 271-90.

Glossop, N. R. J., L. C. Lyons, and P. E. Hardin. "Interlocked Feedback Loops Within The Drosophila Circadian Oscillator." Science 286 (1999): 766-8.

PubMed abstract: Drosophila Clock (dClk) is rhythmically expressed, with peaks in mRNA and protein (dCLK) abundance early in the morning. dClk mRNA cycling is shown here to be regulated by PERIOD-TIMELESS (PER-TIM)-mediated release of dCLK- and CYCLE (CYC)-dependent repression. Lack of both PER-TIM derepression and dCLK-CYC repression results in high levels of dClk mRNA, which implies that a separate dClk activator is present. These results demonstrate that the Drosophila circadian feedback loop is composed of two interlocked negative feedback loops: a per-tim loop, which is activated by dCLK-CYC and repressed by PER-TIM, and a dClk loop, which is repressed by dCLK-CYC and derepressed by PER-TIM.

Johnson and Golden. "Circadian Programs in Cyanobacteria: Adaptiveness and Mechanism" Annu. Rev. Microbiol. 53(1999): 389-409.

PubMed abstract: At least one group of prokaryotes is known to have circadian regulation of cellular activities--the cyanobacteria. Their "biological clock" orchestrates cellular events to occur in an optimal temporal program, and it can keep track of circadian time even when the cells are dividing more rapidly than once per day. Growth competition experiments demonstrate that the fitness of cyanobacteria is enhanced when the circadian period matches the period of the environmental cycle. Three genes have been identified that specifically affect circadian phenotypes. These genes, kaiA, kaiB, and kaiC, are adjacent to each other on the chromosome, thus forming a clock gene cluster. The clock gene products appear to interact with each other and form an autoregulatory feedback loop.

Tyson, et al. "A Simple Model of Circadian Rhythms Based on Dimerization and Proteolysis of PER and TIM." Biophys J. 77 (1999): 2411-7.

PubMed abstract: Many organisms display rhythms of physiology and behavior that are entrained to the 24-h cycle of light and darkness prevailing on Earth. Under constant conditions of illumination and temperature, these internal biological rhythms persist with a period close to 1 day ("circadian"), but it is usually not exactly 24 h. Recent discoveries have uncovered stunning similarities among the molecular circuitries of circadian clocks in mice, fruit flies, and bread molds. A consensus picture is coming into focus around two proteins (called PER and TIM in fruit flies), which dimerize and then inhibit transcription of their own genes. Although this picture seems to confirm a venerable model of circadian rhythms based on time-delayed negative feedback, we suggest that just as crucial to the circadian oscillator is a positive feedback loop based on stabilization of PER upon dimerization. These ideas can be expressed in simple mathematical form (phase plane portraits), and the model accounts naturally for several hallmarks of circadian rhythms, including temperature compensation and the per(L) mutant phenotype. In addition, the model suggests how an endogenous circadian oscillator could have evolved from a more primitive, light-activated switch.

Stochastic Models of Lambda Phage

Arkin, A., J. Ross, and H. H. McAdams. "Stochastic Kinetic Analysis of Developmental Pathway Bifurcation in Phage ?-infected. Escherichia Coli Cells." Genetics 149 (1998): 1633-48.

PubMed abstract: Fluctuations in rates of gene expression can produce highly erratic time patterns of protein production in individual cells and wide diversity in instantaneous protein concentrations across cell populations. When two independently produced regulatory proteins acting at low cellular concentrations competitively control a switch point in a pathway, stochastic variations in their concentrations can produce probabilistic pathway selection, so that an initially homogeneous cell population partitions into distinct phenotypic subpopulations. Many pathogenic organisms, for example, use this mechanism to randomly switch surface features to evade host responses. This coupling between molecular-level fluctuations and macroscopic phenotype selection is analyzed using the phage lambda lysis-lysogeny decision circuit as a model system. The fraction of infected cells selecting the lysogenic pathway at different phage:cell ratios, predicted using a molecular-level stochastic kinetic model of the genetic regulatory circuit, is consistent with experimental observations. The kinetic model of the decision circuit uses the stochastic formulation of chemical kinetics, stochastic mechanisms of gene expression, and a statistical-thermodynamic model of promoter regulation. Conventional deterministic kinetics cannot be used to predict statistics of regulatory systems that produce probabilistic outcomes. Rather, a stochastic kinetic analysis must be used to predict statistics of regulatory outcomes for such stochastically regulated systems.

Gibson, M. A., and J. Bruck. "A Probabilistic Model of a Prokaryotic Gene and its Regulation." In Computational Methods in Molecular Biology: From Genotype to Phenotype. Edited by Bolouri and Bower (in press).

McAdams, H. H., and A. Arkin. "Stochastic Mechanisms in Gene Expression." Proc. Natl. Acad. Sci. USA 94 (1997): 814-9.

PubMed abstract: In cellular regulatory networks, genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. In genetically controlled pathways, the protein product encoded by one gene often regulates expression of other genes. The time delay, after activation of the first promoter, to reach an effective level to control the next promoter depends on the rate of protein accumulation. We have analyzed the chemical reactions controlling transcript initiation and translation termination in a single such "genetically coupled" link as a precursor to modeling networks constructed from many such links. Simulation of the processes of gene expression shows that proteins are produced from an activated promoter in short bursts of variable numbers of proteins that occur at random time intervals. As a result, there can be large differences in the time between successive events in regulatory cascades across a cell population. In addition, the random pattern of expression of competitive effectors can produce probabilistic outcomes in switching mechanisms that select between alternative regulatory paths. The result can be a partitioning of the cell population into different phenotypes as the cells follow different paths. There are numerous unexplained examples of phenotypic variations in isogenic populations of both prokaryotic and eukaryotic cells that may be the result of these stochastic gene expression mechanisms.

Molecular Motors

Howard, J. "Molecular Motors: Structural Adaptations to Cellular Functions." Nature 389 (1997): 561-6.

PubMed abstract: Molecular motors are protein machines whose directed movement along cytoskeletal filaments is driven by ATP hydrolysis. Eukaryotic cells contain motors that help to transport organelles to their correct cellular locations and to establish and alter cellular morphology during cell locomotion and division. The best-studied motors, myosin from skeletal muscle and conventional kinesin from brain, are remarkably similar in structure, yet have very different functions. These differences can be understood in terms of the 'duty ratio', the fraction of the time that a motor is attached to its filament. Differences in duty ratio can explain the diversity of structures, speeds and oligomerization states of members of the large kinesin, myosin and dynein families of motors.

Mehta, A. D., M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons. "Single-molecule Biomechanics With Optical Methods." Science 283 (1999): 1689-95.

PubMed abstract: Single-molecule observation and manipulation have come of age. With the advent of optical tweezers and other methods for probing and imaging single molecules, investigators have circumvented the model-dependent extrapolation from ensemble assays that has been the hallmark of classical biochemistry and biophysics. In recent years, there have been important advances in the understanding of how motor proteins work. The range of these technologies has also started to expand into areas such as DNA transcription and protein folding. Here, recent experiments with rotary motors, linear motors, RNA polymerase, and titin are described.


Reinitz, J., D. Kosman, C. E. Vanario-Alonso, and D. H. Sharp. "Stripe Forming Architecture of the Gap Gene System." Dev. Genetics 23 (1998): 11-27.

PubMed abstract: In this report, we show that gap genes encode exactly one set of pair-rule stripes, which occur in the native even-skipped position. The core of this work is a detailed analysis that shows how this conclusion follows from the arrangement of gap domains in the embryo. This analysis shows that: (1) pattern forming information is transmitted from gap to pair-rule genes by means of a nonredundant set of morphogenetic gradients, and (2) the stripe forming capability of the gap genes is constrained by the arrangement of these gradients and by the fact that each gap domain consists of a pair of correlated gradients. We also show that in the blastoderm, the regulatory sign of a transcriptional regulator is unlikely to change in a concentration dependent manner. The principal analytic tool used to establish these results is the gene circuit method. Here, this method is applied to examine hybrid data sets consisting of real gene expression data for four gap genes and hypothetical pair-rule expression data generated by translating native even-skipped data along the anterior-posterior axis. In this way, we are able to investigate the stripe forming capabilities of the gap gene system in the complete absence of pair-rule cross regulation. We close with an inference about evolutionary development. It is argued that the constraints on gap gene architecture identified here are a consequence of selective pressures that minimize the number of gap genes required to determine segments in long-germ band insects.

Stanojevic, D., S. Small, and M. Levine. "Regulation of a Segmentation Stripe by Overlapping Activators and Repressors in the Drosophilia Embryo." Science 254 (1991): 1385-1387.

PubMed abstract: Gene expression stripes in Drosophila melanogaster embryos provide a model for how eukaryotic promoters are turned on and off in response to combinations of transcriptional regulators. Genetic studies suggested that even-skipped (eve) stripe 2 is controlled by three gap genes, hunchback (hb), Kruppel (Kr), and giant (gt), and by the maternal morphogen bicoid (bcd). A direct link is established between binding sites for these regulatory proteins in the stripe 2 promoter element and the expression of the stripe during early embryogenesis. The bcd and hb protein binding sites mediate activation, whereas neighboring gt and Kr protein sites repress expression and establish the stripe borders. The stripe 2 element has the properties of a genetic on-off switch.

Wolpert, L. "Positional Information and Pattern Formation in Development." Dev. Genetics 15 (1994): 485-490.

PubMed abstract: A widely used mechanism for pattern formation is based on positional information: cells acquire positional identities as in a coordinate system and then interpret this information according to their genetic constitution and developmental history. In Drosophila maternal factors establish the axes and set up a maternal system of positional information on which further patterning is built. There is a cascade of gene activity which leads both to the development of periodic structures, the segments, and to their acquiring a unique identity. This involves the binding of transcription factors to regulatory regions of genes to produce sharp thresholds. Many of the genes involved in these processes, particularly the Hox complex, are also involved in specifying the body axis and limbs of vertebrates. There are striking similarities in the mechanisms for specifying and recording positional identity in Drosophila and vertebrates.

Additional reading:

Lawrence, P. A. "The Making of a Fly: The Genetics of Animal Design." Blackwell (1992).

Cell Cycle

Gardner, T., M. Dolnik, and J. J. Collins. "A Theory for Controlling Cell Cycle Dynamics Using a Reversibly Binding Inhibitor." Proc. Natl. Acad. Sci. USA 95 (1998): 14190-95.

Goldbeter, A. "A Minimal Cascade Model for the Mitotic Oscillator Involving Cyclin and cdc2 Kinase." Proc. Natl. Acad. Sci. USA 88 (1991): 9107-9111.

PubMed abstract: A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Felix, M. A., Labbe, J. C., Doree, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.

Molecular biology of the cell. Chap 17.

Novak, B. and J. J. Tyson. "Modeling the Control of DNA Replication in Fission Yeast." Proc. Natl. Acad. Sci. USA 94 (1997): 9147-52.

PubMed abstract: A central event in the eukaryotic cell cycle is the decision to commence DNA replication (S phase). Strict controls normally operate to prevent repeated rounds of DNA replication without intervening mitoses ("endoreplication") or initiation of mitosis before DNA is fully replicated ("mitotic catastrophe"). Some of the genetic interactions involved in these controls have recently been identified in yeast. From this evidence we propose a molecular mechanism of "Start" control in Schizosaccharomyces pombe. Using established principles of biochemical kinetics, we compare the properties of this model in detail with the observed behavior of various mutant strains of fission yeast: wee1(-) (size control at Start), cdc13Delta and rum1(OP) (endoreplication), and wee1(-) rum1Delta (rapid division cycles of diminishing cell size). We discuss essential features of the mechanism that are responsible for characteristic properties of Start control in fission yeast, to expose our proposal to crucial experimental tests.

Pattern Formation and Slime Molds

Kessler, D. A., and H. Levine. "Pattern Formation in Dictyostelium via the Dynamics of Cooperative Biological Entities." Phys. Rev. E48 (1993):4801-4.

Levine, H., I. Aranson, L. Tsimring, and T. V. Truong. "Positive Genetic Feedback Governs cAMP Spiral Wave Formation in Dictyostelium." Proc. Natl. Acad. Sci. USA 93 (1996): 6382-6.

PubMed abstract: The aggregation stage of the life cycle of Dictyostelium discoideum is governed by the chemotactic response of individual amoebae to excitable waves of cAMP. We modeled this process through a recently introduced hybrid automata-continuum scheme and used computer simulation to unravel the role of specific components of this complex developmental process. Our results indicated an essential role for positive feedback between the cAMP signaling and the expression of the genes encoding the signal transduction and response machinery.

The Dictyostelium Virtual Library.

Cell Sorting

Glazier, J. A., and F. Graner. "Simulation of the Differential Adhesion Driven Rearrangement of Biological Cells." Phys. Rev. E47 (1993): 2128-54.

Graner, F., and J. A. Glazier. "Simulation of Biological Cell Sorting Using a Two Dimensional Extended Potts model." Phys. Rev. Lett. 69 (1992): 2013-6.

Kataoka, N., K. Saito, and Y. Sawada. "NMR Microimaging of the Cell Sorting Process." Phys. Rev. Lett. 82 (1999): 1075.

Steinberg, M. S. "Reconstruction of Tissues by Dissociated Cells." Science, 141, no. 3579 (1963): 401-408.


Herz, A. V. M., S. Bonhoeffer, R. M. Anderson, R. M. May, and M. A. Nowak. "Viral Dynamics in Vivo: Limitations on Estimates of Intracellular Delay and Virus Decay." Proc. Natl. Acad. Sci. USA 93 (1996): 7247-51.

PubMed abstract: Anti-viral drug treatment of human immunodeficiency virus type I (HIV-1) and hepatitis B virus (HBV) infections causes rapid reduction in plasma virus load. Viral decline occurs in several phases and provides information on important kinetic constants of virus replication in vivo and pharmacodynamical properties. We develop a mathematical model that takes into account the intracellular phase of the viral life-cycle, defined as the time between infection of a cell and production of new virus particles. We derive analytic solutions for the dynamics following treatment with reverse transcriptase inhibitors, protease inhibitors, or a combination of both. For HIV-1, our results show that the phase of rapid decay in plasma virus (days 2-7) allows precise estimates for the turnover rate of productively infected cells. The initial quasi-stationary phase (days 0-1) and the transition phase (days 1-2) are explained by the combined effects of pharmacological and intracellular delays, the clearance of free virus particles, and the decay of infected cells. Reliable estimates of the first three quantities are not possible from data on virus load only; such estimates require additional measurements. In contrast with HIV-1, for HBV our model predicts that frequent early sampling of plasma virus will lead to reliable estimates of the free virus half-life and the pharmacological properties of the administered drug. On the other hand, for HBV the half-life of infected cells cannot be estimated from plasma virus decay.

Ho, D. D., et al. "Rapid Turnover of Plasma Virions and CD4 Lymphocytes in HIV-1 Infection." Nature 373 (1995):123-126.

PubMed abstract: Treatment of infected patients with ABT-538, an inhibitor of the protease of human immunodeficiency virus type 1 (HIV-1), causes plasma HIV-1 levels to decrease exponentially (mean half-life, 2.1 +/- 0.4 days) and CD4 lymphocyte counts to rise substantially. Minimum estimates of HIV-1 production and clearance and of CD4 lymphocyte turnover indicate that replication of HIV-1 in vivo is continuous and highly productive, driving the rapid turnover of CD4 lymphocytes.

Molecular biology of the cell. Chap. 23.

Perelson, A. S., and G. Weisbuch. "Immunology for Physicists." Rev. Mod. Phys. 69 (1998): 1219-67.

Wei, Xiping, et al. "Viral Dynamics in Human Immunodeficiency Virus Type 1 Infection." Nature 373:117-122 (1995).

PubMed abstract: The dynamics of HIV-1 replication in vivo are largely unknown yet they are critical to our understanding of disease pathogenesis. Experimental drugs that are potent inhibitors of viral replication can be used to show that the composite lifespan of plasma virus and virus-producing cells is remarkably short (half-life approximately 2 days). Almost complete replacement of wild-type virus in plasma by drug-resistant variants occurs after fourteen days, indicating that HIV-1 viraemia is sustained primarily by a dynamic process involving continuous rounds of de novo virus infection and replication and rapid cell turnover.