Retrieval of spatio-temporal sequence in asynchronous neural network

Multiple-Timescale Neural Networks: Generation of History-Dependent Sequences and Inference Through Autonomous Bifurcations

Sequential transitions between metastable states are ubiquitously observed in the neural system and underlying various cognitive functions such as perception and decision making. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. On the other hand, fine recurrent neural networks trained with supervised machine learning methods can generate complex non-Markov sequences, but these sequences are vulnerable against perturbations and such learning methods are biologically implausible. How stable and complex sequences are generated in the neural system still remains unclear. We have developed a neural network with fast and slow dynamics, which are inspired by the hierarchy of timescales on neural activities in the cortex. The slow dynamics store the history of inputs and outputs and affect the fast dynamics depending on the stored history. We show that the learning rule that requires only local information can form the network generating the complex and robust sequences in the fast dynamics. The slow dynamics work as bifurcation parameters for the fast one, wherein they stabilize the next pattern of the sequence before the current pattern is destabilized depending on the previous patterns. This co-existence period leads to the stable transition between the current and the next pattern in the non-Markov sequence. We further find that timescale balance is critical to the co-existence period. Our study provides a novel mechanism generating robust complex sequences with multiple timescales. Considering the multiple timescales are widely observed, the mechanism advances our understanding of temporal processing in the neural system.

Modelling the interplay between the CD4[Formula: see text]/CD8[Formula: see text] T-cell ratio and the expression of MHC-I in tumours

Describing the anti-tumour immune response as a series of cellular kinetic reactions from known immunological mechanisms, we create a mathematical model that shows the CD4[Formula: see text]/CD8[Formula: see text] T-cell ratio, T-cell infiltration and the expression of MHC-I to be interacting factors in tumour elimination. Methods from dynamical systems theory and non-equilibrium statistical mechanics are used to model the T-cell dependent anti-tumour immune response. Our model predicts a critical level of MHC-I expression which determines whether or not the tumour escapes the immune response. This critical level of MHC-I depends on the helper/cytotoxic T-cell ratio. However, our model also suggests that the immune system is robust against small changes in this ratio. We also find that T-cell infiltration and the specificity of the intra-tumour TCR repertoire will affect the critical MHC-I expression. Our work suggests that the functional form of the time evolution of MHC-I expression may explain the qualitative behaviour of tumour growth seen in patients.

Modeling disease progression in Multiple Myeloma with Hopfield networks and single-cell RNA-seq

Associative memories in Hopfield's neural networks are mapped to gene expression pattern to model different paths of disease progression towards Multiple Myeloma (MM). The model is built using single cell RNA-seq data from bone marrow aspirates of MM patients as well as patients diagnosed with Monoclonal Gammopathy of Undetermined Significance (MGUS) and Smoldering Multiple Myeloma (SMM), two medical conditions that often progress to full MM.

RESULTS

We identify different clusters of MGUS, SMM, and MM cells, map them to Hopfield associative memory patterns, and model the dynamics of transition between the different patterns. The model is then used to identify genes that are differentialy expressed across different MM stages and whose simultaneous inhibition is associated to a delayed disease progression.

Cell cycle time series gene expression data encoded as cyclic attractors in Hopfield systems

Modern time series gene expression and other omics data sets have enabled unprecedented resolution of the dynamics of cellular processes such as cell cycle and response to pharmaceutical compounds. In anticipation of the proliferation of time series data sets in the near future, we use the Hopfield model, a recurrent neural network based on spin glasses, to model the dynamics of cell cycle in HeLa (human cervical cancer) and S. cerevisiae cells. We study some of the rich dynamical properties of these cyclic Hopfield systems, including the ability of populations of simulated cells to recreate experimental expression data and the effects of noise on the dynamics. Next, we use a genetic algorithm to identify sets of genes which, when selectively inhibited by local external fields representing gene silencing compounds such as kinase inhibitors, disrupt the encoded cell cycle. We find, for example, that inhibiting the set of four kinases AURKB, NEK1, TTK, and WEE1 causes simulated HeLa cells to accumulate in the M phase. Finally, we suggest possible improvements and extensions to our model.

Cell cycle—the process in which a parent cell replicates its DNA and divides into two daughter cells—is an upregulated process in many forms of cancer. Identifying gene inhibition targets to regulate cell cycle is important to the development of effective therapies. Although modern high throughput techniques offer unprecedented resolution of the molecular details of biological processes like cell cycle, analyzing the vast quantities of the resulting experimental data and extracting actionable information remains a formidable task. Here, we create a dynamical model of the process of cell cycle using the Hopfield model (a type of recurrent neural network) and gene expression data from human cervical cancer cells and yeast cells. We find that the model recreates the oscillations observed in experimental data. Tuning the level of noise (representing the inherent randomness in gene expression and regulation) to the “edge of chaos” is crucial for the proper behavior of the system. We then use this model to identify potential gene targets for disrupting the process of cell cycle. This method could be applied to other time series data sets and used to predict the effects of untested targeted perturbations.

Multi-associative neural networks and their applications to learning and retrieving complex spatio-temporal sequences

Based on the previous work of a number of authors, we discuss an important class of neural networks which we call multi-associative neural networks (MANNs) and which associate one pattern with multiple patterns. As a computationally efficient example of such networks, we describe a specific MANN, that is, a multi-associative, dynamically generated variant of the counterpropagation network (MCPN). As an application of MANNs, we design a general system that can learn and retrieve complex spatio-temporal sequences with any MANN. This system consists of comparator units, a parallel array of MANNs, and delayed feedback lines from the output of the system to the neural network layer. During learning, pairs of sequences of spatial patterns are presented to the system and the system learns-to associate patterns at successive times in sequence. During retrieving, a cue sequence, which may be obscured by spatial noise and temporal gaps, causes the system to output the stored spatio-temporal sequence. We prove analytically that this system is capable of learning and generating any spatio-temporal sequences within the maximum complexity determined by the number of embedded MANNs, with the maximum length and number of sequences determined by the memory capacity of the embedded MANNs. To demonstrate the applicability of this general system, we present an implementation using the MCPN. The system shows desirable properties such as fast and accurate learning and retrieving, and ability to store a large number of complex sequences consisting of nonorthogonal spatial patterns.

Spatiotemporal learning in analog neural networks using spike-timing-dependent synaptic plasticity

Incorporating the spike-timing-dependent synaptic plasticity (STDP) into a learning rule, we study spatiotemporal learning in analog neural networks. First, we study learning of a finite number of periodic spatiotemporal patterns by deriving the dynamics of the order parameters. When a pattern is retrieved successfully, the order parameters exhibit periodic oscillation. Analyzing this oscillation of the order parameters, we elucidate the relation of the STDP time window to the properties of the retrieval state; the phase of the Fourier transform of the STDP time window determines the retrieval frequency and the time average of the STDP time window crucially affects the storage capacity. We also evaluate the stability of the order parameter oscillation and identify the retrieval state that is stable in single-pattern learning but unstable in multiple-pattern learning even when the retrieval state is independent of a pattern number. To examine the further applicability of the STDP-based learning rule, we also study learning of nonperiodic spatiotemporal Poisson patterns. Our numerical simulations demonstrate that the Poisson patterns are memorized successfully not only in analog neural networks but also in spiking neural networks.

Sequential associative memory with nonuniformity of the layer sizes

Sequence retrieval has a fundamental importance in information processing by the brain, and has extensively been studied in neural network models. Most of the previous sequential associative memory embedded sequences of memory patterns have nearly equal sizes. It was recently shown that local cortical networks display many diverse yet repeatable precise temporal sequences of neuronal activities, termed "neuronal avalanches." Interestingly, these avalanches displayed size and lifetime distributions that obey power laws. Inspired by these experimental findings, here we consider an associative memory model of binary neurons that stores sequences of memory patterns with highly variable sizes. Our analysis includes the case where the statistics of these size variations obey the above-mentioned power laws. We study the retrieval dynamics of such memory systems by analytically deriving the equations that govern the time evolution of macroscopic order parameters. We calculate the critical sequence length beyond which the network cannot retrieve memory sequences correctly. As an application of the analysis, we show how the present variability in sequential memory patterns degrades the power-law lifetime distribution of retrieved neural activities.

Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatiotemporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatiotemporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with function is reduced to the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision.