A modular approach for modeling the cell cycle based on functional response curves

Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.

De novo Explorations of Sarcopenia via a Dynamic Model

Background: The cause of sarcopenia has been observed over decades by clinical trials, which, however, are still insufficient to systematically unravel the enigma of how resistance exercise mediates skeletal muscle mass.Materials and Methods: Here, we proposed a minimal regulatory network and developed a dynamic model to rigorously investigate the mechanism of sarcopenia. Our model is consisted of eight ordinary differential equations and incorporates linear and Hill-function terms to describe positive and negative feedbacks between protein species, respectively.Results: A total of 720 samples with 10 scaled intensities were included in simulations, which revealed the expression level of AKT (maximum around 3.9-fold) and mTOR (maximum around 5.5-fold) at 3, 6, and 24 h at high intensity, and non-monotonic relation (ranging from 1.2-fold to 1.7-fold) between the graded intensities and skeletal muscle mass. Furthermore, continuous dynamics (within 24 h) of AKT, mTOR, and other proteins were obtained accordingly, and we also predicted the delaying effect with the median of maximized muscle mass shifting from 1.8-fold to 4.6-fold during a 4-fold increase of delay coefficient.Conclusion: The de novo modeling framework sheds light on the interdisciplinary methodology integrating computational approaches with experimental results, which facilitates the deeper understandings of exercise training and sarcopenia.

KCC Analysis of a One-Dimensional System During Catastrophic Shift of the Hill Function: Douglas Tensor in the Nonequilibrium Region

This paper considers the stability of a one-dimensional system during a catastrophic shift described by the Hill function. Because the shifting process goes through a nonequilibrium region, we applied the theory of Kosambi, Cartan, and Chern (KCC) to analyze the stability of this region based on the differential geometrical invariants of the system. Our results show that the Douglas tensor, one of the invariants in the KCC theory, affects the robustness of the trajectory during a catastrophic shift. In this analysis, the forward and backward shifts can have different Jacobi stability structures in the nonequilibrium region. Moreover, the bifurcation curve of the catastrophic shift can be interpreted geometrically, as the solution curve where the nonlinear connection and the deviation curvature become zero. KCC analysis also shows that even if the catastrophic pattern itself is similar, the stability structure in the nonequilibrium region is different in some cases, from the viewpoint of the Douglas tensor.

Characterization of Onion Seedlots into Different Storability Groups with 4 Parameter Hill Function (4-PHF)

Onion varieties were classified into different storability groups by comparing two approaches (i)germination and vigor indices (conventional germination parameters) (ii)variables extracted from 4 Parameter Hill Function (4-PHF), after mimicking ageing conditions with accelerated ageing (42 °C and 100% RH). The study revealed that in comparison to evaluation using conventional germination parameters, the parameters extracted using 4-PHF provided realistic characterization of varieties as good, medium and poor storers. Time related parameters like time to maximum germination rate (TMGR), time to 50% germination (T50), difference between time at germination onset (lag) and 50% germination (Dlag-50), uniformity (U) along with germination percent (a) and area under curve (AUC) were decisive in identification of the varieties to a storage category which was misinterpreted with exclusive use of conventional approach. The distinction between good and medium storers was not of much significance but shift of varieties like Bhima Super, Pusa Red and Agrifound Light Red from poor to good performance cluster could be detected exclusively through 4-PHF analysis. Curve fittings highlighted AUC as the most crucial parameter contributing towards clustering of the varieties in different storability groups. Our study is the first reported research of using 4-PHF mathematical function for seedlot characterization into different storability groups.

Diversity increases the stability of ecosystems

In 1972, Robert May showed that diversity is detrimental to an ecosystem since, as the number of species increases, the ecosystem is less stable. This is the so-called diversity-stability paradox, which has been derived by considering a mathematical model with linear interactions between the species. Despite being in contradiction with empirical evidence, the diversity-stability paradox has survived the test of time for over 40+ years. In this paper we first show that this paradox is a conclusion driven solely by the linearity of the model employed in its derivation which allows for the neglection of the fixed point solution in the stability analysis. The linear model leads to an ill-posed solution and along with it, its paradoxical stability predictions. We then consider a model ecosystem with nonlinear interactions between species, which leads to a stable ecosystem when the number of species is increased. The saturating non linear term in the species interaction is analogous to a Hill function appearing in systems like gene regulation, neurons, diffusion of information and ecosystems The exact fixed point solution of this model is based on k-core percolation and shows that the paradox disappears. This theoretical result, which is exact and non-perturbative, shows that diversity is beneficial to the ecosystem in agreement with analyzed experimental evidence

Invariances in a combinatorial olfactory receptor code

Animals can identify an odorant type across a wide range of concentrations, as well as detect changes in concentration for individual odorant type. How olfactory representations are structured to support these functions remains poorly understood. Here, we studied how a full complement of ORNs in the Drosophila larva encodes a broad input space of odorant types and concentrations. We find that dose-response relationships across odorants and ORN types follow the Hill function with shared cooperativity but different activation thresholds. These activation thresholds are drawn from a power law statistical distribution. A fixed activation function and power law distribution of activation thresholds underlie invariances in the encoding of odorant identity and intensity. Moreover, we find similar temporal response filters of ORNs across odorant types and concentrations. Such uniformity in the temporal filter may allow identity invariant coding in fluctuating or turbulent odor environments. Common patterns in ligand-receptor binding and sensory transduction across olfactory receptors may give rise to these observed invariances in the olfactory combinatorial code. Invariant patterns in the activity responses of individual ORNs and the ORN ensemble may simplify decoding by downstream circuits.

Resource Competition Shapes the Response of Genetic Circuits

A common approach to design genetic circuits is to compose gene expression cassettes together. While appealing, this modular approach is challenged by the fact that expression of each gene depends on the availability of transcriptional/translational resources, which is in turn determined by the presence of other genes in the circuit. This raises the question of how competition for resources by different genes affects a circuit’s behavior. Here, we create a library of genetic activation cascades in bacteriaE. coli, where we explicitly tune the resource demand by each gene. We develop a general Hill-function-based model that incorporates resource competition effects through resource demand coefficients. These coefficients lead to non-regulatory interactions among genes that reshape circuit’s behavior. For the activation cascade, such interactions result in surprising biphasic or monotonically decreasing responses. Finally, we use resource demand coefficients to guide the choice of ribosome binding site (RBS) and DNA copy number to restore the cascade’s intended monotonically increasing response. Our results demonstrate how unintended circuit’s behavior arises from resource competition and provide a model-guided methodology to minimize the resulting effects.