Sensitivity of asymmetric rate-dependent critical systems to initial conditions: insights into cellular decision making

The work reported here aims to address the effects of time-dependent parameters and stochasticity on decision-making in biological systems. We achieve this by extending previous studies that resorted to simple normal forms. Yet, we focus primarily on the issue of the system's sensitivity to initial conditions in the presence of different noise distributions. In addition, we assess the impact of two-way sweeping through the critical region of a canonical Pitchfork bifurcation with a constant external asymmetry. The parallel with decision-making in bio-circuits is performed on this simple system since it is equivalent in its available states and dynamics to more complex genetic circuits. Overall, we verify that rate-dependent effects are specific to particular initial conditions. Information processing for each starting state is affected by the balance between sweeping speed through critical regions, and the type of fluctuations added. For a heavy-tail noise, forward-reverse dynamic bifurcations are more efficient in processing the information contained in external signals, when compared to the system relying on escape dynamics, if it starts at an attractor not favoured by the asymmetry and, in conjunction, if the sweeping amplitude is large

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model.

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model

Maternal PlGF and umbilical Dopplers predict pregnancy outcomes at diagnosis of early-onset fetal growth restriction

BACKGROUND: Severe, early-onset fetal growth restriction (FGR) causes significant fetal and neonatal mortality and morbidity. Predicting the outcome of affected pregnancies at the time of diagnosis is difficult, thus preventing accurate patient counseling. We investigated the use of maternal serum protein and ultrasound measurements at diagnosis to predict fetal or neonatal death and 3 secondary outcomes: fetal death or delivery at or before 28+0 weeks, development of abnormal umbilical artery (UmA) Doppler velocimetry, and slow fetal growth. // METHODS: Women with singleton pregnancies (n = 142, estimated fetal weights [EFWs] below the third centile, less than 600 g, 20+0 to 26+6 weeks of gestation, no known chromosomal, genetic, or major structural abnormalities) were recruited from 4 European centers. Maternal serum from the discovery set (n = 63) was analyzed for 7 proteins linked to angiogenesis, 90 additional proteins associated with cardiovascular disease, and 5 proteins identified through pooled liquid chromatography and tandem mass spectrometry. Patient and clinician stakeholder priorities were used to select models tested in the validation set (n = 60), with final models calculated from combined data. // RESULTS: The most discriminative model for fetal or neonatal death included the EFW z score (Hadlock 3 formula/Marsal chart), gestational age, and UmA Doppler category (AUC, 0.91; 95% CI, 0.86–0.97) but was less well calibrated than the model containing only the EFW z score (Hadlock 3/Marsal). The most discriminative model for fetal death or delivery at or before 28+0 weeks included maternal serum placental growth factor (PlGF) concentration and UmA Doppler category (AUC, 0.89; 95% CI, 0.83–0.94). // CONCLUSION: Ultrasound measurements and maternal serum PlGF concentration at diagnosis of severe, early-onset FGR predicted pregnancy outcomes of importance to patients and clinicians. // TRIAL REGISTRATION: ClinicalTrials.gov NCT02097667. // FUNDING: The European Union, Rosetrees Trust, Mitchell Charitable Trust

Speed-Dependent Cellular Decision Making in Nonequilibrium Genetic Circuits

Despite being governed by the principles of nonequilibrium transitions, gene expression dynamics underlying cell fate decision is poorly understood. In particular, the effect of signaling speed on cellular decision making is still unclear. Here we show that the decision between alternative cell fates, in a structurally symmetric circuit, can be biased depending on the speed at which the system is forced to go through the decision point. The circuit consists of two mutually inhibiting and self-activating genes, forced by two external signals with identical stationary values but different transient times. Under these conditions, slow passage through the decision point leads to a consistently biased decision due to the transient signaling asymmetry, whereas fast passage reduces and eventually eliminates the switch imbalance. The effect is robust to noise and shows that dynamic bifurcations, well known in nonequilibrium physics, are important for the control of genetic circuits

Pair-wise average distance between asymptotically stable states induced by input combinations.

<p>(A) Results for time scale ratio calculated through Eq. (3) and (B) . (C) Distance between pairs of vectors , calculated through the distance metric , with being the Pearson coefficient of correlation between the actual vectors and . Parameters: , , , (self-activation) and (cross-repression)(see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040085#s3" target="_blank">Methods</a>), for .</p

Inter-trajectory distance, profile of specific input combinations and typical switching dynamics.

<p>(A) Time-dependent profile for each input for 3 input combinations: , , . (B) Inter-trajectory distance for pairs inducing the same attractors (see Fig. 4A). Pairs exhibiting the highest value for (Eq. (4)) and the lowest value for . Inset: zoom of curve for . (C) Typical evolution of concentrations for all the nodes , . This particular trajectory was generated by applying and noise intensity (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040085#s3" target="_blank">Methods</a>). (D) Amplification of (C) for early times t. (E) Amplification of (C) for concentrations close to zero. , i.e. the concentration of each transcription factor is represented here by and associated with in Eqs. (7) and (8) with (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040085#s3" target="_blank">Methods</a>). Parameters: , , , (self-activation) and (cross-repression), (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040085#s3" target="_blank">Methods</a>), for .</p

Parameters in the high-dimensional decision genetic switch with external stimulation model.

<p>Parameters used in Eqs. (6) to (10) and their respective interpretation and values. See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040085#pone.0040085-Andrecut1" target="_blank">[39]</a>.</p

Representation of the high-dimensional genetic decision switch with external stimulation.

<p>Nodes 6 to 15 represent proteins, transcription factors. Signals represent protein kinases. Only nodes 6 to 10 need to be activated (phosphorylated) to act on any promoter region of the rest of the transcription factors in the network. Each transcription factor reinforces its own expression (black arrows) and represses (red links) all other nodes. Phosphorylation reactions are represented by grey arrows. See also figure legend on right hand side.</p

Distance between final distributions generated by different pairs of input combinations in the presence of fluctuations.

<p>(A) Pair . (B) Pair . is a correlation based metric, where stands for the correlation between the distributions across attractors, induced by and , in the limit of large times. Parameters: , , , (self-activation) and (cross-repression), (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040085#s3" target="_blank">Methods</a>), for . stands for noise intensity (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040085#s3" target="_blank">Methods</a>).</p