Dataset Information

A model of cell biological signaling predicts a phase transition of signaling and provides mathematical formulae.

ABSTRACT: A biological signal is transmitted by interactions between signaling molecules in the cell. To date, there have been extensive studies regarding signaling pathways using numerical simulation of kinetic equations that are based on equations of continuity and Fick's law. To obtain a mathematical formulation of cell signaling, we propose a stability kinetic model of cell biological signaling of a simple two-parameter model based on the kinetics of the diffusion-limiting step. In the present model, the signaling is regulated by the binding of a cofactor, such as ATP. Non-linearity of the kinetics is given by the diffusion fluctuation in the interaction between signaling molecules, which is different from previous works that hypothesized autocatalytic reactions. Numerical simulations showed the presence of a critical concentration of the cofactor beyond which the cell signaling molecule concentration is altered in a chaos-like oscillation with frequency, which is similar to a discontinuous phase transition in physics. Notably, we found that the frequency is given by the logarithm function of the difference of the outside cofactor concentration from the critical concentration. This implies that the outside alteration of the cofactor concentration is transformed into the oscillatory alteration of cell inner signaling. Further, mathematical stability kinetic analysis predicted a discontinuous dynamic phase transition in the critical state at which the cofactor concentration is equivalent to the critical concentration. In conclusion, the present model illustrates a unique feature of cell signaling, and the stability analysis may provide an analytical framework of the cell signaling system and a novel formulation of biological signaling.

SUBMITTER: Tsuruyama T

PROVIDER: S-EPMC4117461 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

A model of cell biological signaling predicts a phase transition of signaling and provides mathematical formulae.

Tsuruyama Tatsuaki T

PloS one 20140731 7

A biological signal is transmitted by interactions between signaling molecules in the cell. To date, there have been extensive studies regarding signaling pathways using numerical simulation of kinetic equations that are based on equations of continuity and Fick's law. To obtain a mathematical formulation of cell signaling, we propose a stability kinetic model of cell biological signaling of a simple two-parameter model based on the kinetics of the diffusion-limiting step. In the present model, ...[more]

PMID: 25079957

Similar Datasets

Project description:The beef cow-calf sector accounts for 70% of feed consumed and greenhouse gases emitted for the beef industry, but there is no straightforward method to measure biological efficiency in grazing conditions. The objective of this study was to evaluate a mathematical nutrition model to estimate the feed intake and biological efficiency of mature beef cows. Data from dams (N = 160) and their second and third progeny (312 pairs) were collected from 1953 through 1980. Individual feed intake was measured at 28-d intervals year-round for dams and during 240-d lactation for progeny. Body weights of progeny were measured at 28-d intervals from birth to weaning, and of dams at parturition and weaning each production cycle. The milk yield of dams was measured at 14-d intervals. Dam metabolizable energy intake (DMEI) and milk energy yield (MEL) of each cow were predicted using the Cattle Value Discovery System beef cow (CVDSbc) model for each parity. Biological efficiency (Mcal/kg) was computed as the ratio of observed or predicted DMEI to observed calf weaning weight (PWW). Pearson correlation coefficients were computed using corr.test function and model evaluation was performed using the epiR function in R software. Average (SD) dam weight, PWW, DMEI, and observed MEL were 527 (86) kg, 291 (47) kg, 9584 (2701) Mcal/production cycle, and 1029 (529) Mcal, respectively. Observed and predicted DMEI (r = 0.93 and 0.91), and observed and predicted MEL (r = 0.58 and 0.59) were positively correlated for progeny 2 and 3, respectively. The CVDSbc model under-predicted DMEI (mean bias [MB] = 1,120 ± 76 Mcal, 11.7% of observed value) and MEL (MB = 30 ± 25 Mcal, 2.9% of observed value). Observed and predicted progeny feed intake were not correlated (r = 0.01, P-value = 0.79). Observed and predicted biological efficiency were positively correlated (r = 0.80 and 0.80, P-value ≤ 0.05) for parity 2 and 3, respectively, and the CVDSbc model under-predicted biological efficiency by 11% (MB = 3.59 ± 0.25 Mcal/kg). The CVDSbc provides reasonable predictions of feed intake and biological efficiency of mature beef cows, but further refinement of the relationship between calf feed intake and milk yield is recommended to improve predictions. Mathematical nutrition models can assist in the discovery of the biological efficiency of mature beef cows.

Project description:BACKGROUND: Phase transition widely exists in the biological world, such as transformation of cell cycle phases, cell differentiation stages, disease development, and so on. Such a nonlinear phenomenon is considered as the conversion of a biological system from one phenotype/state to another. Studies on the molecular mechanisms of biological phase transition have attracted much attention, in particular, on different genotypes (or expression variations) in a specific phase, but with less of focus on cascade changes of genes' functions (or system state) during the phase shift or transition process. However, it is a fundamental but important mission to trace the temporal characteristics of a biological system during a specific phase transition process, which can offer clues for understanding dynamic behaviors of living organisms. RESULTS: By overcoming the hurdles of traditional time segmentation and temporal biclustering methods, a causal process model (CPM) in the present work is proposed to study the biological phase transition in a systematic manner, i.e. first, we make gene-specific segmentation on time-course expression data by developing a new boundary gene estimation scheme, and then infer functional cascade dynamics by constructing a temporal block network. After the computational validation on synthetic data, CPM was used to analyze the well-known Yeast cell cycle data. It was found that the dynamics of the boundary genes are periodic and consistent with the phases of the cell cycle, and the temporal block network indeed demonstrates a meaningful cascade structure of the enriched biological functions. In addition, we further studied protein modules based on the temporal block network, which reflect temporal features in different cycles. CONCLUSIONS: All of these results demonstrate that CPM is effective and efficient comparing to traditional methods, and is able to elucidate essential regulatory mechanism of a biological system even with complicated nonlinear phase transitions.

Project description:Protrusion and retraction of lamellipodia are common features of eukaryotic cell motility. As a cell migrates through its extracellular matrix (ECM), lamellipod growth increases cell-ECM contact area and enhances engagement of integrin receptors, locally amplifying ECM input to internal signaling cascades. In contrast, contraction of lamellipodia results in reduced integrin engagement that dampens the level of ECM-induced signaling. These changes in cell shape are both influenced by, and feed back onto ECM signaling. Motivated by experimental observations on melanoma cells lines (1205Lu and SBcl2) migrating on fibronectin (FN) coated topographic substrates (anisotropic post-density arrays), we probe this interplay between intracellular and ECM signaling. Experimentally, cells exhibited one of three lamellipodial dynamics: persistently polarized, random, or oscillatory, with competing lamellipodia oscillating out of phase (Park et al., 2017). Pharmacological treatments, changes in FN density, and substrate topography all affected the fraction of cells exhibiting these behaviours. We use these observations as constraints to test a sequence of hypotheses for how intracellular (GTPase) and ECM signaling jointly regulate lamellipodial dynamics. The models encoding these hypotheses are predicated on mutually antagonistic Rac-Rho signaling, Rac-mediated protrusion (via activation of Arp2/3 actin nucleation) and Rho-mediated contraction (via ROCK phosphorylation of myosin light chain), which are coupled to ECM signaling that is modulated by protrusion/contraction. By testing each model against experimental observations, we identify how the signaling layers interact to generate the diverse range of cell behaviors, and how various molecular perturbations and changes in ECM signaling modulate the fraction of cells exhibiting each. We identify several factors that play distinct but critical roles in generating the observed dynamic: (1) competition between lamellipodia for shared pools of Rac and Rho, (2) activation of RhoA by ECM signaling, and (3) feedback from lamellipodial growth or contraction to cell-ECM contact area and therefore to the ECM signaling level.

Project description:Circadian clocks are endogenous biochemical oscillators that control daily behavioral rhythms in all living organisms. In fruit fly, the circadian rhythms are typically studied using power spectra of multiday behavioral recordings. Despite decades of study, a quantitative understanding of the temporal shape of Drosophila locomotor rhythms is missing. Locomotor recordings have been used mostly to extract the period of the circadian clock, leaving these data-rich time series largely underutilized. The power spectra of Drosophila and mouse locomotion often show multiple peaks in addition to the expected at T ~ 24 h. Several theoretical and experimental studies have previously used these data to examine interactions between the circadian and other endogenous rhythms, in some cases, attributing peaks in the T < 24 h regime to ultradian oscillators. However, the analysis of fly locomotion was typically performed without considering the shape of time series, while the shape of the signal plays important role in its power spectrum. To account for locomotion patterns in circadian studies we construct a mathematical model of fly activity. Our model allows careful analysis of the temporal shape of behavioral recordings and can provide important information about biochemical mechanisms that control fly activity.Here we propose a mathematical model with four exponential terms and a single period of oscillation that closely reproduces the shape of the locomotor data in both time and frequency domains. Using our model, we reexamine interactions between the circadian and other endogenous rhythms and show that the proposed single-period waveform is sufficient to explain the position and height of >88 % of spectral peaks in the locomotion of wild-type and circadian mutants of Drosophila. In the time domain, we find the timescales of the exponentials in our model to be ~1.5 h(-1) on average.Our results indicate that multiple spectral peaks from fly locomotion are simply harmonics of the circadian period rather than independent ultradian oscillators as previously reported. From timescales of the exponentials we hypothesize that model rates reflect activity of the neuropeptides that likely transduce signals of the circadian clock and the sleep-wake homeostat to shape behavioral outputs.

Project description:BackgroundIn cell signaling pathways, proteins interact with each other to determine cell fate in response to either cell-extrinsic (micro-environmental) or intrinsic cues. One of the well-studied pathways, the mitogen-activated protein kinase (MAPK) signaling pathway, regulates cell processes such as differentiation, proliferation, apoptosis, and survival in response to various micro-environmental stimuli in eukaryotes. Upon micro-environmental stimulus, receptors on the cell membrane become activated. Activated receptors initiate a cascade of protein activation in the MAPK pathway. This activation involves protein binding, creating scaffold proteins, which are known to facilitate effective MAPK signaling transduction.ResultsThis paper presents a novel mathematical model of a cell signaling pathway coordinated by protein scaffolding. The model is based on the extended Boolean network approach with stochastic processes. Protein production or decay in a cell was modeled considering the stochastic process, whereas the protein-protein interactions were modeled based on the extended Boolean network approach. Our model fills a gap in the binary set applied to previous models. The model simultaneously considers the stochastic process directly. Using the model, we simulated a simplified mitogen-activated protein kinase (MAPK) signaling pathway upon stimulation of both a single receptor at the initial time and multiple receptors at several time points. Our simulations showed that the signal is amplified as it travels down to the pathway from the receptor, generating substantially amplified downstream ERK activity. The noise generated by the stochastic process of protein self-activity in the model was also amplified as the signaling propagated through the pathway.ConclusionsThe signaling transduction in a simplified MAPK signaling pathway could be explained by a mathematical model based on the extended Boolean network model with a stochastic process. The model simulations demonstrated signaling amplifications when it travels downstream, which was already observed in experimental settings. We also highlight the importance of stochastic activity in regulating protein inactivation.

Dataset Information

A model of cell biological signaling predicts a phase transition of signaling and provides mathematical formulae.

Publications

A model of cell biological signaling predicts a phase transition of signaling and provides mathematical formulae.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets