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The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA and protein concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the regulatory level. Theoretical and computational work on stochastic gene expression has tended to focus on instantaneous transcriptional and translational events, whereas the role of realistic delay times in these stochastic processes has received little attention. Here, we explore the combined effects of time delay and intrinsic noise on gene regulation. Beginning with a set of biochemical reactions, some of which are delayed, we deduce a truncated master equation for the reactive system and derive an analytical expression for the correlation function and power spectrum. We develop a generalized Gillespie algorithm that accounts for the non-Markovian properties of random biochemical events with delay and compare our analytical findings with simulations. We show how time delay in gene expression can cause a system to be oscillatory even when its deterministic counterpart exhibits no oscillations. We demonstrate how such delay-induced instabilities can compromise the ability of a negative feedback loop to reduce the deleterious effects of noise. Given the prevalence of negative feedback in gene regulation, our findings may lead to new insights related to expression variability at the whole-genome scale.

Recent progress in reconstructing gene regulatory networks has established a framework for a quantitative description of the dynamics of many important cellular processes. Such a description will require novel experimental techniques that enable the generation of time-series data for the governing regulatory proteins in a large number of individual living cells. Here, we utilize microfabrication to construct a Tesla microchemostat that permits single-cell fluorescence imaging of gene expression over many cellular generations. The device is used to capture and constrain asymmetrically dividing or motile cells within a trapping region and to deliver nutrients and regulate the cellular population within this region. We illustrate the operation of the microchemostat with Saccharomyces cerevisiae and explore the evolution of single-cell gene expression and cycle time as a function of generation. Our findings highlight the importance of novel assays for quantifying the dynamics of gene expression and cellular growth, and establish a methodology for exploring the effects of gene expression on long-term processes such as cellular aging.

The deduction of phenotypic cellular responses from the structure and behavior of complex gene regulatory networks is one of the defining challenges of systems biology. This goal will require a quantitative understanding of the modular components that constitute such networks. We pursued an integrated approach, combining theory and experiment, to analyze and describe the dynamics of an isolated genetic module, an in vivo autoregulatory gene network. As predicted by the model, temperature-induced protein destabilization led to the existence of two expression states, thus elucidating the trademark bistability of the positive feedback-network architecture. After sweeping the temperature, observed population distributions and coefficients of variation were in quantitative agreement with those predicted by a stochastic version of the model. Because model fluctuations originated from small molecule-number effects, the experimental validation underscores the importance of internal noise in gene expression. This work demonstrates that isolated gene networks, coupled with proper quantitative descriptions, can elucidate key properties of functional genetic modules. Such an approach could lead to the modular dissection of naturally occurring gene regulatory networks, the deduction of cellular processes such as differentiation, and the development of engineered cellular control.

While the fundamental building blocks of biology are being tabulated by the various genome projects, microarray technology is setting the stage for the task of deducing the connectivity of large-scale gene networks. We show how the perturbation of carefully chosen genes in a microarray experiment can be used in conjunction with a reverse engineering algorithm to reveal the architecture of an underlying gene regulatory network. Our iterative scheme identifies the network topology by analyzing the steady-state changes in gene expression resulting from the systematic perturbation of a particular node in the network. We highlight the validity of our reverse engineering approach through the successful deduction of the topology of a linear in numero gene network and a recently reported model for the segmentation polarity network in Drosophila melanogaster. Our method may prove useful in identifying and validating specific drug targets and in deconvolving the effects of chemical compounds.

A central focus of postgenomic research will be to understand how cellular phenomena arise from the connectivity of genes and proteins. This connectivity generates molecular network diagrams that resemble complex electrical circuits, and a systematic understanding will require the development of a mathematical framework for describing the circuitry. From an engineering perspective, the natural path towards such a framework is the construction and analysis of the underlying submodules that constitute the network. Recent experimental advances in both sequencing and genetic engineering have made this approach feasible through the design and implementation of synthetic gene networks amenable to mathematical modelling and quantitative analysis. These developments have signalled the emergence of a gene circuit discipline, which provides a framework for predicting and evaluating the dynamics of cellular processes. Synthetic gene networks will also lead to new logical forms of cellular control, which could have important applications in functional genomics, nanotechnology, and gene and cell therapy.

We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to a periodic process that is intrinsic to the cell. We investigate the synchronization properties of the coupled system, and show how the oscillator can be constructed to yield a significant amplification of cellular oscillations. We reduce the driven oscillator equations to a normal form, and analytically determine the amplification as a function of the strength of the cellular oscillations. The ability to couple naturally occurring genetic oscillations to a synthetically designed network could lead to possible strategies for entraining and/or amplifying oscillations in cellular protein levels.

The ability to design and construct synthetic gene regulatory networks offers the prospect of studying issues related to cellular function in a simplified context; such networks also have many potential applications in biotechnology. A synthetic network exhibiting oscillatory behavior has recently been constructed [Elowitz, M. B. & Leibler, S. (2000) Nature (London) 403, 335-338]. It has also been shown that a natural bacterial quorum-sensing mechanism can be used in a synthetic system to communicate a signal between two populations of cells, such that receipt of the signal causes expression of a target gene [Weiss, R. & Knight, T. F. (2000) in DNA6: Sixth International Meeting on DNA-Based Computers, June 13-17, 2000, Leiden, The Netherlands]. We propose a synthetic gene network in Escherichia coli which combines these two features: the system acts as a relaxation oscillator and uses an intercell signaling mechanism to couple the oscillators and induce synchronous oscillations. We model the system and show that the proposed coupling scheme does lead to synchronous behavior across a population of cells. We provide an analytical treatment of the synchronization process, the dominant mechanism of which is "fast threshold modulation."

We have investigated variations in the excitability of mammalian cutaneous mechanoreceptor neurons. We focused on the phase dynamics of an action potential relative to a periodic stimulus, showing that the excitability of these sensory neurons has interesting nonstationary oscillations. Using a wavelet analysis, these oscillations were characterized through the depiction of their period as a function of time. It was determined that the induced oscillations are weakly dependent on the stimulus frequency, and that lower temperatures significantly reduce the frequency of the phase response. Our results reveal novel excitability properties in sensory neurons, and, more generally, could prove significant in the deduction of mechanistic attributes underlying the nonstationary excitability in neuronal systems. Since peripheral neurons feed information to the CNS, variable responses observed in higher regions may be generated in part at the site of sensory detection.

When n types of univalent ligands are competing for the binding to m types of protein sites, the determination of the system composition at equilibrium reduces to the solving of a non-linear system of n equations in C = [0; 1](n). We present an iterative method to solve such a system. We show that the sequence presented here is always convergent, regardless of the initial value in C. We also prove that the limit of this sequence is the unique solution in C of the non-linear system of equations.

Remarkable progress in genomic research is leading to a complete map of the building blocks of biology. Knowledge of this map is, in turn, setting the stage for a fundamental description of cellular function at the DNA level. Such a description will entail an understanding of gene regulation, in which proteins often regulate their own production or that of other proteins in a complex web of interactions. The implications of the underlying logic of genetic networks are difficult to deduce through experimental techniques alone, and successful approaches will probably involve the union of new experiments and computational modelling techniques.

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics. We first review the relevant work on synthetic gene networks, highlighting the important experimental findings with regard to genetic switches and oscillators. We then present the derivation of a deterministic model describing the temporal evolution of the concentration of protein in a single-gene network. Bistability in the steady-state protein concentration arises naturally as a consequence of autoregulatory feedback, and we focus on the hysteretic properties of the protein concentration as a function of the degradation rate. We then formulate the effect of an external noise source which interacts with the protein degradation rate. We demonstrate the utility of such a formulation by constructing a protein switch, whereby external noise pulses are used to switch the protein concentration between two values. Following the lead of earlier work, we show how the addition of a second network component can be used to construct a relaxation oscillator, whereby the system is driven around the hysteresis loop. We highlight the frequency dependence on the tunable parameter values, and discuss design plausibility. We emphasize how the model equations can be used to develop design criteria for robust oscillations, and illustrate this point with parameter plots illuminating the oscillatory regions for given parameter values. We then turn to the utilization of an intrinsic cellular process as a means of controlling the oscillations. We consider a network design which exhibits self-sustained oscillations, and discuss the driving of the oscillator in the context of synchronization. Then, as a second design, we consider a synthetic network with parameter values near, but outside, the oscillatory boundary. In this case, we show how resonance can lead to the induction of oscillations and amplification of a cellular signal. Finally, we construct a toggle switch from positive regulatory elements, and compare the switching properties for this network with those of a network constructed using negative regulation. Our results demonstrate the utility of model analysis in the construction of synthetic gene regulatory networks. (c) 2001 American Institute of Physics.

The regulation of cellular function is often controlled at the level of gene transcription. Such genetic regulation usually consists of interacting networks, whereby gene products from a single network can act to control their own expression or the production of protein in another network. Engineered control of cellular function through the design and manipulation of such networks lies within the constraints of current technology. Here we develop a model describing the regulation of gene expression and elucidate the effects of noise on the formulation. We consider a single network derived from bacteriophage lambda and construct a two-parameter deterministic model describing the temporal evolution of the concentration of lambda repressor protein. Bistability in the steady-state protein concentration arises naturally, and we show how the bistable regime is enhanced with the addition of the first operator site in the promotor region. We then show how additive and multiplicative external noise can be used to regulate expression. In the additive case, we demonstrate the utility of such control through the construction of a protein switch, whereby protein production is turned "on" and "off" by using short noise pulses. In the multiplicative case, we show that small deviations in the transcription rate can lead to large fluctuations in the production of protein, and we describe how these fluctuations can be used to amplify protein production significantly. These results suggest that an external noise source could be used as a switch and/or amplifier for gene expression. Such a development could have important implications for gene therapy.

The mechanisms by which graduated compression stockings prevent deep vein thrombosis are not completely understood. Recent work has suggested that venous distension plays a role in initiating the process. Our previous work has shown that the deep veins of the lower limb distend in patients undergoing surgical procedures. We have investigated 40 patients receiving surgical treatment on the abdomen or neck. A medial gastrocnemius vein was studied using ultrasound imaging during the operations. In half the patients a graduated compression anti-embolism stocking was applied to the limb under study at the start of the operation, immediately after initial measurements of vein diameter. The median vein diameter in both groups was the same at the start of the operative procedures (control, 2.6 mm, interquartile range 2.1-3.3 mm; stocking, 2.6 mm, interquartile range 2.1-3.7 mm). After application of a stocking the median diameter in this group fell to 1.6 mm (interquartile range 1.3-2.8 mm) and then decreased slightly at the end of the operation. In the control group the vein diameter increased to 2.9 mm (interquartile range 2.3-4.0 mm) during the operative procedure.

In summary we have developed a VTE risk assessment system for medical patients based on our prior experience in surgical patients. In this model we divide individuals into low, moderate, and high-risk categories. We realize that our system needs further validation with appropriate diagnostic endpoints to correlate the actual occurrence of venous thromboembolism with the predicted risk on the basis of our score system. Nevertheless, the proposed model reflects one approach to achieving a prophylaxis tailored to the patients' risk.

Prophylaxis against postoperative venous thromboembolism should be tailored according to the patient's level of risk. However, risk assessment is not yet in widespread use in surgical practice. In this study, 538 general surgical patients were prospectively assessed based on a scoring system containing 20 risk factors. Depending on the total risk factor score, the patients were grouped into low (0 to 1, 34.5%), moderate (2 to 4, 48.5%), or high risk (more than 4, 17.2%) categories. Statistically significant (p less than 0.0001) correlation was found between our results and those of three existing risk assessment systems. Overall, of the 538 patients, 37.2% received prophylaxis; 10%, 42.1%, and 76% received prophylaxis in the low-, moderate-, and high-risk categories, respectively. Mechanical prophylactic modalities (graduated elastic compression and sequential intermittent compression) were preferred over pharmacologic modalities. These results suggest that implementation of prophylaxis remains underutilized despite published reports, including NIH guidelines. Our results indicate that the majority of surgical patients seen in this suburban hospital have two or more risk factors for developing venous thromboembolism.

The treatment of venous ulcers has remained largely unchanged for centuries. The application of properly applied graduated compression bandages, the use of graduated compression stockings, and surgery have been shown to achieve healing. However, some ulcers persist despite appropriate management. A randomized study was undertaken to compare two regimens of treatment for such patients. Both regimens included ulcer debridement, cleaning, nonadherent dressing, and graduated compression stockings. In one regimen, sequential gradient intermittent pneumatic compression was applied for 4 hours each day. Only one of 24 patients in the control group had complete healing of all ulcers compared with 10 of 21 patients healed in the intermittent pneumatic compression group. The median rate of ulcer healing in the control group was 2.1% area per week compared to 19.8% area per week in the intermittent pneumatic compression group. The results indicate that sequential gradient intermittent pneumatic compression is beneficial in the treatment of venous ulcers.

The incidence of deep venous thrombosis (DVT) was assessed in a series of 78 patients undergoing major surgical operations to compare the prophylactic effectiveness of intermittent sequential pneumatic compression alone with the simultaneous use of graduated compression stockings and intermittent sequential pneumatic compression. The diagnosis of DVT was determined with the I-125 fibrinogen-uptake test, Doppler ultrasound, maximum venous outflow by strain-gauge plethysmography, and contrast venography. The incidence of DVT in nonstockinged legs was 9% while that in the stockinged legs was 1%. The simultaneous use of graduated elastic compression stockings and intermittent pneumatic compression is more effective than pneumatic compression alone in the prevention of postoperative DVT.

Determination of the optimal compression to reduce venous stasis was studied in terms of the amount of pressure and manner of application (graded or uniform pressure). Both lower extremities of seven inactive recumbent subjects were tested using transcutaneous Doppler ultrasonic measurement of femoral vein blood flow velocity. Optimal compression was defined as the externally applied pressure that produced the greatest increase in femoral vein flow velocity consistent with safety and the practicality of hospital use of elastic stockings. Optimal compression for elastic stockings to be used by hospitalized patients who spend substantial time in bed should be 18 to 8 mm Hg (ankle to midthigh). At this compression, average femoral vein blood flow velocity is increased to 138.4% of base line. Gradient compression at this level was found to produce a greater femoral vein flow velocity than the same amount of compression distributed uniformly over the lower extremity.

During the past decade, we have learned a great deal about the etiology, pathogenesis, diagnosis, and treatment of thromboembolic disease. Subcutaneous heparin has emerged as a major deterrent worldwide for thrombosis prevention but is associated with the potential risk of bleeding and cannot be used in certain patient situations. External compression modalities have emerged as major alternate forms of prophylaxis. We have learned that these devices stimulate the fibrinolytic system, prevent stasis and the endothelial injury that can accompany extreme venous distention. Since they are not associated with bleeding or other serious complications, they are attractive methods for most surgeons, including those performing delicate or complex surgical procedures. Independent studies worldwide have demonstrated their effectiveness in reducing deep vein thrombosis, as recognized by the NIH Consensus Development Panel, and the evidence is compelling that DVT efficacy is a valid marker for PE efficacy. Since these devices reduce the incidence of deep vein thrombosis, they almost certainly must prevent pulmonary emboli; however, a properly designed protocol should be conducted to validate these assumptions. Evidence suggests that full-leg sequential compression is superior to calf compression, but further study is necessary. We believe that a hospital-wide plan, including risk-factor assessment and application of clinical management guidelines, including all available modalities, is important to provide the maximum protection of patients with the lowest risk of side effects. Such a program has been very successful in our community.