Estimation of non-equilibrium transition rate from gene expression data

The dynamical properties of many complex physical and biological systems can be quantified from the energy landscape theory. Previous approaches focused on estimating the transition rate from landscape reconstruction based on data. However, for general non-equilibrium systems (such as gene regulatory systems), both the energy landscape and the probability flux are important to determine the transition rate between attractors. In this work, we proposed a data-driven approach to estimate non-equilibrium transition rate, which combines the kernel density estimation and non-equilibrium transition rate theory. Our approach shows superior performance in estimating transition rate from data, compared with previous methods, due to the introduction of a nonparametric density estimation method and the new saddle point by considering the effects of flux. We demonstrate the practical validity of our approach by applying it to a simplified cell fate decision model and a high-dimensional stem cell differentiation model. Our approach can be applied to other biological and physical systems.

Waiting time dependence of aging

Aging phenomena have been observed in many non-equilibrium systems such as polymers and glasses, where physical properties depend on the waiting time between the starting time of observation and the time when the temperature is changed. The aging is classified into two types on the basis of the waiting time dependence of an instantaneous relaxation time: When the relaxation time is always an increasing function of the waiting time, the aging is called Type I and when it depends on the protocol of the temperature change, the aging is called Type II. Aging of a random walk in three dimensions is investigated when the free energy landscape controlling the jump rate responds to temperature change with a delay. It is shown that the intermediate scattering function of the random walk model exhibits Type II aging. It is also shown that the relaxation time of the free energy landscape can be deduced from the waiting time dependence of the instantaneous relaxation time.

Construction of Supramolecular Systems That Achieve Lifelike Functions

The Nobel Prize in Chemistry was awarded in 1987 and 2016 for research in supramolecular chemistry on the “development and use of molecules with structure-specific interactions of high selectivity” and the “design and production of molecular machines”, respectively. This confirmed the explosive development of supramolecular chemistry. In addition, attempts have been made in systems chemistry to embody the complex functions of living organisms as artificial non-equilibrium chemical systems, which have not received much attention in supramolecular chemistry. In this review, we explain recent developments in supramolecular chemistry through four categories: stimuli-responsiveness, time evolution, dissipative self-assembly, and hierarchical expression of functions. We discuss the development of non-equilibrium supramolecular systems, including the use of molecules with precisely designed properties, to achieve functions found in life as a hierarchical chemical system.

Large deviations and gradient flows

In recent work we uncovered intriguing connections between Otto's characterization of diffusion as an entropic gradient flow on the one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other. In this paper, we sketch this connection, show how it generalizes to a wider class of systems and comment on consequences and implications. Specifically, we connect macroscopic gradient flows with large-deviation principles, and point out the potential of a bigger picture emerging: we indicate that, in some non-equilibrium situations, entropies and thermodynamic free energies can be derived via large-deviation principles. The approach advocated here is different from the established hydrodynamic limit passage but extends a link that is well known in the equilibrium situation.

The cost of sensitive response and accurate adaptation in networks with an incoherent type-1 feed-forward loop

The incoherent type-1 feed-forward loop (I1-FFL) is ubiquitous in biological regulatory circuits. Although much is known about the functions of the I1-FFL motif, the energy cost incurred in the network and how it affects the performance of the network have not been investigated. Here, we study a generic I1-FFL enzymatic reaction network modelled after the GEF-GAP-Ras pathway responsible for chemosensory adaptation in eukaryotic cells. Our analysis shows that the I1-FFL network always operates out of equilibrium. Continuous energy dissipation is necessary to drive an internal phosphorylation-dephosphorylation cycle that is crucial in achieving strong short-time response and accurate long-time adaptation. In particular, we show quantitatively that the energy dissipated in the I1-FFL network is used (i) to increase the system's initial response to the input signals; (ii) to enhance the adaptation accuracy at steady state; and (iii) to expand the range of such accurate adaptation. Moreover, we find that the energy dissipation rate, the catalytic speed and the maximum adaptation accuracy in the I1-FFL network satisfy the same energy-speed-accuracy relationship as in the negative-feedback-loop (NFL) networks. Because the I1-FFL and NFL are the only two basic network motifs that enable accurate adaptation, our results suggest that a universal cost-performance trade-off principle may underlie all cellular adaptation processes independent of the detailed biochemical circuit architecture.

The energy-speed-accuracy tradeoff in sensory adaptation

Adaptation is the essential process by which an organism becomes better suited to its environment. The benefits of adaptation are well documented, but the cost it incurs remains poorly understood. Here, by analysing a stochastic model of a minimum feedback network underlying many sensory adaptation systems, we show that adaptive processes are necessarily dissipative, and continuous energy consumption is required to stabilize the adapted state. Our study reveals a general relation among energy dissipation rate, adaptation speed and the maximum adaptation accuracy. This energy-speed-accuracy relation is tested in the Escherichia coli chemosensory system, which exhibits near-perfect chemoreceptor adaptation. We identify key requirements for the underlying biochemical network to achieve accurate adaptation with a given energy budget. Moreover, direct measurements confirm the prediction that adaptation slows down as cells gradually de-energize in a nutrient-poor medium without compromising adaptation accuracy. Our work provides a general framework to study cost-performance tradeoffs for cellular regulatory functions and information processing.

Relationships between climate, productivity and vegetation in southern Mongolian drylands

We assessed the relationship between open-source data on net primary production and precipitation for the southern Mongolian Gobi, and related this information to data obtained from a set of 1418 vegetation relevés sampled in the region. Gradients determining plant community diversity and composition were examined, and the relation between α-diversity and key environmental parameters was tested.The correlation between net primary production and precipitation within our working area was fairly high (r(2) = 0.66). The variance of the net primary production was related to the average annual precipitation; at sites with more than ~220 mm/a precipitation the median coefficient of variation in productivity data decreased, indicating a rather gradual shift from a non-equilibrium ecosystem towards an equilibrium ecosystem with increasing moisture. A DCA-ordination showed that the main gradient in plant community composition was closely correlated to environmental variables for altitude, precipitation and net primary production. All three parameters were also significant predictors of the species diversity. The final model, which included an additional quadratic term for longitude, predicted local plant biodiversity at r(2) = 0.57.The results can be directly applied to both resource management and nature conservation within the area. For future studies a closer focus on the characterisation of non-equilibrium rangelands based on modelled productivity layers is suggested.