Towards Optimal Control of Amyloid Fibrillation.

Epigallocatechin-3-gallate, as a representative amyloid inhibitors, has shown a promising ability against A[Formula: see text] fibrillation by directly degradating the mature fibrils. Most previous studies have been focusing on its functional mechanisms, meanwhile its optimal dosage has been seldom considered. To solve this critical issue, we refer to the generalized Logistic model for amyloid fibrillation and inhibition and adopt the optimal control theory to balance the effectiveness and cost (or toxicity) of inhibitors. The optimal control trajectory of inhibitors is analytically solved, based on which the influence of model parameters, the difference between the optimal control strategy and several other traditional drug dosing strategies are systematically compared and validated through experiments. It is found that the strategy of multiple-times adding is more suitable for a long-term disease treatment, while single high-dose therapy is preferred for a short-term treatment. We hope our findings can shed light on the rational usage of amyloid inhibitors in clinic.

Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes.

The main purpose of this review is to summarize the recent advances of the Conservation-Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF's physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker-Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.

Rational evaluation of various epidemic models based on the COVID-19 data of China.

In this paper, based on the Akaike information criterion, root mean square error and robustness coefficient, a rational evaluation of various epidemic models/methods, including seven empirical functions, four statistical inference methods and five dynamical models, on their forecasting abilities is carried out. With respect to the outbreak data of COVID-19 epidemics in China, we find that before the inflection point, all models fail to make a reliable prediction. The Logistic function consistently underestimates the final epidemic size, while the Gompertz's function makes an overestimation in all cases. Towards statistical inference methods, the methods of sequential Bayesian and time-dependent reproduction number are more accurate at the late stage of an epidemic. And the transition-like behavior of exponential growth method from underestimation to overestimation with respect to the inflection point might be useful for constructing a more reliable forecast. Compared to ODE-based SIR, SEIR and SEIR-AHQ models, the SEIR-QD and SEIR-PO models generally show a better performance on studying the COVID-19 epidemics, whose success we believe could be attributed to a proper trade-off between model complexity and fitting accuracy. Our findings not only are crucial for the forecast of COVID-19 epidemics, but also may apply to other infectious diseases.

When machine learning meets multiscale modeling in chemical reactions.

Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face many difficulties. In this study, through two concrete examples with biological background, we illustrate how the key ideas of multiscale modeling can help to greatly reduce the computational cost of machine learning, as well as how machine learning algorithms perform model reduction automatically in a time-scale separated system. Our study highlights the necessity and effectiveness of an integration of machine learning algorithms and multiscale modeling during the study of chemical reactions.

Thermodynamics of Markov processes with nonextensive entropy and free energy.

Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a "thermodynamic" theory can also be developed based on Tsallis' generalized entropy S^{(q)}=∑_{i=1}^{N}(p_{i}-p_{i}^{q})/[q(q-1)] and Shiino's generalized free energy F^{(q)}=[∑_{i=1}^{N}p_{i}(p_{i}/π_{i})^{q-1}-1]/[q(q-1)], where π_{i} is the stationary distribution. dF^{(q)}/dt=-f_{d}^{(q)}≤0 and it is zero if and only if the system is in its stationary state. dS^{(q)}/dt-Q_{ex}^{(q)}=f_{d}^{(q)}, where Q_{ex}^{(q)} characterizes the heat exchange. For systems approaching equilibrium with detailed balance, f_{d}^{(q)} is the product of Onsager's thermodynamic flux and force. However, it is discovered that the Onsager's force is nonlocal. This is a consequence of the particular transformation invariance for zero energy of Tsallis' statistics.

Conservation-Dissipation Formalism for soft matter physics: I. Augmentation to Doi's variational approach.

In the first paper of this series, we prove that by choosing the proper variational function and variables, the variational approach proposed by Doi in soft matter physics is equivalent to the Conservation-Dissipation Formalism. To illustrate the correspondence between these two theories, several novel examples in soft matter physics, including the particle diffusion in dilute solutions, polymer phase separation dynamics and nematic liquid crystal flows, are carefully examined. Based on our work, a deep connection among the generalized Gibbs relation, the second law of thermodynamics and the variational principle in non-equilibrium thermodynamics is revealed.

Conservation-Dissipation Formalism for soft matter physics: II. Application to non-isothermal nematic liquid crystals.

For most existing non-equilibrium theories, the modeling of non-isothermal processes is a hard task. Intrinsic difficulties involve the non-equilibrium temperature, the coexistence of conserved energy and dissipative entropy, etc. In this paper, by taking the non-isothermal flow of nematic liquid crystals as a typical example, we illustrate that thermodynamically consistent models in either vectorial or tensorial forms can be constructed within the framework of the Conservation-Dissipation Formalism (CDF). And the classical isothermal Ericksen-Leslie model and Qian-Sheng model are shown to be special cases of our new vectorial and tensorial models in the isothermal, incompressible and stationary limit. Most importantly, from the above examples, it is known that CDF can easily solve the issues relating with non-isothermal situations in a systematic way. The first and second laws of thermodynamics are satisfied simultaneously. The non-equilibrium temperature is defined self-consistently as a partial derivative of the entropy function. Relaxation-type constitutive relations are constructed, which give rise to classical linear constitutive relations, like Newton's law and Fourier's law, in stationary limits. Therefore, CDF is expected to have a broad scope of applications in soft matter physics, especially under complicated situations, such as non-isothermal, compressible and nanoscale systems.

Generalized Onsager's reciprocal relations for the master and Fokker-Planck equations.

The Onsager's reciprocal relation plays a fundamental role in the nonequilibrium thermodynamics. However, unfortunately, its classical version is valid only within a narrow region near equilibrium due to the linear regression hypothesis, which largely restricts its usage. In this paper, based on the conservation-dissipation formalism, a generalized version of Onsager's relations for the master equations and Fokker-Planck equations was derived. Nonlinear constitutive relations with nonsymmetric and positively stable operators, which become symmetric under the detailed balance condition, constitute key features of this new generalization. Similar conclusions also hold for many other classical models in physics and chemistry, which in turn make the current study as a benchmark for the application of generalized Onsager's relations in nonequilibrium thermodynamics.