Yangyang Wang – Tenure Dossier

Main Documents

• Curriculum Vitae (PDF)
• Personal Statement (PDF) (covering research, teaching, and service)

Teaching

Brandeis University

List of instructional activities at Brandeis University

The University of Iowa (2019–2022)

The Ohio State University (2017–2019)

Publications

1. X. Lin, F. Antoneli and Y. Wang, “Automated Classification of Homeostasis Structure in Input-Output Networks,” Submitted, 2026. [PDF]
   Abstract

   Homeostasis is widely observed in biological systems and refers to their ability to maintain an output quantity approximately constant despite variations in external disturbances. Mathematically, homeostasis can be formulated through an input-output function mapping an external parameter to an output variable. Infinitesimal homeostasis occurs at isolated points where the derivative of this input-output function vanishes, allowing tools from singularity theory and combinatorial matrix theory to characterize and classify homeostatic mechanisms in terms of network topology. Although the theoretical framework allows homeostasis subnetworks to be identified directly from combinatorial structures of the input-output network without numerical simulation, the required combinatorial enumeration becomes increasingly intractable as network size grows. Moreover, the reliance on advanced graph-theoretic concepts limits its broader accessibility and practical use across disciplines, particularly in biological applications. To overcome these limitations, we develop a Python-based algorithm that automates the identification of homeostasis subnetworks and their associated homeostasis conditions directly from network topology. Given an input-output network specified solely by its connectivity structure and the designation of input and output nodes, the algorithm automatically identifies the relevant graph-theoretical structures and enumerates all homeostatic mechanisms. We demonstrate the applicability of the algorithm across a range of biological examples, including small and large networks, networks with a single input parameter (with single or multiple input nodes), multiple input parameters, and cases where input and output coincide. This wide applicability stems from our extension of the theoretical framework from single-input-single-output networks to networks with multiple input nodes through an augmented single-input-node representation. The resulting computational framework provides a scalable and systematic approach to classifying homeostatic mechanisms in complex biological networks, facilitating the application of advanced mathematical theory to a broad range of biological systems.

2. C. Wei, Y. Wang and X. Zhu, “Robust Parameter and State Estimation in Multiscale Neuronal Systems Using Physics-Informed Neural Networks,” Submitted, 2026. [PDF]
   Abstract

   Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast-slow spiking and bursting models, where strong nonlinearities, multiscale dynamics, and limited observational data often lead to severe sensitivity to initial parameter guesses and convergence failure in methods relying on traditional numerical forward solvers. In this work, we developed a physics-informed neural network (PINN) framework for the joint reconstruction of unobserved state variables and the estimation of unknown biophysical parameters in neuronal models. We demonstrate the effectiveness of the method on biophysical neuron models, including the Morris-Lecar model across multiple spiking and bursting regimes and a respiratory model neuron. The method requires only partial voltage observations over short observation windows and remains robust even when initialized with non-informative parameter guesses. These results suggest that PINN can deliver robust and accurate parameter inference and state reconstruction, providing a promising alternative for inverse problems in multiscale neuronal dynamics, where traditional techniques often struggle.

3. A.K. Tryba, J.C. Viemari, Y. Wang and A.J. Garcia III, “Noradrenergic neuromodulation produces a NMDAR-dependent network state of respiratory rhythmogenesis in the preBötzinger Complex,” Submitted, 2026. [PDF]
   Abstract

   Norepinephrine (NE) is an important mediator of sympathetic activity that influences breathing. At the level of the inspiratory neural network, the preBötzinger complex (preBötC), NE modulation orchestrates changes in neuronal network dynamics that influence the stability of inspiratory rhythmogenesis. While this phenomenon has largely been attributed to NE-modulation of intrinsic excitability of inspiratory preBötC neurons, NE is also capable of modulating synaptic drive. Here, we resolve how NE affects synaptic properties and changes the activity dynamics of interconnected preBötC neurons in rhythmic brainstem slice preparations. Increased network burst amplitude and frequency coincided with enhanced inspiratory drive currents at the single neuron level. This increased drive was blocked by the NMDA receptor (NMDAR) antagonist, APV. Our in silico modeling indicated that synaptic calcium entry via NMDAR is key to maintaining network synchrony during this elevated state of excitability. This was consistent with our multi-electrode array studies revealing that NE-dependent NMDAR activity enhances and preserves synchrony during inspiratory network bursts. This synaptic mechanism may be a critical determinant for shaping inspiratory drive associated with changed neuromodulatory environments.

4. Y. Wang and B.R. Pittman-Polletta, “Dynamical mechanisms of flexible phase-locking in cortical theta oscillators,” Submitted, 2026. [PDF]
   Abstract

   Oscillatory activity in auditory cortex is thought to play a central role in auditory and speech processing by synchronizing neural rhythms to external acoustic features of the speech stream. To support this function, cortical oscillators must flexibly phase-lock to inputs spanning a wide range of timescales, including rhythms substantially slower than their intrinsic frequency. Here we identify a general dynamical mechanism by which intrinsic inhibitory currents operating on multiple timescales enable such flexible phase-locking. Using tools from dynamical systems theory, including geometric singular perturbation theory and bifurcation analysis, we show that interactions between slow and superslow inhibitory processes generate prolonged post-input recovery delays through delayed Hopf phenomena, thereby substantially expanding the frequency range over which entrainment can occur. We demonstrate this mechanism in a biophysically grounded cortical theta oscillator model for speech segmentation. Specifically, we show that both a theta-timescale (4–8 Hz) inhibitory current I_m and a slower delta-timescale (1–4 Hz) inhibitory potassium current I_KSS are crucial for entrainment flexibility. Their interaction creates a three-timescale structure that gives rise to pronounced delay phenomena associated with a delayed Hopf bifurcation (DHB). Interestingly, the superslow I_KSS and the associated DHB play little role in the unforced oscillatory dynamics, but are recruited to support phase locking under external forcing. Moreover, the intermediate-timescale current I_m, rather than being redundant, further expands the phase-locking range by prolonging delayed recovery along the superslow manifold. Together, these results suggest that coordination among intrinsic inhibitory currents operating on multiple timescales may represent a key mechanism supporting flexible phase locking to rhythmic inputs in the brain.

5. S. Venkatakrishnan, A.K. Tryba, A.J. Garcia III and Y. Wang, “Dual mechanisms for heterogeneous responses of inspiratory neurons to noradrenergic modulation,” SIAM Journal on Life Sciences, 1(1), 58–98 (2026). [PDF]
   Abstract

   Respiration is an essential involuntary function necessary for survival. This poses a challenge for the control of breathing. The pre-Bötzinger complex (preBötC) is a heterogeneous neuronal network responsible for driving the inspiratory rhythm. While neuromodulators such as norepinephrine (NE) allow it to be both robust and flexible for all living beings to interact with their environment, the basis for how neuromodulation impacts neuron-specific properties remains poorly understood. In this work, we examine how NE influences different preBötC neuronal subtypes by modeling its effects through modulating two key parameters: calcium-activated nonspecific cationic current gating conductance (g_CAN) and inositol-triphosphate (IP3), guided by experimental studies. Our computational model captures the experimentally observed differential effects of NE on distinct preBötC bursting patterns. We show that this dual-modulation mechanism is critical for inducing conditional bursting and identify specific parameter regimes where silent neurons remain inactive in the presence of NE. Furthermore, using methods from dynamical systems theory, we uncover the mechanisms by which NE differentially modulates burst frequency and duration in NaP-dependent and CAN-dependent bursting neurons. These results align well with previously reported experimental findings and provide a deeper understanding of cell-specific neuromodulatory responses within the respiratory network.

6. H. Mofidi and Y. Wang, “Studying synchronization of neural oscillators through NMDA-AMPA receptor interactions,” Chaos, Solitons & Fractals, 202, 117479 (2026). [PDF]
   Abstract

   This study investigates how NMDA and AMPA receptors influence synchronization in neural oscillators modeled by coupled Morris-Lecar systems. By analyzing the interplay between receptor kinetics, synaptic coupling strengths, and voltage-dependent magnesium block, we identify the mechanisms that govern neural synchronization. We show that fast AMPAR kinetics yield perfect synchrony at substantially lower coupling than NMDARs, which produce only near-synchrony even when Mg²⁺ block is absent. To resolve subtle regimes, we pair a time-domain mean phase difference (MPD) with the phase-locking value (PLV) and overlay bifurcation continuations (LP/HB/PD), exposing boundaries that PLV alone can miss. Although NMDARs sustain prolonged conductance, their slow decay and Mg²⁺ dependence blur spike timing and limit precise locking. These results provide a quantitative, mechanism-based account of glutamatergic control of synchrony and suggest experimentally testable predictions relevant to coordination deficits in disorders such as schizophrenia.

7. P. Gandhi and Y. Wang, “A conceptual framework for modeling a latching mechanism for cell cycle regulation,” Mathematical Biosciences, 109396 (2025). [PDF]
   Abstract

   Two identical van der Pol oscillators with mutual inhibition are considered as a conceptual framework for modeling a latching mechanism for cell cycle regulation. In particular, the oscillators are biased to a latched state in which there is a globally attracting steady-state equilibrium without coupling. The inhibitory coupling induces stable alternating large-amplitude oscillations that model the normal cell cycle. A homoclinic bifurcation within the model is found to be responsible for the transition from normal cell cycling to endocycles in which only one of the two oscillators undergoes large-amplitude oscillations.

8. Z. Yu, Y. Wang, P.J. Thomas and H.J. Chiel, “Tradeoffs in the Energetic Value of Neuromodulation in a Closed-Loop Neuromechanical System,” Journal of Theoretical Biology, 604, 112050 (2025). [PDF]
   Abstract

   Rhythmic motor behaviors controlled by neuromechanical systems, consisting of central neural circuitry, biomechanics, and sensory feedback, show efficiency in energy expenditure. The biomechanical elements (e.g., muscles) are modulated by peripheral neuromodulation which may improve their strength and speed properties. However, there are relatively few studies on neuromodulatory control of muscle function and metabolic mechanical efficiency in neuromechanical systems. To investigate the role of neuromodulation on the system's mechanical efficiency, we consider a neuromuscular model of motor patterns for feeding in the marine mollusk Aplysia californica. By incorporating muscle energetics and neuromodulatory effects into the model, we demonstrate tradeoffs in the energy efficiency of Aplysia's rhythmic swallowing behavior as a function of the level of neuromodulation. A robust efficiency optimum arises from an intermediate level of neuromodulation, and excessive neuromodulation may be inefficient and disadvantageous to an animal's metabolism.

9. N.A. Phan and Y. Wang, “Mixed-Mode Oscillations in a Three-Timescale Coupled Morris-Lecar System,” Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(5), 053119 (2024). Editor's Pick [PDF]
   Abstract

   Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov-Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris-Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

10. Y. Wang, J.P. Gill, H.J. Chiel and P.J. Thomas, “Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems,” Biological Cybernetics, 116, 687–710 (2022). [PDF]
    Abstract

    Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al. in J Comput Neurosci 38(1):25–51, 2015; Lyttle et al. in Biol Cybern 111(1):25–47, 2017). We established in (Wang et al. in SIAM J Appl Dyn Syst 20(2):701–744, 2021) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates’ hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties.

11. Y. Wang, Z. Huang, F. Antoneli and M. Golubitsky, “The Structure of Infinitesimal Homeostasis in Input-Output Networks,” Journal of Mathematical Biology, 82(7), 1–43 (2021). [PDF]
    Abstract

    Homeostasis refers to a phenomenon whereby the output x_o of a system is approximately constant on variation of an input I. Homeostasis occurs frequently in biochemical networks and in other networks of interacting elements where mathematical models are based on differential equations associated to the network. These networks can be abstracted as digraphs G with a distinguished input node ι, a different distinguished output node o, and a number of regulatory nodes ρ₁, …, ρ_n. In these models the input-output map x_o(I) is defined by a stable equilibrium X₀ at I₀. Stability implies that there is a stable equilibrium X(I) for each I near I₀ and infinitesimal homeostasis occurs at I₀ when (dx_o/dI)(I₀) = 0. We show that there is an (n+1) × (n+1) homeostasis matrix H(I) for which dx_o/dI = 0 if and only if det(H) = 0. We note that the entries in H are linearized couplings and det(H) is a homogeneous polynomial of degree n+1 in these entries. We use combinatorial matrix theory to factor the polynomial det(H) and thereby determine a menu of different types of possible homeostasis associated with each digraph G. Specifically, we prove that each factor corresponds to a subnetwork of G. The factors divide into two combinatorially defined classes: structural and appendage. Structural factors correspond to feedforward motifs and appendage factors correspond to feedback motifs. Finally, we discover an algorithm for determining the homeostasis subnetwork motif corresponding to each factor of det(H) without performing numerical simulations on model equations. The algorithm allows us to classify low degree factors of det(H). There are two types of degree 1 homeostasis (negative feedback loops and kinetic or Haldane motifs) and there are two types of degree 2 homeostasis (feedforward loops and a degree two appendage motif).

12. Y. Wang, J.P. Gill, H.J. Chiel and P.J. Thomas, “Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbation,” SIAM Journal on Applied Dynamical Systems, 20(2), 701–744 (2021). [Manuscript] [Supplement]
    Abstract

    When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface. Examples include heel-ground interaction in locomotion, firing rate rectification in neural networks, and stick-slip oscillators. In many rhythmic systems, robustness against external perturbations involves response of both the shape and the timing of the limit cycle trajectory. The existing methods of infinitesimal phase response curve (iPRC) and variational analysis are well established for quantifying changes in timing and shape, respectively, for smooth systems. These tools have recently been extended to nonsmooth dynamics with transversal crossing boundaries. In this work, we further extend the iPRC method to nonsmooth systems with sliding components, which enables us to make predictions about the synchronization properties of weakly coupled stick-slip oscillators. We observe a new feature of the isochrons in a planar limit cycle with hard sliding boundaries: a nonsmooth kink in the asymptotic phase function, originating from the point at which the limit cycle smoothly departs the constraint surface and propagating away from the hard boundary into the interior of the domain. Moreover, the classical variational analysis neglects timing information and is restricted to instantaneous perturbations. By defining the “infinitesimal shape response curve” (iSRC), we incorporate timing sensitivity of an oscillator to describe the shape response of this oscillator to parametric perturbations. In order to extract timing information, we also develop a “local timing response curve” (lTRC) that measures the timing sensitivity of a limit cycle within any given region. We demonstrate in a specific example that taking into account local timing sensitivity in a nonsmooth system greatly improves the accuracy of the iSRC over the global timing analysis given by the iPRC.

13. B. Pittman-Polletta, Y. Wang, D. Stanley, C. Schroeder, M. Whittington, N. Kopell, “Differential contributions of synaptic and intrinsic inhibitory currents to parsing via flexible phase-locking in neural oscillators,” PLoS Computational Biology, 17(4), e1008783 (2021). [PDF]
    Abstract

    Current hypotheses suggest that speech segmentation—the initial division and grouping of the speech stream into candidate phrases, syllables, and phonemes for further linguistic processing—is executed by a hierarchy of oscillators in auditory cortex. Theta (3–12 Hz) rhythms play a key role by phase-locking to recurring acoustic features marking syllable boundaries. Reliable synchronization to quasi-rhythmic inputs, whose variable frequency can dip below cortical theta frequencies (down to 1 Hz), requires “flexible” theta oscillators whose underlying neuronal mechanisms remain unknown. Using biophysical computational models, we found that the flexibility of phase-locking in neural oscillators depended on the types of hyperpolarizing currents that paced them. Simulated cortical theta oscillators flexibly phase-locked to slow inputs when these inputs caused both (i) spiking and (ii) the subsequent buildup of outward current sufficient to delay further spiking until the next input. The greatest flexibility in phase-locking arose from a synergistic interaction between intrinsic currents that was not replicated by synaptic currents at similar timescales. Flexibility in phase-locking enabled improved entrainment to speech input, optimal at mid-vocalic channels, which in turn supported syllabic-timescale segmentation through identification of vocalic nuclei. Our results suggest that synaptic and intrinsic inhibition contribute to frequency-restricted and -flexible phase-locking in neural oscillators, respectively. Their differential deployment may enable neural oscillators to play diverse roles, from reliable internal clocking to adaptive segmentation of quasi-regular sensory inputs like speech.

14. Y. Wang and J. Rubin, “Complex bursting dynamics in an embryonic respiratory neuron model,” Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(4), 043127 (2020). [PDF]
    Abstract

    Pre-Bötzinger complex (pre-BötC) network activity within the mammalian brainstem controls the inspiratory phase of the respiratory rhythm. While bursting in pre-BötC neurons during the postnatal period has been extensively studied, less is known regarding inspiratory pacemaker neuron behavior at embryonic stages. Recent data in mouse embryo brainstem slices have revealed the existence of a variety of bursting activity patterns depending on distinct combinations of burst-generating I_NaP and I_CAN conductances. In this work, we consider a model of an isolated embryonic pre-BötC neuron featuring two distinct bursting mechanisms. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to uncover mechanisms underlying several different types of intrinsic bursting dynamics observed experimentally including several forms of plateau bursts, bursts involving depolarization block, and various combinations of these patterns. Our analysis also yields predictions about how changes in the balance of the two bursting mechanisms contribute to alterations in an inspiratory pacemaker neuron activity during prenatal development.

15. P. Gandhi, M. Golubitsky, C. Postlethwaite, I. Stewart and Y. Wang, “Bifurcations on fully inhomogeneous networks,” SIAM Journal on Applied Dynamical Systems, 19(1), 366–411 (2020). [Manuscript] [Supplement]
    Abstract

    Center manifold reduction is a standard technique in bifurcation theory, reducing the essential features of local bifurcations to equations in a small number of variables corresponding to critical eigenvalues. This method can be applied to admissible differential equations for a network, but it bears no obvious relation to the network structure. A fully inhomogeneous network is one in which all nodes and couplings can be different. For this class of networks, there are general circumstances in which the center manifold reduced equations inherit a network structure of their own. This structure arises by decomposing the network into path components, which connect to each other in a feedforward manner. Critical eigenvalues can then be associated with specific components, and the network structure on the center manifold depends on how these critical components connect within the network. This observation is used to analyze codimension-1 and codimension-2 local bifurcations. For codimension-1, only one critical component is involved, and generic local bifurcations are saddle-node and standard Hopf. For codimension-2, we focus on the case when one component is downstream from the other in the feedforward structure. This gives rise to four cases: steady or Hopf upstream combined with steady or Hopf downstream. Here the generic bifurcations, within the realm of network-admissible equations, differ significantly from generic codimension-2 bifurcations in a general dynamical system. In each case, we derive singularity-theoretic normal forms and unfoldings, present bifurcation diagrams, and tabulate the bifurcating states and their stabilities.

16. M. Golubitsky and Y. Wang, “Infinitesimal homeostasis in three-node input–output networks,” Journal of Mathematical Biology, 1–23 (2020). [PDF]
    Abstract

    Homeostasis occurs in a system where an output variable is approximately constant on an interval on variation of an input variable I. Homeostasis plays an important role in the regulation of biological systems, cf. Ferrell (Cell Syst 2:62–67, 2016), Tang and McMillen (J Theor Biol 408:274–289, 2016), Nijhout et al. (BMC Biol 13:79, 2015), and Nijhout et al. (Wiley Interdiscip Rev Syst Biol Med 11:e1440, 2018). A method for finding homeostasis in mathematical models is given in the control theory literature as points where the derivative of the output variable with respect to I is identically zero. Such points are called perfect homeostasis or perfect adaptation. Alternatively, Golubitsky and Stewart (J Math Biol 74:387–407, 2017) use an infinitesimal notion of homeostasis (namely, the derivative of the input-output function is zero at an isolated point) to introduce singularity theory into the study of homeostasis. Reed et al. (Bull Math Biol 79(9):1–24, 2017) give two examples of infinitesimal homeostasis in three-node chemical reaction systems: feedforward excitation and substrate inhibition. In this paper we show that there are 13 different three-node networks leading to 78 three-node input-output network configurations, under the assumption that there is one input node, one output node, and they are distinct. The different configurations are based on which node is the input node and which node is the output node. We show nonetheless that there are only three basic mechanisms for three-node input-output networks that lead to infinitesimal homeostasis and we call them structural homeostasis, Haldane homeostasis, and null-degradation homeostasis. Substantial parts of this classification are given in Ma et al. (Cell 138:760–773, 2009) and Ferrell (2016) among others. Our contributions include giving a complete classification using general admissible systems (Golubitsky and Stewart in Bull Am Math Soc 43:305–364, 2006) rather than specific biochemical models, relating the types of infinitesimal homeostasis to the graph theoretic existence of simple paths, and providing the basis to use singularity theory to study higher codimension homeostasis singularities such as the chair singularities introduced in Nijhout and Reed (Integr Comp Biol 54(2):264–275, 2014) and Nijhout et al. (Math Biosci 257:104–110, 2014).

17. M. Golubitsky, I. Stewart, F. Antoneli, Z. Huang and Y. Wang, “Input-Output Networks, Singularity Theory, and Homeostasis,” in Proceedings of the Workshop on Dynamics, Optimization and Computation, pp. 31–65, Springer, Cham (2020). [PDF]
    Abstract

    Homeostasis is a regulatory mechanism that keeps some specific variable close to a set value as other variables fluctuate, and is of particular interest in biochemical networks. We review and investigate a reformulation of homeostasis in which the system is represented as an input-output network, with two distinguished nodes ‘input’ and ‘output’, and the dynamics of the network determines the corresponding input-output function of the system. Interpreting homeostasis as an infinitesimal notion—namely, the derivative of the input-output function is zero at an isolated point—we apply methods from singularity theory to characterise homeostasis points in the input-output function. This approach, coupled to graph-theoretic ideas from combinatorial matrix theory, provides a systematic framework for calculating homeostasis points in models, classifying different types of homeostasis in input-output networks, and describing all small perturbations of the input-output function near a homeostasis point.

18. M.N. Fitzpatrick, Y. Wang, P.J. Thomas, R.D. Quinn and N.S. Szczecinski, “Robotics Application of a Method for Analytically Computing Infinitesimal Phase Response Curves,” in Conference on Biomimetic and Biohybrid Systems, pp. 104–115, Springer, Cham (2020). [PDF]
    Abstract

    This work explores a method for analytically computing the infinitesimal phase response curves (iPRCs) of a synthetic nervous system (SNS) for a hybrid exoskeleton. Phase changes, in response to perturbations, revealed by the iPRCs, could assist in tuning the strength and locations of sensory pathways. We model the SNS exoskeleton controller in a reduced form using a state-space representation that interfaces neural and motor dynamics. The neural dynamics are modeled after non-spiking neurons configured as a central pattern generator (CPG), while the motor dynamics model a power unit for the hip joint of the exoskeleton. Within the dynamics are piecewise functions and hard boundaries (i.e. “sliding conditions”), which cause discontinuities in the vector field at their boundaries. The analytical methods for computing the iPRCs used in this work apply the adjoint equation method with jump conditions that are able to account for these discontinuities. To show the accuracy and speed provided by these methods, we compare the analytical and brute-force solutions.

19. C.M. Czeisler, T.M. Silva, S.R. Fair, J. Liu, S. Tupal, B. Kaya, A. Cowgill, S. Mahajan, P.E. Silva, Y. Wang, ... and J.J. Otero, “The role of PHOX2B-derived astrocytes in chemosensory control of breathing and sleep homeostasis,” The Journal of Physiology, 597(8), 2225–2251 (2019). [PDF]
    Abstract

    We identify in mice a population of ~800 retrotrapezoid nucleus (RTN) astrocytes derived from PHOX2B-positive, OLIG3-negative progenitor cells, that interact with PHOX2B-expressing RTN chemosensory neurons. PHOX2B-derived astrocyte ablation during early life results in adult-onset O2 chemoreflex deficiency. These animals also display changes in sleep homeostasis, including fragmented sleep and disturbances in delta power after sleep deprivation, all without observable changes in anxiety or social behaviours. Ultrastructural evaluation of the RTN demonstrates that PHOX2B-derived astrocyte ablation results in features characteristic of degenerative neuro-axonal dystrophy, including abnormally dilated axon terminals and increased amounts of synapses containing autophagic vacuoles/phagosomes. We conclude that PHOX2B-derived astrocytes are necessary for maintaining a functional O2 chemosensory reflex in the adult, modulate sleep homeostasis, and are key regulators of synaptic integrity in the RTN region, which is necessary for the chemosensory control of breathing. These data also highlight how defects in embryonic development may manifest as neurodegenerative pathology in an adult.

20. S. Clifton, C. Davis, S. Erwin, G. Hamerlinck, A. Veprauskas, Y. Wang, W. Zhang and H. Gaff, “Modeling the argasid tick (Ornithodoros moubata) life cycle,” in Understanding Complex Biological Systems with Mathematics, pp. 63–87, Springer International Publishing (2018). [PDF]
    Abstract

    The first mathematical models for an argasid tick are developed to explore the dynamics and identify knowledge gaps of these poorly studied ticks. These models focus on Ornithodoros moubata, an important tick species throughout Africa and Europe. Ornithodoros moubata is a known vector for African swine fever (ASF), a catastrophically fatal disease for domesticated pigs in Africa and Europe. In the absence of any previous models for soft-bodied ticks, we propose two mathematical models of the life cycle of O. moubata. One is a continuoustime differential equation model that simplifies the tick life cycle to two stages, and the second is a discrete-time difference equation model that uses four stages. Both models use two host types: small hosts and large hosts, and both models find that either host type alone could support the tick population and that the final tick density is a function of host density. While both models predict similar tick equilibrium values, we observe significant differences in the time to equilibrium. The results demonstrate the likely establishment of these ticks if introduced into a new area even if there is only one type of host. These models provide the basis for developing future models that include disease states to explore infection dynamics and possible management of ASF.

21. Y. Wang and J. Rubin, “Timescales and Mechanisms of Sigh-like Bursting and Spiking in Models of Rhythmic Respiratory Neurons,” Journal of Mathematical Neuroscience, 7(1), 3 (2017). [PDF]
    Abstract

    Neural networks generate a variety of rhythmic activity patterns, often involving different timescales. One example arises in the respiratory network in the pre-Bötzinger complex of the mammalian brainstem, which can generate the eupneic rhythm associated with normal respiration as well as recurrent low-frequency, large-amplitude bursts associated with sighing. Two competing hypotheses have been proposed to explain sigh generation: the recruitment of a neuronal population distinct from the eupneic rhythm-generating subpopulation or the reconfiguration of activity within a single population. Here, we consider two recent computational models, one of which represents each of the hypotheses. We use methods of dynamical systems theory, such as fast-slow decomposition, averaging, and bifurcation analysis, to understand the multiple-timescale mechanisms underlying sigh generation in each model. In the course of our analysis, we discover that a third timescale is required to generate sighs in both models. Furthermore, we identify the similarities of the underlying mechanisms in the two models and the aspects in which they differ.

22. Y. Wang and J. Rubin, “Multiple Time Scale Mixed Bursting Dynamics in a Respiratory Neuron Model,” Journal of Computational Neuroscience, 41(3), 245–268 (2016). [PDF]
    Abstract

    Experimental results in rodent medullary slices containing the pre-Bötzinger complex (pre-BötC) have identified multiple bursting mechanisms based on persistent sodium current (I_NaP) and intracellular Ca²⁺. The classic two-timescale approach to the analysis of pre-BötC bursting treats the inactivation of I_NaP, the calcium concentration, as well as the Ca²⁺-dependent inactivation of IP3 as slow variables and considers other evolving quantities as fast variables. Based on its time course, however, it appears that a novel mixed bursting (MB) solution, observed both in recordings and in model pre-BötC neurons, involves at least three timescales. In this work, we consider a single-compartment model of a pre-BötC inspiratory neuron that can exhibit both I_NaP and Ca²⁺ oscillations and has the ability to produce MB solutions. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to better understand the mechanisms underlying the MB solution pattern. Rather surprisingly, we discover that a third timescale is not actually required to generate mixed bursting solutions. Through our analysis of timescales, we also elucidate how the pre-BötC neuron model can be tuned to improve the robustness of the MB solution.

23. P. Nan, Y. Wang, V. Kirk, J. Rubin, “Understanding and Distinguishing Three-Time-Scale Oscillations: Case Study in a Coupled Morris-Lecar System,” SIAM Journal on Applied Dynamical Systems, 14(3), 1518–1557 (2015). [PDF]
    Abstract

    Many physical systems feature interacting components that evolve on disparate time scales. Significant insights about the dynamics of such systems have resulted from grouping time scales into two classes and exploiting the time scale separation between classes through the use of geometric singular perturbation theory. It is natural to expect, however, that some dynamic phenomena cannot be captured by a two-time-scale decomposition. In this work, we are motivated by applications in neural dynamics to focus on a model consisting of a pair of Morris–Lecar systems coupled so that there are three time scales in the full system. We demonstrate that two approaches previously developed in the context of geometric singular perturbation theory for the analysis of two-time-scale systems extend naturally to the three-time-scale setting, where they complement each other nicely. Our analysis explains the dynamic mechanisms underlying solution features in the three-time-scale model. By comparison with certain two-time-scale versions of the same system, we identify some solution properties that truly require three time scales and thus can be viewed as indicators that the presence of three time scales in a system is functionally relevant.

24. L. Liu, A. Vainchtein and Y. Wang, “Kinetics of a Twinning Step,” Mathematics and Mechanics of Solids, 19(7), 832–851 (2014). [PDF]
    Abstract

    We study the kinetics of a step propagating along a twin boundary in a cubic lattice undergoing an antiplane shear deformation. To model twinning, we consider a piecewise quadratic double-well interaction potential with respect to one component of the shear strain and harmonic interaction with respect to another. We construct semi-analytical traveling wave solutions that correspond to a steady step propagation and obtain the kinetic relation between the applied stress and the velocity of the step. We show that this relation strongly depends on the width of the spinodal region where the double-well potential is non-convex and on the material anisotropy parameter. In the limiting case when the spinodal region degenerates to a point, we construct new solutions that extend the kinetic relation obtained in the earlier work of Celli, Flytzanis and Ishioka into the low-velocity regime. Numerical simulations suggest stability of some of the obtained solutions, including low-velocity step motion when the spinodal region is sufficiently wide. When the applied stress is above a certain threshold, nucleation and steady propagation of multiple steps are observed.