Computational inference in systems biology

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs

Quantitative analysis of regulatory flexibility under changing environmental conditions

The circadian clock controls 24-h rhythms in many biological processes, allowing appropriate timing of biological rhythms relative to dawn and dusk. Known clock circuits include multiple, interlocked feedback loops. Theory suggested that multiple loops contribute the flexibility for molecular rhythms to track multiple phases of the external cycle. Clear dawn- and dusk-tracking rhythms illustrate the flexibility of timing in Ipomoea nil. Molecular clock components in Arabidopsis thaliana showed complex, photoperiod-dependent regulation, which was analysed by comparison with three contrasting models. A simple, quantitative measure, Dusk Sensitivity, was introduced to compare the behaviour of clock models with varying loop complexity. Evening-expressed clock genes showed photoperiod-dependent dusk sensitivity, as predicted by the three-loop model, whereas the one- and two-loop models tracked dawn and dusk, respectively. Output genes for starch degradation achieved dusk-tracking expression through light regulation, rather than a dusk-tracking rhythm. Model analysis predicted which biochemical processes could be manipulated to extend dusk tracking. Our results reveal how an operating principle of biological regulators applies specifically to the plant circadian clock

Evolutionary relationships among barley and <i>Arabidopsis</i> core circadian clock and clock-associated genes

The circadian clock regulates a multitude of plant developmental and metabolic processes. In crop species, it contributes significantly to plant performance and productivity and to the adaptation and geographical range over which crops can be grown. To understand the clock in barley and how it relates to the components in the Arabidopsis thaliana clock, we have performed a systematic analysis of core circadian clock and clock-associated genes in barley, Arabidopsis and another eight species including tomato, potato, a range of monocotyledonous species and the moss, Physcomitrella patens. We have identified orthologues and paralogues of Arabidopsis genes which are conserved in all species, monocot/dicot differences, species-specific differences and variation in gene copy number (e.g. gene duplications among the various species). We propose that the common ancestor of barley and Arabidopsis had two-thirds of the key clock components identified in Arabidopsis prior to the separation of the monocot/dicot groups. After this separation, multiple independent gene duplication events took place in both monocot and dicot ancestors. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s00239-015-9665-0) contains supplementary material, which is available to authorized users

The HY5-PIF regulatory module coordinates light and temperature control of photosynthetic gene transcription

The ability to interpret daily and seasonal alterations in light and temperature signals is essential for plant survival. This is particularly important during seedling establishment when the phytochrome photoreceptors activate photosynthetic pigment production for photoautotrophic growth. Phytochromes accomplish this partly through the suppression of phytochrome interacting factors (PIFs), negative regulators of chlorophyll and carotenoid biosynthesis. While the bZIP transcription factor long hypocotyl 5 (HY5), a potent PIF antagonist, promotes photosynthetic pigment accumulation in response to light. Here we demonstrate that by directly targeting a common promoter cis-element (G-box), HY5 and PIFs form a dynamic activation-suppression transcriptional module responsive to light and temperature cues. This antagonistic regulatory module provides a simple, direct mechanism through which environmental change can redirect transcriptional control of genes required for photosynthesis and photoprotection. In the regulation of photopigment biosynthesis genes, HY5 and PIFs do not operate alone, but with the circadian clock. However, sudden changes in light or temperature conditions can trigger changes in HY5 and PIFs abundance that adjust the expression of common target genes to optimise photosynthetic performance and growth

Complex and unexpected dynamics in simple genetic regulatory networks

Peer reviewedPublisher PD

FKF1 conveys timing information for CONSTANS stabilization in photoperiodic flowering

Plants use day-length information to coordinate flowering time with the appropriate season to maximize reproduction. In Arabidopsis, the long-day specific expression of CONSTANS (CO) protein is crucial for flowering induction. Although light signaling regulates CO protein stability, the mechanism by which CO is stabilized in the long-day afternoon has remained elusive. Here we demonstrate that FLAVIN-BINDING, KELCH REPEAT, F-BOX 1 (FKF1) protein stabilizes CO protein in the afternoon in long days. FKF1 interacts with CO through its LOV domain, and blue light enhances this interaction. In addition, FKF1 simultaneously removes CYCLING DOF FACTOR 1 (CDF1) that represses CO and FLOWERING LOCUS T (FT) transcription. Together with CO transcriptional regulation, FKF1 protein controls robust FT mRNA induction through multiple feedforward mechanisms that accurately control flowering timing

Kernel Architecture of the Genetic Circuitry of the Arabidopsis Circadian System

A wide range of organisms features molecular machines, circadian clocks, which generate endogenous oscillations with ~24 h periodicity and thereby synchronize biological processes to diurnal environmental fluctuations. Recently, it has become clear that plants harbor more complex gene regulatory circuits within the core circadian clocks than other organisms, inspiring a fundamental question: are all these regulatory interactions between clock genes equally crucial for the establishment and maintenance of circadian rhythms? Our mechanistic simulation for Arabidopsis thaliana demonstrates that at least half of the total regulatory interactions must be present to express the circadian molecular profiles observed in wild-type plants. A set of those essential interactions is called herein a kernel of the circadian system. The kernel structure unbiasedly reveals four interlocked negative feedback loops contributing to circadian rhythms, and three feedback loops among them drive the autonomous oscillation itself. Strikingly, the kernel structure, as well as the whole clock circuitry, is overwhelmingly composed of inhibitory, rather than activating, interactions between genes. We found that this tendency underlies plant circadian molecular profiles which often exhibit sharply-shaped, cuspidate waveforms. Through the generation of these cuspidate profiles, inhibitory interactions may facilitate the global coordination of temporally-distant clock events that are markedly peaked at very specific times of day. Our systematic approach resulting in experimentally-testable predictions provides insights into a design principle of biological clockwork, with implications for synthetic biology.Comment: Supplementary material is available at the journal websit

A mathematical model of mitochondrial swelling

<p>Abstract</p> <p>Background</p> <p>The <it>permeabilization </it>of mitochondrial membranes is a decisive event in apoptosis or necrosis culminating in cell death. One fundamental mechanism by which such permeabilization events occur is the calcium-induced mitochondrial permeability transition. Upon Ca²⁺-uptake into mitochondria an increase in inner membrane permeability occurs by a yet unclear mechanism. This leads to a net water influx in the mitochondrial matrix, mitochondrial swelling, and finally the rupture of the outer membrane. Although already described more than thirty years ago, many unsolved questions surround this important biological phenomenon. Importantly, theoretical modeling of the mitochondrial permeability transition has only started recently and the existing mathematical models fail to characterize the swelling process throughout the whole time range.</p> <p>Results</p> <p>We propose here a new mathematical approach to the mitochondrial permeability transition introducing a specific delay equation and resulting in an optimized representation of mitochondrial swelling. Our new model is in accordance with the experimentally determined course of volume increase throughout the whole swelling process, including its initial lag phase as well as its termination. From this new model biological consequences can be deduced, such as the confirmation of a positive feedback of mitochondrial swelling which linearly depends on the Ca²⁺-concentration, or a negative exponential dependence of the average swelling time on the Ca²⁺-concentration. Finally, our model can show an initial shrinking phase of mitochondria, which is often observed experimentally before the actual swelling starts.</p> <p>Conclusions</p> <p>We present a model of the mitochondrial swelling kinetics. This model may be adapted and extended to diverse other inducing/inhibiting conditions or to mitochondria from other biological sources and thus may benefit a better understanding of the mitochondrial permeability transition.</p

Analysis and Practical Guideline of Constraint-Based Boolean Method in Genetic Network Inference

Boolean-based method, despite of its simplicity, would be a more attractive approach for inferring a network from high-throughput expression data if its effectiveness has not been limited by high false positive prediction. In this study, we explored factors that could simply be adjusted to improve the accuracy of inferring networks. Our work focused on the analysis of the effects of discretisation methods, biological constraints, and stringency of Boolean function assignment on the performance of Boolean network, including accuracy, precision, specificity and sensitivity, using three sets of microarray time-series data. The study showed that biological constraints have pivotal influence on the network performance over the other factors. It can reduce the variation in network performance resulting from the arbitrary selection of discretisation methods and stringency settings. We also presented the master Boolean network as an approach to establish the unique solution for Boolean analysis. The information acquired from the analysis was summarised and deployed as a general guideline for an efficient use of Boolean-based method in the network inference. In the end, we provided an example of the use of such a guideline in the study of Arabidopsis circadian clock genetic network from which much interesting biological information can be inferred

Dawn and Dusk Set States of the Circadian Oscillator in Sprouting Barley (Hordeum vulgare) Seedlings

The plant circadian clock is an internal timekeeper that coordinates biological processes with daily changes in the external environment. The transcript levels of clock genes, which oscillate to control circadian outputs, were examined during early seedling development in barley (Hordeum vulgare), a model for temperate cereal crops. Oscillations of clock gene transcript levels do not occur in barley seedlings grown in darkness or constant light but were observed with day-night cycles. A dark-to-light transition influenced transcript levels of some clock genes but triggered only weak oscillations of gene expression, whereas a light-to-dark transition triggered robust oscillations. Single light pulses of 6, 12 or 18 hours induced robust oscillations. The light-to-dark transition was the primary determinant of the timing of subsequent peaks of clock gene expression. After the light-to-dark transition the timing of peak transcript levels of clock gene also varied depending on the length of the preceding light pulse. Thus, a single photoperiod can trigger initiation of photoperiod-dependent circadian rhythms in barley seedlings. Photoperiod-specific rhythms of clock gene expression were observed in two week old barley plants. Changing the timing of dusk altered clock gene expression patterns within a single day, showing that alteration of circadian oscillator behaviour is amongst the most rapid molecular responses to changing photoperiod in barley. A barley EARLY FLOWERING3 mutant, which exhibits rapid photoperiod–insensitive flowering behaviour, does not establish clock rhythms in response to a single photoperiod. The data presented show that dawn and dusk cues are important signals for setting the state of the circadian oscillator during early development of barley and that the circadian oscillator of barley exhibits photoperiod-dependent oscillation states