49 research outputs found
Network Topology as a Driver of Bistability in the lac Operon
The lac operon in Escherichia coli has been studied extensively and is one of
the earliest gene systems found to undergo both positive and negative control.
The lac operon is known to exhibit bistability, in the sense that the operon is
either induced or uninduced. Many dynamical models have been proposed to
capture this phenomenon. While most are based on complex mathematical
formulations, it has been suggested that for other gene systems network
topology is sufficient to produce the desired dynamical behavior.
We present a Boolean network as a discrete model for the lac operon. We
include the two main glucose control mechanisms of catabolite repression and
inducer exclusion in the model and show that it exhibits bistability. Further
we present a reduced model which shows that lac mRNA and lactose form the core
of the lac operon, and that this reduced model also exhibits the same dynamics.
This work corroborates the claim that the key to dynamical properties is the
topology of the network and signs of interactions.Comment: 15 pages, 13 figures, supplemental information include
A Mathematical Framework for Agent Based Models of Complex Biological Networks
Agent-based modeling and simulation is a useful method to study biological
phenomena in a wide range of fields, from molecular biology to ecology. Since
there is currently no agreed-upon standard way to specify such models it is not
always easy to use published models. Also, since model descriptions are not
usually given in mathematical terms, it is difficult to bring mathematical
analysis tools to bear, so that models are typically studied through
simulation. In order to address this issue, Grimm et al. proposed a protocol
for model specification, the so-called ODD protocol, which provides a standard
way to describe models. This paper proposes an addition to the ODD protocol
which allows the description of an agent-based model as a dynamical system,
which provides access to computational and theoretical tools for its analysis.
The mathematical framework is that of algebraic models, that is, time-discrete
dynamical systems with algebraic structure. It is shown by way of several
examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog
Modeling Stochasticity and Variability in Gene Regulatory Networks
Modeling stochasticity in gene regulatory networks is an important and
complex problem in molecular systems biology. To elucidate intrinsic noise,
several modeling strategies such as the Gillespie algorithm have been used
successfully. This paper contributes an approach as an alternative to these
classical settings. Within the discrete paradigm, where genes, proteins, and
other molecular components of gene regulatory networks are modeled as discrete
variables and are assigned as logical rules describing their regulation through
interactions with other components. Stochasticity is modeled at the biological
function level under the assumption that even if the expression levels of the
input nodes of an update rule guarantee activation or degradation there is a
probability that the process will not occur due to stochastic effects. This
approach allows a finer analysis of discrete models and provides a natural
setup for cell population simulations to study cell-to-cell variability. We
applied our methods to two of the most studied regulatory networks, the outcome
of lambda phage infection of bacteria and the p53-mdm2 complex.Comment: 23 pages, 8 figure
Boolean dynamics revisited through feedback interconnections
Boolean models of physical or biological systems describe the global dynamics of the system and their attractors typically represent asymptotic behaviors. In the case of large networks composed of several modules, it may be difficult to identify all the attractors. To explore Boolean dynamics from a novel viewpoint, we will analyse the dynamics emerging from the composition of two known Boolean modules. The state transition graphs and attractors for each of the modules can be combined to construct a new asymptotic graph which will (1) provide a reliable method for attractor computation with partial information; (2) illustrate the differences in dynamical behavior induced by the updating strategy (asynchronous, synchronous, or mixed); and (3) show the inherited organization/structure of the original network’s state transition graph.publishe
A comparative study of qualitative and quantitative dynamic models of biological regulatory networks
Sources of Variability in a Synthetic Gene Oscillator
Synthetic gene oscillators are small, engineered genetic circuits that produce periodic variations in target protein expression. Like other gene circuits, synthetic gene oscillators are noisy and exhibit fluctuations in amplitude and period. Understanding the origins of such variability is key to building predictive models that can guide the rational design of synthetic circuits. Here, we developed a method for determining the impact of different sources of noise in genetic oscillators by measuring the variability in oscillation amplitude and correlations between sister cells. We first used a combination of microfluidic devices and time-lapse fluorescence microscopy to track oscillations in cell lineages across many generations. We found that oscillation amplitude exhibited high cell-to-cell variability, while sister cells remained strongly correlated for many minutes after cell division. To understand how such variability arises, we constructed a computational model that identified the impact of various noise sources across the lineage of an initial cell. When each source of noise was appropriately tuned the model reproduced the experimentally observed amplitude variability and correlations, and accurately predicted outcomes under novel experimental conditions. Our combination of computational modeling and time-lapse data analysis provides a general way to examine the sources of variability in dynamic gene circuits