Spiking neural networks (SNNs) possess energy-efficient potential due to event-based computation. However, supervised training of SNNs remains a challenge as spike activities are non-differentiable. ...Previous SNNs training methods can be generally categorized into two basic classes, i.e., backpropagation-like training methods and plasticity-based learning methods. The former methods are dependent on energy-inefficient real-valued computation and non-local transmission, as also required in artificial neural networks (ANNs), whereas the latter are either considered to be biologically implausible or exhibit poor performance. Hence, biologically plausible (bio-plausible) high-performance supervised learning (SL) methods for SNNs remain deficient. In this paper, we proposed a novel bio-plausible SNN model for SL based on the symmetric spike-timing dependent plasticity (sym-STDP) rule found in neuroscience. By combining the sym-STDP rule with bio-plausible synaptic scaling and intrinsic plasticity of the dynamic threshold, our SNN model implemented SL well and achieved good performance in the benchmark recognition task (MNIST dataset). To reveal the underlying mechanism of our SL model, we visualized both layer-based activities and synaptic weights using the t-distributed stochastic neighbor embedding (t-SNE) method after training and found that they were well clustered, thereby demonstrating excellent classification ability. Furthermore, to verify the robustness of our model, we trained it on another more realistic dataset (Fashion-MNIST), which also showed good performance. As the learning rules were bio-plausible and based purely on local spike events, our model could be easily applied to neuromorphic hardware for online training and may be helpful for understanding SL information processing at the synaptic level in biological neural systems.
Ice nucleation on the surface plays a vital role in diverse areas, ranging from physics and cryobiology to atmospheric science. Compared to ice nucleation in the bulk, the water-surface interactions ...present in heterogeneous ice nucleation complicate the nucleation process, making heterogeneous ice nucleation less comprehended, especially the relationship between the kinetics and the structures of the critical ice nucleus. Here we combine Markov State Models and transition path theory to elucidate the ensemble pathways of heterogeneous ice nucleation. Our Markov State Models reveal that the classical one-step and non-classical two-step nucleation pathways can surprisingly co-exist with comparable fluxes at T = 230 K. Interestingly, we find that the disordered mixing of rhombic and hexagonal ice leads to a favorable configurational entropy that stabilizes the critical nucleus, facilitating the non-classical pathway. In contrast, the favorable energetics promotes the formation of hexagonal ice, resulting in the classical pathway. Furthermore, we discover that, at elevated temperatures, the nucleation process prefers to proceed via the classical pathway, as opposed to the non-classical pathway, since the potential energy contributions override the configurational entropy compensation. This study provides insights into the mechanisms of heterogeneous ice nucleation and sheds light on the rational designs to control crystallization processes.
Speech recognition (SR) has been improved significantly by artificial neural networks (ANNs), but ANNs have the drawbacks of biologically implausibility and excessive power consumption because of the ...nonlocal transfer of real-valued errors and weights. While spiking neural networks (SNNs) have the potential to solve these drawbacks of ANNs due to their efficient spike communication and their natural way to utilize kinds of synaptic plasticity rules found in brain for weight modification. However, existing SNN models for SR either had bad performance, or were trained in biologically implausible ways. In this paper, we present a biologically inspired convolutional SNN model for SR. The network adopts the time-to-first-spike coding scheme for fast and efficient information processing. A biological learning rule, spike-timing-dependent plasticity (STDP), is used to adjust the synaptic weights of convolutional neurons to form receptive fields in an unsupervised way. In the convolutional structure, the strategy of local weight sharing is introduced and could lead to better feature extraction of speech signals than global weight sharing. We first evaluated the SNN model with a linear support vector machine (SVM) on the TIDIGITS dataset and it got the performance of 97.5%, comparable to the best results of ANNs. Deep analysis on network outputs showed that, not only are the output data more linearly separable, but they also have fewer dimensions and become sparse. To further confirm the validity of our model, we trained it on a more difficult recognition task based on the TIMIT dataset, and it got a high performance of 93.8%. Moreover, a linear spike-based classifier-tempotron-can also achieve high accuracies very close to that of SVM on both the two tasks. These demonstrate that an STDP-based convolutional SNN model equipped with local weight sharing and temporal coding is capable of solving the SR task accurately and efficiently.
The spiking neural network (SNN), as a promising brain-inspired computational model with binary spike information transmission mechanism, rich spatially-temporal dynamics, and event-driven ...characteristics, has received extensive attention. However, its intricately discontinuous spike mechanism brings difficulty to the optimization of the deep SNN. Since the surrogate gradient method can greatly mitigate the optimization difficulty and shows great potential in directly training deep SNNs, a variety of direct learning-based deep SNN works have been proposed and achieved satisfying progress in recent years. In this paper, we present a comprehensive survey of these direct learning-based deep SNN works, mainly categorized into accuracy improvement methods, efficiency improvement methods, and temporal dynamics utilization methods. In addition, we also divide these categorizations into finer granularities further to better organize and introduce them. Finally, the challenges and trends that may be faced in future research are prospected.
The function of complex biomolecular machines relies heavily on their conformational changes. Investigating these functional conformational changes is therefore essential for understanding the ...corresponding biological processes and promoting bioengineering applications and rational drug design. Constructing Markov State Models (MSMs) based on large‐scale molecular dynamics simulations has emerged as a powerful approach to model functional conformational changes of the biomolecular system with sufficient resolution in both time and space. However, the rapid development of theory and algorithms for constructing MSMs has made it difficult for nonexperts to understand and apply the MSM framework, necessitating a comprehensive guidance toward its theory and practical usage. In this study, we introduce the MSM theory of conformational dynamics based on the projection operator scheme. We further propose a general protocol of constructing MSM to investigate functional conformational changes, which integrates the state‐of‐the‐art techniques for building and optimizing initial pathways, performing adaptive sampling and constructing MSMs. We anticipate this protocol to be widely applied and useful in guiding nonexperts to study the functional conformational changes of large biomolecular systems via the MSM framework. We also discuss the current limitations of MSMs and some alternative methods to alleviate them. WIREs Comput Mol Sci 2018, 8:e1343. doi: 10.1002/wcms.1343
This article is categorized under:
Structure and Mechanism > Computational Biochemistry and Biophysics
Theoretical and Physical Chemistry > Statistical Mechanics
A protocol for constructing Markov State Models to study the functional conformational changes of biomolecular systems.
The generalized master equation (GME) provides a powerful approach to study biomolecular dynamics via non-Markovian dynamic models built from molecular dynamics (MD) simulations. Previously, we have ...implemented the GME, namely the quasi Markov State Model (qMSM), where we explicitly calculate the memory kernel and propagate dynamics using a discretized GME. qMSM can be constructed with much shorter MD trajectories than the MSM. However, since qMSM needs to explicitly compute the time-dependent memory kernels, it is heavily affected by the numerical fluctuations of simulation data when applied to study biomolecular conformational changes. This can lead to numerical instability of predicted long-time dynamics, greatly limiting the applicability of qMSM in complicated biomolecules. We present a new method, the Integrative GME (IGME), in which we analytically solve the GME under the condition when the memory kernels have decayed to zero. Our IGME overcomes the challenges of the qMSM by using the time integrations of memory kernels, thereby avoiding the numerical instability caused by explicit computation of time-dependent memory kernels. Using our solutions of the GME, we have developed a new approach to compute long-time dynamics based on MD simulations in a numerically stable, accurate and efficient way. To demonstrate its effectiveness, we have applied the IGME in three biomolecules: the alanine dipeptide, FIP35 WW-domain, and Taq RNA polymerase. In each system, the IGME achieves significantly smaller fluctuations for both memory kernels and long-time dynamics compared to the qMSM. We anticipate that the IGME can be widely applied to investigate biomolecular conformational changes.
•Shadow price of CO2 emissions for China's coal-fired power plants is estimated.•We introduce the quantile regression (QR) for perturbations and outliers. The average shadow price by the QR is lower. ...The spatial distribution is reported.
Estimating the shadow price of carbon dioxide (CO2) emissions is the key to understanding the cost of low-carbon transition for China. This study estimates the shadow price of CO2 emissions for China's coal-fired power plants over the period 2005 to 2010 by applying a conventional approach introduced by Färe et al. (2012), which combines quadratic directional distance function (DDF) with the stochastic frontier analysis (SFA). We further extend the model by introducing the quantile regression (QR) method, which is more robust to perturbations and outliers. We also compare the estimated shadow price from QR with the prices obtained from the ordinary least square (OLS) regression and standard SFA. The estimated average shadow price of CO2 emissions is 10,442.70 Yuan/ton and 10,231.97 Yuan/ton for the OLS regression and SFA, respectively. The average shadow price of CO2 emissions estimated by the QR is lower: 9623.95 Yuan/ton at the 50th percentile, 9304.21 Yuan/ton at the 56th percentile, 9588.74 Yuan/ton at the 80th percentile, and 9565.11 Yuan/ton at the 95th percentile. Finally, the spatial distribution of estimated shadow prices is reported. The results show that coastal provinces and municipalities have higher shadow prices of CO2 emissions.
A small‐molecular acceptor, tetraphenylpyrazine‐perylenediimide tetramer (TPPz‐PDI4), which has a reduced extent of intramolecular twisting compared to two other small‐molecular acceptors is ...designed. Benefiting from the lowest extent of intramolecular twisting, TPPz‐PDI4 exhibits the highest aggregation tendency and electron mobility, and therefore achieves a highest power conversion efficiency of 7.1%.
Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale ...dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called "lag time"). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5-10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.
•We introduce a state-of-the-art protocol to build the MSM.•We recommend spectral oASIS to automatically select physical features.•We review applications of MSM on studying protein functional ...conformational changes.•We discuss the perspective of quasi-MSM and deep learning methods for MSM.
Functional conformational changes of proteins can facilitate numerous biological events in cells. The Markov state model (MSM) built from molecular dynamics simulations provide a powerful approach to study them. We here introduce a protocol that is tailor-made for constructing MSMs to study the functional conformational changes of proteins. In this protocol, one of the important steps is to select proper molecular features that can collectively describe the slowest timescales of conformational changes of interest. We recommend spectral oASIS, the modified version of oASIS, as a promising approach for automatic feature selection. Recently developed deep learning methods could also serve efficient approaches for selecting features and finding collective variables. Using DNA repair enzymes and RNA polymerases as examples, we review recent applications of MSMs to elucidate molecular mechanisms of functional conformational changes. Finally, we discuss remaining challenges and future perspectives for constructing MSMs to study functional conformational changes of proteins.
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