Zipf's Law in Gene Expression

Abstract

Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law distribution with an exponent close to -1, i.e., they obey Zipf's law. Furthermore, by simulations of a simple model with an intra-cellular reaction network, we found that Zipf's law of chemical abundance is a universal feature of cells where such a network optimizes the efficiency and faithfulness of self-reproduction. These findings provide novel insights into the nature of the organization of reaction dynamics in living cells.

revtex, 11 pages, 3 figures, submitted to Phys. Rev. Lett

Cited by in corpus (72)

• Colloquium: Criticality and dynamical scaling in living systems
• Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size Systems
• Large-scale analysis of Zipf's law in English texts
• Power-law size distributions in geoscience revisited
• Reduction of dynamical biochemical reaction networks in computational biology
• Linguistic laws in biology
• Evolution of scaling emergence in large-scale spatial epidemic spreading
• Formation of Dominant Mode by Evolution in Biological Systems
• Similarity of symbol frequency distributions with heavy tails
• Transition state theory: a generalization to nonequilibrium systems with power-law distributions
• The Mathematical Relationship between Zipf's Law and the Hierarchical Scaling Law
• Statistical Indicators of Collective Behavior and Functional Clusters in Gene Networks of Yeast
• Evolutionary dimension reduction in phenotypic space
• The distinct flavors of Zipf's law in the rank-size and in the size-distribution representations, and its maximum-likelihood fitting
• Log-log Convexity of Type-Token Growth in Zipf's Systems
• Recursiveness, Switching, and Fluctuations in a Replicating Catalytic Network
• Adaptive coupling induced multi-stable states in complex networks
• Theory for transitions between log and stationary phases: universal laws for lag time
• Reproduction of a Protocell by Replication of Minority Molecule in Catalytic Reaction Network
• The power-law reaction rate coefficient for an elementary bimolecular reaction
• Zipf's law from a Fisher variational-principle
• Universality and Shannon entropy of codon usage
• Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equations
• "Glassy" Relaxation in Catalytic Reaction Networks
• Growth states of catalytic reaction networks exhibiting energy metabolism
• Entropy production of a steady-growth cell with catalytic reactions
• Maximal Diversity and Zipf's Law
• The collision theory reaction rate coefficient for power-law distributions
• Recursive Subdivision of Urban Space and Zipf's law
• Kramers escape rate in overdamped systems with the power-law distribution
• Discreteness-induced Transition in Catalytic Reaction Networks
• Fisher-information and the thermodynamics of scale-invariant systems
• Ubiquitous power law scaling in nonlinear self-excited Hawkes processes
• The advantage of leakage of essential metabolites and resultant symbiosis of diverse species
• The rate coefficients of unimolecular reactions in the systems with power-law distributions
• Evolutionary origin of power-laws in Biochemical Reaction Network; embedding abundance distribution into topology
• Universal relationship in gene-expression changes for cells in steady-growth state
• Universal Complex Structures in Written Language
• Predicted and Verified Deviation from Zipf's Law in Growing Social Networks
• Quantifying the Unexpected: a scientific approach to Black Swans
• Horizontal transfer between loose compartments stabilizes replication of fragmented ribozymes
• A Constructive Approach to Gene Expression Dynamics
• The mean first passage time in an energy-diffusion controlled regime with power-law distributions
• Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products
• Escape rate for the power-law distribution in low-to-intermediate damping
• Chaotic Griffiths Phase with Anomalous Lyapunov Spectra in Coupled Map Networks
• $1/f$ noise on the brink of wet granular melting
• Inverse Relationship Between Molecular Diversity And Resource Abundances
• From Boltzmann to Zipf through Shannon and Jaynes
• The power-law TST reaction rate coefficient with tunneling correction
• A stochastic approach to multi-gene expression dynamics
• Evidence of Scale-Free Topology and Dynamics in Gene Regulatory Networks
• Probabilistic analysis of the human transcriptome with side information
• Discreteness-Induced Slow Relaxation in Reversible Catalytic Reaction Networks
• Telling apart <I>Felidae</I> and <I>Ursidae</I> from the distribution of nucleotides in mitochondrial DNA
• The power-law reaction rate coefficient for barrierless reactions
• Ubiquity of Log-normal Distributions in Intra-cellular Reaction Dynamic
• The peculiar statistical mechanics of Optimal Learning Machines
• The calculation of the probability density and distribution function of a strictly stable law in the vicinity of zero
• Application of the fractional stable distributions for approximation of gene expression profiles
• Inverse Modeling of Complex Networks Using Embedded Complex Logistic Maps
• Conjugate Distribution Laws in Cultural Evolution via Statistical Learning
• Universal Transitions between Growth and Dormancy via Intermediate Complex Formation
• Exponential growth for self-reproduction in a catalytic reaction network: relevance of a minority molecular species and crowdedness
• Approaches to the classification of complex systems: Words, texts, and more
• Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature
• Bifurcation in cellular evolution
• Macroscopic and microscopic statistical properties observed in blog entries
• Molecular Diversity and Network Complexity in Growing Protocells
• Starvation suppression in dense scale-free metabolic networks: Dynamical mean-field analysis of catalytic reaction networks
• Universal emergence of local Zipf-Mandelbrot law
• Zipf's law for share price and company fundamentals