Epigenetic cell memory: The gene's inner chromatin modification circuit.

Epigenetic cell memory allows distinct gene expression patterns to persist in different cell types despite a common genotype. Although different patterns can be maintained by the concerted action of transcription factors (TFs), it was proposed that long-term persistence hinges on chromatin state. Here, we study how the dynamics of chromatin state affect memory, and focus on a biologically motivated circuit motif, among histones and DNA modifications, that mediates the action of TFs on gene expression. Memory arises from time-scale separation among three circuit's constituent processes: basal erasure, auto and cross-catalysis, and recruited erasure of modifications. When the two latter processes are sufficiently faster than the former, the circuit exhibits bistability and hysteresis, allowing active and repressed gene states to coexist and persist after TF stimulus removal. The duration of memory is stochastic with a mean value that increases as time-scale separation increases, but more so for the repressed state. This asymmetry stems from the cross-catalysis between repressive histone modifications and DNA methylation and is enhanced by the relatively slower decay rate of the latter. Nevertheless, TF-mediated positive autoregulation can rebalance this asymmetry and even confers robustness of active states to repressive stimuli. More generally, by wiring positively autoregulated chromatin modification circuits under time scale separation, long-term distinct gene expression patterns arise, which are also robust to failure in the regulatory links.

Comparison Theorems for Stochastic Chemical Reaction Networks.

Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications.

Criticality and Adaptivity in Enzymatic Networks.

The contrast between the stochasticity of biochemical networks and the regularity of cellular behavior suggests that biological networks generate robust behavior from noisy constituents. Identifying the mechanisms that confer this ability on biological networks is essential to understanding cells. Here we show that queueing for a limited shared resource in broad classes of enzymatic networks in certain conditions leads to a critical state characterized by strong and long-ranged correlations between molecular species. An enzymatic network reaches this critical state when the input flux of its substrate is balanced by the maximum processing capacity of the network. We then consider enzymatic networks with adaptation, when the limiting resource (enzyme or cofactor) is produced in proportion to the demand for it. We show that the critical state becomes an attractor for these networks, which points toward the onset of self-organized criticality. We suggest that the adaptive queueing motif that leads to significant correlations between multiple species may be widespread in biological systems.

Translational cross talk in gene networks.

It has been shown experimentally that competition for limited translational resources by upstream mRNAs can lead to an anticorrelation between protein counts. Here, we investigate a stochastic model for this phenomenon, in which gene transcripts of different types compete for a finite pool of ribosomes. Throughout, we utilize concepts from the theory of multiclass queues to describe a qualitative shift in protein count statistics as the system transitions from being underloaded (ribosomes exceed transcripts in number) to being overloaded (transcripts exceed ribosomes in number). The exact analytical solution of a simplified stochastic model, in which the numbers of competing mRNAs and ribosomes are fixed, exhibits weak positive correlations between steady-state protein counts when total transcript count slightly exceeds ribosome count, whereas the solution can exhibit strong negative correlations when total transcript count significantly exceeds ribosome count. Extending this analysis, we find approximate but reasonably accurate solutions for a more realistic model, in which abundances of mRNAs and ribosomes are allowed to fluctuate randomly. Here, ribosomal fluctuations contribute positively and mRNA fluctuations contribute negatively to correlations, and when mRNA fluctuations dominate ribosomal fluctuations, a strong anticorrelation extremum reliably occurs near the transition from the underloaded to the overloaded regime.

Queueing up for enzymatic processing: correlated signaling through coupled degradation.

High-throughput technologies have led to the generation of complex wiring diagrams as a post-sequencing paradigm for depicting the interactions between vast and diverse cellular species. While these diagrams are useful for analyzing biological systems on a large scale, a detailed understanding of the molecular mechanisms that underlie the observed network connections is critical for the further development of systems and synthetic biology. Here, we use queueing theory to investigate how 'waiting lines' can lead to correlations between protein 'customers' that are coupled solely through a downstream set of enzymatic 'servers'. Using the E. coli ClpXP degradation machine as a model processing system, we observe significant cross-talk between two networks that are indirectly coupled through a common set of processors. We further illustrate the implications of enzymatic queueing using a synthetic biology application, in which two independent synthetic networks demonstrate synchronized behavior when common ClpXP machinery is overburdened. Our results demonstrate that such post-translational processes can lead to dynamic connections in cellular networks and may provide a mechanistic understanding of existing but currently inexplicable links.

Correlation resonance generated by coupled enzymatic processing.

A major challenge for systems biology is to deduce the molecular interactions that underlie correlations observed between concentrations of different intracellular molecules. Although direct explanations such as coupled transcription or direct protein-protein interactions are often considered, potential indirect sources of coupling have received much less attention. Here we show how correlations can arise generically from a posttranslational coupling mechanism involving the processing of multiple protein species by a common enzyme. By observing a connection between a stochastic model and a multiclass queue, we obtain a closed form expression for the steady-state distribution of the numbers of molecules of each protein species. Upon deriving explicit analytic expressions for moments and correlations associated with this distribution, we discover a striking phenomenon that we call correlation resonance: for small dilution rate, correlations peak near the balance-point where the total rate of influx of proteins into the system is equal to the maximum processing capacity of the enzyme. Given the limited number of many important catalytic molecules, our results may lead to new insights into the origin of correlated behavior on a global scale.

Homotopy methods for counting reaction network equilibria.

Dynamical system models of complex biochemical reaction networks are usually high-dimensional, non-linear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for all values of the parameters in the model. In other cases multiple equilibria exist if and only if special relationships between these parameters are satisfied. We describe methods based on homotopy invariance of degree which allow us to determine the number of equilibria for complex biochemical reaction networks and how this number depends on parameters in the model.

Some properties of a simple stochastic epidemic model of SIR type.

We investigate the properties of a simple discrete time stochastic epidemic model. The model is Markovian of the SIR type in which the total population is constant and individuals meet a random number of other individuals at each time step. Individuals remain infectious for R time units, after which they become removed or immune. Individual transition probabilities from susceptible to diseased states are given in terms of the binomial distribution. An expression is given for the probability that any individuals beyond those initially infected become diseased. In the model with a finite recovery time R, simulations reveal large variability in both the total number of infected individuals and in the total duration of the epidemic, even when the variability in number of contacts per day is small. In the case of no recovery, R=infinity, a formal diffusion approximation is obtained for the number infected. The mean for the diffusion process can be approximated by a logistic which is more accurate for larger contact rates or faster developing epidemics. For finite R we then proceed mainly by simulation and investigate in the mean the effects of varying the parameters p (the probability of transmission), R, and the number of contacts per day per individual. A scale invariant property is noted for the size of an outbreak in relation to the total population size. Most notable are the existence of maxima in the duration of an epidemic as a function of R and the extremely large differences in the sizes of outbreaks which can occur for small changes in R. These findings have practical applications in controlling the size and duration of epidemics and hence reducing their human and economic costs.

Forecasting emergency department presentations.

OBJECTIVE: To forecast the number of patients who will present each month at the emergency department of a hospital in regional Victoria. METHODS: The data on which the forecasts are based are the number of presentations in the emergency department for each month from 2000 to 2005. The statistical forecasting methods used are exponential smoothing and Box-Jenkins methods as implemented in the software package SPSS version 14.0 (SPSS Inc, Chicago, Ill, USA). RESULTS: For the particular time series, of the available models, a simple seasonal exponential smoothing model provides optimal forecasting performance. Forecasts for the first five months in 2006 compare well with the observed attendance data. CONCLUSIONS: Time series analysis is shown to provide a useful, readily available tool for predicting emergency department demand. The approach and lessons from this experience may assist other hospitals and emergency departments to conduct their own analysis to aid planning.

Assessing the impact of streaming in a regional emergency department.

OBJECTIVE: To evaluate the impact of a streaming model, previously validated in metropolitan EDs, on selected performance indicators in a regional ED. METHOD: Multiple linear regression models were applied to monthly time series data from 43 months prior to the intervention and 15 months following the intervention to measure the impact of the streaming model on the following performance indicators: (i) percentage of emergency patients admitted to an inpatient bed within 8 h; (ii) percentage of non-admitted emergency patients with a length of stay of less than 4 h; and (iii) percentage of emergency patients who left without being seen by a doctor or nurse practitioner. SETTING: Bendigo Health ED in regional Victoria. RESULTS: Prior to the introduction of streaming, there was a downward trend in both the percentage of emergency patients admitted to an inpatient bed within 8 h, and the percentage of non-admitted emergency patients with a length of stay of less than 4 h. After the introduction of streaming, these trends were reversed (P = 0.008 and P = 0.004, respectively). There was no statistically significant change in the trend associated with the percentage of emergency patients who left without being seen (P = 0.904). CONCLUSIONS: The implementation of the streaming model had an impact on the two performance indicators associated with length of stay in this regional ED, but did not have a significant impact (positive or negative) on the percentage of patients who did not wait to be seen. These results might interest other EDs in regional hospitals.

The development of a questionnaire to assess the perceptions of care staff towards people with intellectual disabilities who display challenging behaviour.

The perceptions of staff about challenging behaviour may be a key factor in designing successful behavioural interventions. There is a lack of robust psychometric instruments designed to assess staff attributions towards incidents of challenging behaviour. The aim of this research was to develop a scale based upon the self-regulation theory of illness behaviour. Two staff focus groups identified and clarified relevant constructs to be included in the Challenging Behaviour Perception Questionnaire (CBPQ), which was then completed by 51 staff. Some correlations between the CBPQ and the Attributional Style Questionnaire were found. A significant amount of the variance in the perception of challenging behaviour was explained by the subscales of the new questionnaire. In particular, episodic timeline would seem to be a promising area for further investigation.

The actin gene ACT1 is required for phagocytosis, motility, and cell separation of Tetrahymena thermophila.

A previously identified Tetrahymena thermophila actin gene (C. G. Cupples and R. E. Pearlman, Proc. Natl. Acad. Sci. USA 83:5160-5164, 1986), here called ACT1, was disrupted by insertion of a neo3 cassette. Cells in which all expressed copies of this gene were disrupted exhibited intermittent and extremely slow motility and severely curtailed phagocytic uptake. Transformation of these cells with inducible genetic constructs that contained a normal ACT1 gene restored motility. Use of an epitope-tagged construct permitted visualization of Act1p in the isolated axonemes of these rescued cells. In ACT1Delta mutant cells, ultrastructural abnormalities of outer doublet microtubules were present in some of the axonemes. Nonetheless, these cells were still able to assemble cilia after deciliation. The nearly paralyzed ACT1Delta cells completed cleavage furrowing normally, but the presumptive daughter cells often failed to separate from one another and later became reintegrated. Clonal analysis revealed that the cell cycle length of the ACT1Delta cells was approximately double that of wild-type controls. Clones could nonetheless be maintained for up to 15 successive fissions, suggesting that the ACT1 gene is not essential for cell viability or growth. Examination of the cell cortex with monoclonal antibodies revealed that whereas elongation of ciliary rows and formation of oral structures were normal, the ciliary rows of reintegrated daughter cells became laterally displaced and sometimes rejoined indiscriminately across the former division furrow. We conclude that Act1p is required in Tetrahymena thermophila primarily for normal ciliary motility and for phagocytosis and secondarily for the final separation of daughter cells.