139 research outputs found
The validity of quasi steady-state approximations in discrete stochastic simulations
In biochemical networks, reactions often occur on disparate timescales and
can be characterized as either "fast" or "slow." The quasi-steady state
approximation (QSSA) utilizes timescale separation to project models of
biochemical networks onto lower-dimensional slow manifolds. As a result, fast
elementary reactions are not modeled explicitly, and their effect is captured
by non-elementary reaction rate functions (e.g. Hill functions). The accuracy
of the QSSA applied to deterministic systems depends on how well timescales are
separated. Recently, it has been proposed to use the non-elementary rate
functions obtained via the deterministic QSSA to define propensity functions in
stochastic simulations of biochemical networks. In this approach, termed the
stochastic QSSA, fast reactions that are part of non-elementary reactions are
not simulated, greatly reducing computation time. However, it is unclear when
the stochastic QSSA provides an accurate approximation of the original
stochastic simulation. We show that, unlike the deterministic QSSA, the
validity of the stochastic QSSA does not follow from timescale separation
alone, but also depends on the sensitivity of the non-elementary reaction rate
functions to changes in the slow species. The stochastic QSSA becomes more
accurate when this sensitivity is small. Different types of QSSAs result in
non-elementary functions with different sensitivities, and the total QSSA
results in less sensitive functions than the standard or the pre-factor QSSA.
We prove that, as a result, the stochastic QSSA becomes more accurate when
non-elementary reaction functions are obtained using the total QSSA. Our work
provides a novel condition for the validity of the QSSA in stochastic
simulations of biochemical reaction networks with disparate timescales.Comment: 21 pages, 4 figure
Pooling and Correlated Neural Activity
Correlations between spike trains can strongly modulate neuronal activity and affect the ability of neurons to encode information. Neurons integrate inputs from thousands of afferents. Similarly, a number of experimental techniques are designed to record pooled cell activity. We review and generalize a number of previous results that show how correlations between cells in a population can be amplified and distorted in signals that reflect their collective activity. The structure of the underlying neuronal response can significantly impact correlations between such pooled signals. Therefore care needs to be taken when interpreting pooled recordings, or modeling networks of cells that receive inputs from large presynaptic populations. We also show that the frequently observed runaway synchrony in feedforward chains is primarily due to the pooling of correlated inputs
Effects of cell cycle noise on excitable gene circuits
We assess the impact of cell cycle noise on gene circuit dynamics. For
bistable genetic switches and excitable circuits, we find that transitions
between metastable states most likely occur just after cell division and that
this concentration effect intensifies in the presence of transcriptional delay.
We explain this concentration effect with a 3-states stochastic model. For
genetic oscillators, we quantify the temporal correlations between daughter
cells induced by cell division. Temporal correlations must be captured properly
in order to accurately quantify noise sources within gene networks.Comment: 15 pages, 8 figure
Molecular mechanisms that regulate the coupled period of the mammalian circadian clock
In mammals, most cells in the brain and peripheral tissues generate circadian
(~24hr) rhythms autonomously. These self-sustained rhythms are coordinated and
entrained by a master circadian clock in the suprachiasmatic nucleus (SCN).
Within the SCN, the individual rhythms of each neuron are synchronized through
intercellular signaling. One important feature of SCN is that the synchronized
period is close to the cell population mean of intrinsic periods. In this way,
the synchronized period of the SCN stays close to the periods of cells in
peripheral tissues. This is important for SCN to entrain cells throughout the
body. However, the mechanism that drives the period of the coupled SCN cells to
the population mean is not known. We use mathematical modeling and analysis to
show that the mechanism of transcription repression plays a pivotal role in
regulating the coupled period. Specifically, we use phase response curve
analysis to show that the coupled period within the SCN stays near the
population mean if transcriptional repression occurs via protein sequestration.
In contrast, the coupled period is far from the mean if repression occurs
through highly nonlinear Hill-type regulation (e.g. oligomer- or
phosphorylation-based repression). Furthermore, we find that the timescale of
intercellular coupling needs to be fast compared to that of intracellular
feedback to maintain the mean period. These findings reveal the important
relationship between the intracellular transcriptional feedback loop and
intercellular coupling. This relationship explains why transcriptional
repression appears to occur via protein sequestration in multicellular
organisms, mammals and Drosophila, in contrast with the phosphorylation-based
repression in unicellular organisms. That is, transition to protein
sequestration is essential for synchronizing multiple cells with a period close
to the population mean (~24hr).Comment: 21 pages, 16 figure
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