Project Description

Home / Members / Faculty / Lyle Muller


  • Computational/ Theoretical Neuroscience

  • Neural Networks

  • Network Dynamics



Assistant Professor,
Department of Mathematics, Western University

Lyle Muller’s research spans computational/theoretical neuroscience, neural networks, and applied mathematics. After studying computational neuroscience at Brown University, Dr. Muller completed a PhD in computational/theoretical neuroscience with Alain Destexhe (CNRS Gif-sur-Yvette). He then moved to San Diego for postdoctoral research with Terry Sejnowski in the Computational Neurobiology Laboratory (CNL) at the Salk Institute for Biological Studies.

Dr. Muller’s research employs advanced signal processing, computational modeling, and graph theory to understand the spatiotemporal structure of neural activity. In this research, Dr. Muller has introduced a fundamentally new signal processing technique for analyzing spatiotemporal dynamics in large-scale multisite recordings. This technique has revealed fundamentally new features of cortical activity, from stimulus-evoked traveling waves in primary visual cortex of the awake monkey, to global rotating waves associated with learning and memory during human sleep, and even in the absence of sensory input.

These results have appeared in Nature, Nature Communications, and eLife, and they have shaped our fundamental understanding of the structure in cortical activity during wake and sleep. Dr. Muller’s research team at Western is currently developing new mathematical approaches to understand how these spatiotemporal dynamics shape computations in cortical circuits.

My research program develops new algorithms, neural networks, and applied mathematics to understand the complex spatiotemporal dynamics of cortical circuits. Over the past few years, I have built a strong independent research program in computational/theoretical neuroscience at Western, and I believe this could be an outstanding addition to the strength in bringing together neuroscience and philosophy at Rotman.

My central research focus is developing new algorithms for understanding neural data. In this work, I have introduced new computational techniques for understanding the moment-by-moment spatiotemporal dynamics of cortex. These tools are important, because instead of averaging over trials or windows of time, we can now look at the dynamics of neural systems with millisecond precision to understand how perceptual, cognitive, and motor behaviours occur on the fly.

Applying these algorithms has led to several fundamental discoveries during my research career. By studying optical imaging data in primary visual cortex (V1) of the awake monkey, we discovered that small visual stimuli evoke waves traveling outward from the point of input to the cortex (Muller et al., Nature Communications, 2014). These waves were previously obscured by trial-averaging, and they are an important finding because they show that a local population influences networks far across V1 in a highly structured manner. This in turn has important consequences for theories of sensory processing, and we have introduced a framework for thinking about computational roles for these waves in recent work (Muller et al., Nature Reviews Neuroscience, 2018).

In my postdoctoral research with Terry Sejnowski (Salk Institute), I adapted these techniques to study sleep rhythms in intracranial recordings from human clinical patients. With these methods, we discovered that the 11-15 Hz sleep “spindle” rhythm is organized into a global wave rotating across the whole cortex during sleep (Muller et al., eLife, 2016). These waves rotate in a preferred direction (from temporal, to parietal, to frontal lobe, and back again), and are likely mediated by the long-range white matter fibres in cortex. Because the sleep spindle has previously been causally implicated in consolidation of memories from hippocampus to the neocortex, we have good reason to believe that this spatiotemporal pattern may be the way cortical networks communicate over long distances to link information across distant cortical areas into a whole, coherent memory.

More recently, we have extended our computational techniques to analyze complex, non-narrowband fluctuations of activity in the moments before stimulus onset, and we have found that spontaneous activity is structured into waves traveling across visual cortex (Davis*, Muller*, et al., Nature, 2020). In this work, we found that these waves modulate the instantaneous state of networks in visual cortex. Further, depending on alignment of these traveling waves with incoming sensory input, they can influence both the magnitude of sensory-evoked activity and the probability that an animal will detect faint visual stimuli. These results have revealed an important role for spontaneous traveling waves in sensory processing through modulating neural and perceptual sensitivity. We are currently seeking to reveal the network-level mechanisms of these waves in computational studies of spiking neural networks (Davis*, Benigno*, et al., Muller, Nature Communications, 2021). Finally, we are also developing a new mathematical techniques to link the structure of individual networks to the resulting nonlinear dynamics. This is, in general, a very difficult problem when the dynamics of individual nodes in a network are nonlinear; however, I recently developed a new approach that enables making this link in networks of nonlinear oscillators (Muller et al., Physical Review E, 2021), which have been important in studying neural population dynamics. This approach has not only allowed us to make specific theoretical predictions for phenomena in nonlinear dynamics (Budzinski*, Nguyen*, et al., Muller, Chaos, 2022; Nguyen, et al., Muller, SIAM Applied Dynamical Systems, 2023), but it has also led to novel real-world applications, allowing us to build new neural network models that provide insight into short-term predictions in the visual system (Benigno, et al., Muller, Nature Communications, 2023).

Davis ZD*, Muller L*, Martinez-Trujillo J, Sejnowski TJ, Reynolds J (2020) Spontaneous traveling cortical waves gate perception in awake behaving primates. Nature 587: 432 –436. (*Equal contribution)

Sullivan et al. (2021) New frontiers in translational research: Touchscreens, open science,and the mouse translational research accelerator platform. Genes, Brain and Behavior 20:e12705.

Muller L, Mináč J, Nguyen T (2021) An algebraic approach to the Kuramoto model. Physical Review E 104: L022201.

Davis Z*, Benigno G*, Fletterman C*, Desbordes T, Sejnowski TJ, Reynolds J, Muller L(2021) Spontaneous traveling waves naturally emerge from horizontal fiber time delays andtravel through locally asynchronous-irregular states. Nature Communications 12: 6057. (*Equal contribution)

Budzinski RC*, Nguyen TT*, Doan J, Mináč J, Sejnowski TJ, Muller L (2022) Geometryunites synchrony, chimeras, and waves in nonlinear oscillator networks. Chaos Fast Track 32: 031104.

Doan J, Mináč J, Muller L, Nguyen TT, Pasini F (2022) Joins of circulant matrices. Linear Algebra and its Applications 650: 190 – 209. (‡Alphabetical order, following conventions in pure mathematics)

Davis ZD, Muller L, Reynolds J (2022) Spontaneous Spiking Is Governed By Broadband Fluctuations. J Neurosci 42: 5159 – 5172.

Mofrad M, Gilmore G, Mirsattari SM, Burneo JG, Steven DA, Khan A, Suller Marti A, Muller L (2022) Waveform detection by deep learning reveals multi-area spindles that are selectively modulated by memory load. eLife 11: e75769.

Ichiyama A, Mestern S, Benigno GB, Scott K, Allman B, Muller L†, Inoue W† (2022) Statedependent activity dynamics of hypothalamic stress effector neurons. eLife 11: e76832. (†Co-senior authorship)

Mok RSF, Zhang W,Sheikh TI, Pradeepan K, Fernandes IR, DeJong LC, Benigno G, Hildebrandt MR, Mufteev M, Rodrigues DC, Wei W, Piekna A, Liu J, Muotri AR, Vincent JB, Muller L, Martinez-Trujillo JM, Salter MW, Ellis J (2022) Wide phenotypic spectrum of human stem cell-derived excitatory neurons with Rett syndrome-associated MECP2 mutations. Translational Psychiatry, in press.

Nguyen TT, Budzinski RC, Doan J, Mináč J, Muller L (2023) Equilibria in Kuramoto oscillator networks: an algebraic approach. SIAM Applied Dynamical Systems 22: 802-824.

Davis ZW, Dotson NM, Franken T, Muller L†, Reynolds J† (2023) Spike-phase coupling patterns reveal laminar identity in primate cortex. eLife 12: e84512. (†Co-senior authorship)

Benigno G, Budzinski RB, Davis Z, Reynolds J, Muller L (2023) Waves traveling over a map of visual space can ignite short-term predictions of sensory input. Nature Communications 14: 3409.

Pasini F*, Busch A*, Mináč J, Padmanabhan K, Muller L (2023) An algebraic approach to spike-time neural codes in the hippocampus. Physical Review E, in press.

Muller L, Churchland P, Sejnowski TJ (2023) Transformers and cortical waves: encoders for pulling in temporal contextual information. Trends in Neurosciences, invited perspective.