The Potential Landscape of Genetic Circuits Imposes the Arrow of Time in Stem Cell Differentiation

Wang, Jin; Xu, Li; Wang, Erkang; Huang, Sui

doi:10.1016/j.bpj.2010.03.058

Cited by 228 publications

(325 citation statements)

References 68 publications

(96 reference statements)

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“…The driving force F in the general neural networks cannot usually be written as a gradient of a potential. As we have mentioned earlier in this paper, the dynamical driving force F can be decomposed into a gradient of a potential related to steady-state probability distribution and a divergent free flux (12)(13)(14)(15).…”

Section: Resultsmentioning

confidence: 99%

“…However, it is hard to solve this equation directly due to the huge dimensions. We therefore used the selfconsistent mean field approximation to reduce the dimensionality (13,14).…”

Section: Models and Methodsmentioning

confidence: 99%

“…The curl flux can lead to spiral motion, the underlying network dynamics deviating from the gradient path, and even generate coherent oscillations, which are not possible under pure gradient force. We show a potential landscape as Lyapunov function of monotonically decreasing along the dynamics in time still exists even with asymmetric connections (12)(13)(14) for the neural networks. Our approach is based on the statistical probabilistic description of nonequilibrium dynamical systems.…”

mentioning

confidence: 89%

“…The barrier heights are shown to be associated with the escape time from one state to another. Therefore, the topography of the landscape through barrier height can provide a good measurement of global stability and function (12,(14)(15)(16)(17). Such probability landscape can be constructed through solving the corresponding probabilistic equation.…”

Section: Significancementioning

confidence: 99%

“…We see the dynamical driving force F of neural networks can be decomposed into a gradient of a nonequilibrium potential [the nonequilibrium potential U here is naturally defined as UðuÞ ¼ − lnðP ss ðuÞÞ related to the steady-state probability distribution, analogous to equilibrium systems where the energy is related to the equilibrium distribution through the Boltzman law] and a divergent free flux, modulo to the inhomogeneity of the diffusion, which can be absorbed and redefined in the total driving force (12)(13)(14)(15). The divergent free force J ss has no source or sink to go to or come out.…”

Section: Significancementioning

confidence: 99%

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Nonequilibrium landscape theory of neural networks

Yan

Zhao

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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148

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The brain map project aims to map out the neuron connections of the human brain. Even with all of the wirings mapped out, the global and physical understandings of the function and behavior are still challenging. Hopfield quantified the learning and memory process of symmetrically connected neural networks globally through equilibrium energy. The energy basins of attractions represent memories, and the memory retrieval dynamics is determined by the energy gradient. However, the realistic neural networks are asymmetrically connected, and oscillations cannot emerge from symmetric neural networks. Here, we developed a nonequilibrium landscape-flux theory for realistic asymmetrically connected neural networks. We uncovered the underlying potential landscape and the associated Lyapunov function for quantifying the global stability and function. We found the dynamics and oscillations in human brains responsible for cognitive processes and physiological rhythm regulations are determined not only by the landscape gradient but also by the flux. We found that the flux is closely related to the degrees of the asymmetric connections in neural networks and is the origin of the neural oscillations. The neural oscillation landscape shows a closed-ring attractor topology. The landscape gradient attracts the network down to the ring. The flux is responsible for coherent oscillations on the ring. We suggest the flux may provide the driving force for associations among memories. We applied our theory to rapid-eye movement sleep cycle. We identified the key regulation factors for function through global sensitivity analysis of landscape topography against wirings, which are in good agreements with experiments.neural circuits | free energy | entropy production | nonequilibrium thermodynamics A grand goal of biology is to understand the function of the human brain. The brain is a complex dynamical system (1-6). The individual neurons can develop action potentials and connect with each other through synapses to form the neural circuits. The neural circuits of the brain perpetually generate complex patterns of activity that have been shown to be related with special biological functions, such as learning, long-term associative memory, working memory, olfaction, decision making and thinking (7-9), etc. Many models have been proposed for understanding how neural circuits generate different patterns of activity. HodgkinHuxley model gives a quantitative description of a single neuronal behavior based on the voltage-clamp measurements of the voltage (4). However, various vital functions are carried out by the circuit rather than individual neurons. It is at present still challenging to explore the underlying global natures of the large neural networks built from individual neurons.Hopfield developed a model (5, 6) that makes it possible to explore the global natures of the large neural networks without losing the information of essential biological functions. For symmetric neural circuits, an energy landscape can be constructed that decreas...

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Section: Resultsmentioning

confidence: 99%

“…However, it is hard to solve this equation directly due to the huge dimensions. We therefore used the selfconsistent mean field approximation to reduce the dimensionality (13,14).…”

Section: Models and Methodsmentioning

confidence: 99%

mentioning

confidence: 89%

Section: Significancementioning

confidence: 99%

Section: Significancementioning

confidence: 99%

See 3 more Smart Citations

Nonequilibrium landscape theory of neural networks

Yan

Zhao

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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148

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Stochastic and Deterministic Decision in Cell Fate

Menn

Wang

2014

Encyclopedia of Life Sciences

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From bacteria to mammals, individual cells from an isogenic population are able to assume roles resulting in phenotypic heterogeneity. The mechanisms used to make these cell fate decisions range from highly deterministic to essentially random. This wide range of behaviour springs from the interplay of intracellular molecular kinetics, the topologies of underlying gene regulator networks, epigenetic control mechanisms and cell–environment interactions. Cells utilise these factors to implement differentiation strategies such as developmental rigidity, which ensures the development of key structures in multicellular organisms, and bet hedging, the introduction of nongenetic variability to promote population fitness. Because decision‐making genes in natural systems are integrated with myriad other pathways, they can be difficult to study on their own. Synthetic biology offers a means to study cell differentiation in vivo in a manner separated from normal cellular functions. Key Concepts: Gene expression is an inherently stochastic process. Despite stochastic gene expression, differentiation can proceed deterministically. Other cell fate decisions are random due to stochastic gene expression. Gene network topologies are employed to attenuate or increase the effects of noise. The field of synthetic biology is uniquely suited for exploring the complex interactions that inform cell decisions.

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Reprogramming cell fates: reconciling rarity with robustness

2009

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The stunning possibility of “reprogramming” differentiated somatic cells to express a pluripotent stem cell phenotype (iPS, induced pluripotent stem cell) and the “ground state” character of pluripotency reveal fundamental features of cell fate regulation that lie beyond existing paradigms. The rarity of reprogramming events appears to contradict the robustness with which the unfathomably complex phenotype of stem cells can reliably be generated. This apparent paradox, however, is naturally explained by the rugged “epigenetic landscape” with valleys representing “preprogrammed” attractor states that emerge from the dynamical constraints of the gene regulatory network. This article provides a pedagogical primer to the fundamental principles of gene regulatory networks as integrated dynamic systems and reviews recent insights in gene expression noise and fate determination, thereby offering a formal framework that may help us to understand why cell fate reprogramming events are inherently rare and yet so robust.

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The Potential Landscape of Genetic Circuits Imposes the Arrow of Time in Stem Cell Differentiation

Cited by 228 publications

References 68 publications

Nonequilibrium landscape theory of neural networks

Nonequilibrium landscape theory of neural networks

Stochastic and Deterministic Decision in Cell Fate

Reprogramming cell fates: reconciling rarity with robustness

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