Emergent Self-Organized Criticality in Gene Expression Dynamics: Temporal Development of Global Phase Transition Revealed in a Cancer Cell Line

Tsuchiya, Masa; Giuliani, Alessandro; Hashimoto, Midori; Ērenpreisa, Jekaterina; Yoshikawa, Kenichi

doi:10.1371/journal.pone.0128565

Cited by 54 publications

(178 citation statements)

References 60 publications

Supporting

Mentioning

162

Contrasting

Unclassified

Order By: Relevance

“…For instance, Ref. [13] demonstrated an emerging property in whole-genome expression through the transition from a unimodal distribution to a bimodal distribution due to bistability and claimed self-organized criticality (SOC) [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Geometric structure and information change in phase transitions

Kim

Hollerbach

2017

Phys. Rev. E

View full text Add to dashboard Cite

We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent probability density functions (PDFs) and the information length L, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behavior in FPs and BPs. In particular, FPs driven by instability undergo the broadening of the PDF with a large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale τ of information change is constant in time, independent of the strength of the stochastic noise. In comparison, BPs are mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BPs than in FPs, increasing linearly with the deviation γ of a control parameter from the critical state in BPs while increasing logarithmically with γ in FPs. L scales as | ln D| and D −1/2 in FPs and BPs, respectively, where D measures the strength of the stochastic forcing. These differing scalings with γ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g., fitness).

show abstract

Section: Introductionmentioning

confidence: 99%

Geometric structure and information change in phase transitions

Kim

Hollerbach

2017

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The purpose of this paper is to investigate how these two models are affected by stochastic noise, which is now believed to be crucial in many systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. For instance, variability has emerged to be a key factor in understanding the development of tumours [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Time-dependent probability density functions and information geometry in stochastic logistic and Gompertz models

2017

View full text Add to dashboard Cite

A probabilistic description is essential for understanding growth processes far from equilibrium.In this paper, we compute time-dependent Probability Density Functions (PDFs) in order to investigate stochastic logistic and Gompertz models, which are two of the most popular growth models.We consider different types of short-correlated internal (multiplicative) and external (additive) stochastic noises and compare the time-dependent PDFs in the two models, elucidating the effects of the additive and multiplicative noises on the form of PDFs. We demonstrate an interesting transition from a unimodal to a bimodal PDF as the multiplicative noise increases for a fixed value of the additive noise. A much weaker (leaky) attractor in the Gompertz model leads to a significant (singular) growth of the population of a very small size. We point out the limitation of using stationary PDFs, mean value and variance in understanding statistical properties of the growth far from equilibrium, highlighting the importance of time-dependent PDFs. We further compare these two models from the perspective of information change that occurs during the growth process. Specifically, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory quantifies the total number of different states that the system undergoes in time, and is called the information length. We show that the time-evolution of the two models become more similar when measured in units of the information length and point out the merit of using the information length in unifying and understanding the dynamic evolution of different growth processes.

show abstract

“…The self-regulation between macroscopic and microscopic variables leads to a dynamical equilibrium (self-organisation), which involves fluctuations as an essential part [6]. There has been accumulating evidence for relevance and important role of self-organisation in different systems such as shear flows or vortices in fluids or plasmas, pattern formation in chemical oscillators, homoeostasis in biosystems and even traffic flows [4,[7][8][9][10][11][12][13][14][15][16]. In particular, self-organised shear (zonal) flows are now believed to play a crucial role in stabilising laboratory plasmas, beneficial for extracting fusion energy [7].…”

Section: Introductionmentioning

confidence: 99%

Information Geometry of Non-Equilibrium Processes in a Bistable System with a Cubic Damping

Hollerbach¹,

Kim²

2017

Preprint

View full text Add to dashboard Cite

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic systems and information geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate the information geometry of non-equilibrium processes involved in disorder-order transitions between the critical and subcritical states in a bistable system. Specifically, we compute time-dependent PDFs, information length, the rate of change in information length, entropy change and Fisher information in disorder-to-order and order-to-disorder transitions and discuss similarities and disparities between the two transitions. In particular, we show that the total information length in order-to-disorder transition is much larger than that in disorder-to-order transition and elucidate the link to the drastically different evolution of entropy in both transitions. We also provide the comparison of the results with those in the case of the transition between the subcritical and supercritical states and discuss implications for fitness.

show abstract

Emergent Self-Organized Criticality in Gene Expression Dynamics: Temporal Development of Global Phase Transition Revealed in a Cancer Cell Line

Cited by 54 publications

References 60 publications

Geometric structure and information change in phase transitions

Geometric structure and information change in phase transitions

Time-dependent probability density functions and information geometry in stochastic logistic and Gompertz models

Information Geometry of Non-Equilibrium Processes in a Bistable System with a Cubic Damping

Contact Info

Product

Resources

About