Multiple Internal States Research Articles

Population coding of predator imminence in the hypothalamus.

Distinct subsets of VMHdm SF1 neurons encode multiple predator-evoked internal states. Anti-correlated subsets encode safety vs. threat in a bi-directional mannerA population code for predator imminence is identified using a novel assay VMHdm SF1 dynamics correlate with individual variation in predator defensiveness.

Understanding the neural principles of interacting multiple internal states

In dynamic ethological environments, animals are constantly confronted with conflicting choices driven by interacting internal motivations. This intricate dance between internal states prompts the question: How do these states interact to determine the optimal innate behavior at any given moment? Specifically, when hungry animals encounter food and potential intruders, how do they navigate between feeding, attack, and mating behaviors? Despite extensive neuroscience research on instinctive behaviors, our understanding of the mechanisms governing adaptive behavioral decisions in the face of competing internal signals remains limited. This research aims to shed light on the complex interplay of internal physiological homeostasis in modulating defensive, aggressive, and sexual behaviors. Our focus lies on exploring the intricate network between the body and the brain to unravel the most adaptive responses within a concise time window. Currently, our investigations center around the hypothalamus, a crucial region known for representing emotional states upon encountering conspecifics or predators. Intriguingly, this same hypothalamic nucleus plays a pivotal role in regulating homeostatic metabolic states, including glucose homeostasis. Here, I will share the observation from innate behaviors of animals and the associated neural activity patterns in the hypothalamus. We will explore the current understanding of how these behaviors are modulated by internal physiological states and discuss the future directions of our research. Additionally, we aim to highlight the significance of combining the measurement of physiological signals to comprehensively address how multiple internal states interact with each other. By unraveling the complexities of these interactions, our research contributes to a deeper comprehension of the adaptive decision-making processes that animals employ in the face of conflicting choices. Helen Hay Whitney Foundation, HHMI. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

A multi-state dynamic process confers mechano-adaptation to a biological nanomachine

Adaptation is a defining feature of living systems. The bacterial flagellar motor adapts to changes in the external mechanical load by adding or removing torque-generating (stator) units. But the molecular mechanism behind this mechano-adaptation remains unclear. Here, we combine single motor eletrorotation experiments and theoretical modeling to show that mechano-adaptation of the flagellar motor is enabled by multiple mechanosensitive internal states. Dwell time statistics from experiments suggest the existence of at least two bound states with a high and a low unbinding rate, respectively. A first-passage-time analysis of a four-state model quantitatively explains the experimental data and determines the transition rates among all four states. The torque generated by bound stator units controls their effective unbinding rate by modulating the transition between the bound states, possibly via a catch bond mechanism. Similar force-mediated feedback enabled by multiple internal states may apply to adaptation in other macromolecular complexes.

Stochastic harmonic trapping of a Lévy walk: transport and first-passage dynamics under soft resetting strategies

We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.

Numerical algorithm for the space-time fractional Fokker–Planck system with two internal states

The fractional Fokker-Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., $\mathbf{13}$, 10 (2018)], where the space derivative is Laplace operator. If the jump length distribution of the particles is power law instead of Gaussian, the space derivative should be replaced with fractional Laplacian. This paper focuses on solving the two state Fokker-Planck system with fractional Laplacian. We first provide a priori estimate for this system under different regularity assumptions on the initial data. Then we use $L_1$ scheme to discretize the time fractional derivatives and finite element method to approximate the fractional Laplacian operators. Furthermore, we give the error estimates for the space semidiscrete and fully discrete schemes without any assumption on regularity of solutions. Finally, the effectiveness of the designed scheme is verified by numerical experiments.

Traveling fronts in self-replicating persistent random walks with multiple internal states

Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle transport. Many physical and biological systems are, however, better described by persistent random walks that switch between multiple states of ballistic motion. So far, traveling fronts in persistent random walk models have only been analyzed in special, simplified cases. Here, we formulate the general model of reaction-transport processes in such systems and show how to compute the expansion velocity for arbitrary number of states. For the two-state model, we obtain a closed-form expression for the velocity and report how it is affected by different transport and replication parameters. We also show that nonzero death rates result in a discontinuous transition from quiescence to propagation. We compare our results to a recent observation of a discontinuous onset of propagation in microtubule asters and comment on the universal nature of the underlying mechanism.

Numerical Scheme for the Fokker–Planck Equations Describing Anomalous Diffusions with Two Internal States

Recently, the fractional Fokker-Planck equations (FFPEs) with multiple internal states are built for the particles undergoing anomalous diffusion with different waiting time distributions for different internal states, which describe the distribution of positions of the particles [Xu and Deng, Math. Model. Nat. Phenom., $\mathbf{13}$, 10 (2018)]. In this paper, we first develop the Sobolev regularity of the FFPEs with two internal states, including the homogeneous problem with smooth and nonsmooth initial values and the inhomogeneous problem with vanishing initial value, and then we design the numerical scheme for the system of fractional partial differential equations based on the finite element method for the space derivatives and convolution quadrature for the time fractional derivatives. The optimal error estimates of the scheme under the above three different conditions are provided for both space semidiscrete and fully discrete schemes. Finally, one- and two-dimensional numerical experiments are performed to confirm our theoretical analysis and the predicted convergence order.

Anisotropic Nonlocal Diffusion Operators for Normal and Anomalous Dynamics

The Laplacian $\Delta$ is the infinitesimal generator of isotropic Brownian motion, being the limit process of normal diffusion, while the fractional Laplacian $\Delta^{\beta/2}$ serves as the infinitesimal generator of the limit process of isotropic L\'{e}vy process. Taking limit, in some sense, means that the operators can approximate the physical process well after sufficient long time. We introduce the nonlocal operators (being effective from the starting time), which describe the general processes undergoing normal diffusion. For anomalous diffusion, we extend to the anisotropic fractional Laplacian $\Delta_m^{\beta/2}$ and the tempered one $\Delta_m^{\beta/2,\lambda}$ in $\mathbb{R}^n$. Their definitions are proved to be equivalent to an alternative one in Fourier space. Based on these new nonlocal diffusion operators, we further derive the deterministic governing equations of some interesting statistical observables of the very general jump processes with multiple internal states. Finally, we consider the associated initial and boundary value problems and prove their well-posedness of the Galerkin weak formulation in $\mathbb{R}^n$. To obtain the coercivity, we claim that the probability density function $m(Y)$ should be nondegenerate.

Lévy Walk with Multiple Internal States

Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for dealing with the dependence of the PDF of waiting time on the energy of the animal and richness of the food at a particular location, etc; the framework can also be used to model the moving trajectories of smart animals without returning to the directions or locations which they come from immediately. After building the Levy walk model with multiple internal states and deriving the governing equation of the distribution of the positions of the particles, some applications are discussed with specific transition matrices. The type of diffusion for non-immediately-repeating L\'{e}vy walk is uncovered, and the distribution and average of first passage time are numerically simulated.

Fractional compound Poisson processes with multiple internal states

For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and functional distributions of the trajectories of particles; in particular, the equations governing the functional distribution of internal states are also obtained. The dynamics of the stochastic processes are analyzed and the applications, calculating the distribution of the first passage time and the distribution of the fraction of the occupation time, of the equations are given. For the further application of the newly built models, we make very detailed discussions on the none-immediately-repeated stochastic process, e.g., the random walk of smart animals.

Memristive response of a new class of hydrated vanadium oxide intercalation compounds

Abstract

A compact cyclic plasticity model with parameter evolution

The paper presents a compact model for cyclic plasticity based on energy in terms of external and internal variables, and plastic yielding described by kinematic hardening and a flow potential with an additive term controlling the nonlinear cyclic hardening. The model is basically described by five parameters: external and internal stiffness, a yield stress and a limiting ultimate stress, and finally a parameter controlling the gradual development of plastic deformation. Calibration against numerous experimental results indicates that typically larger plastic strains develop than predicted by the Armstrong–Frederick model, contained as a special case of the present model for a particular choice of the shape parameter. In contrast to previous work, where shaping the stress-strain loops is derived from multiple internal stress states, this effect is here represented by a single parameter, and it is demonstrated that this simple formulation enables very accurate representation of experimental results. An extension of the theory to account for model parameter evolution effects, e.g. in the form of changing yield level, is included in the form of extended evolution equations for the model parameters. Finally, it is demonstrated that the model in combination with a simple parameter interpolation scheme enables representation of ratcheting effects.

Sub-Doppler laser cooling using electromagnetically induced transparency

We propose a sub-Doppler laser cooling mechanism that takes advantage of the unique spectral features and extreme dispersion generated by the phenomenon of electromagnetically induced transparency (EIT). EIT is a destructive quantum interference phenomenon experienced by atoms with multiple internal quantum states when illuminated by laser fields with appropriate frequencies. By detuning the lasers slightly from the "dark resonance", we observe that, within the transparency window, atoms can be subject to a strong viscous force, while being only slightly heated by the diffusion caused by spontaneous photon scattering. In contrast to other laser cooling schemes, such as polarization gradient cooling or EIT-sideband cooling, no external magnetic field or strong external confining potential is required. Using a semiclassical approximation, we derive analytically quantitative expressions for the steady-state temperature, which is confirmed by full quantum mechanical numerical simulations. We find that the lowest achievable temperatures approach the single-photon recoil energy. In addition to dissipative forces, the atoms are subject to a stationary conservative potential, leading to the possibility of spatial confinement. We find that under typical experimental parameters this effect is weak and stable trapping is not possible.

Microscopic derivation of multichannel Hubbard models for ultracold nonreactive molecules in an optical lattice

Recent experimental advances in the cooling and manipulation of bialkali dimer molecules have enabled the production of gases of ultracold molecules that are not chemically reactive. It has been presumed in the literature that in the absence of an electric field the low-energy scattering of such nonreactive molecules (NRMs) will be similar to atoms, in which a single $s$-wave scattering length governs the collisional physics. However, in Ref. [1], it was argued that the short-range collisional physics of NRMs is much more complex than for atoms, and that this leads to a many-body description in terms of a multi-channel Hubbard model. In this work, we show that this multi-channel Hubbard model description of NRMs in an optical lattice is robust against the approximations employed in Ref. [1] to estimate its parameters. We do so via an exact, albeit formal, derivation of a multi-channel resonance model for two NRMs from an ab initio description of the molecules in terms of their constituent atoms. We discuss the regularization of this two-body multi-channel resonance model in the presence of a harmonic trap, and how its solutions form the basis for the many-body model of Ref. [1]. We also generalize the derivation of the effective lattice model to include multiple internal states (e.g., rotational or hyperfine). We end with an outlook to future research.

Noise and Information Transmission in Promoters with Multiple Internal States

Based on the measurements of noise in gene expression performed during the past decade, it has become customary to think of gene regulation in terms of a two-state model, where the promoter of a gene can stochastically switch between an ON and an OFF state. As experiments are becoming increasingly precise and the deviations from the two-state model start to be observable, we ask about the experimental signatures of complex multistate promoters, as well as the functional consequences of this additional complexity. In detail, we i), extend the calculations for noise in gene expression to promoters described by state transition diagrams with multiple states, ii), systematically compute the experimentally accessible noise characteristics for these complex promoters, and iii), use information theory to evaluate the channel capacities of complex promoter architectures and compare them with the baseline provided by the two-state model. We find that adding internal states to the promoter generically decreases channel capacity, except in certain cases, three of which (cooperativity, dual-role regulation, promoter cycling) we analyze in detail.

Nonlinear dynamics of complex hysteretic systems: Oscillator in a magnetic field

Complex hysteresis is a well-known phenomenon in many branches of science. The most prominent examples come from materials with a complex microscopic structure such as magnetic materials, shape-memory alloys, or, porous materials. Their hysteretic behavior is characterized by the existence of multiple internal system states for a given external parameter and by a non-local memory. The input-output behavior of such systems is well studied and in a standard phenomenological approach described by the so-called Preisach operator. What is not well understood, are situations, where such a hysteretic system is dynamically coupled to its environment. Since the hysteretic sub-system provides a complicated form of nonlinearity, one expects non-trivial, possibly chaotic behavior of the combined dynamical system. We study such a combined dynamical system with hysteretic nonlinearity. In this original contribution a simple differential-operator equation with hysteretic damping, which describes a magnetic pendulum is considered. We find, for instance, a fractal dependence of the asymptotic behavior as function of the starting values. The sensitivity of the system to perturbations is investigated by several methods, such as the 0–1 test for chaos and sub-Lyapunov exponents. The power spectral density is also calculated and compared with analytical results for simple input-output scenarios.

Life stressors, emotional distress, and trauma-related thoughts occurring in the 24 h preceding active duty U.S. Soldiers' suicide attempts

External life events and internal experiences (i.e., emotional distress and trauma-related thoughts) occurring in the 24 h preceding suicide attempts were examined in a sample of active duty U.S. Soldiers. Seventy-two Soldiers (66 male, 6 female; 65.3% Caucasian, 9.7% African-American, 2.8% Asian, 2.8% Pacific Islander, 4.2% Native American, and 9.7% “other”; age M = 27.34, SD = 6.50) were interviewed using the Suicide Attempt Self Injury Interview to assess the occurrence of external events and internal experiences on the day of their suicide attempts, and to determine their associations with several dimensions of suicide risk: suicidal intent, lethality, and deliberation about attempting. Multiple external stressors and internal states were experienced by Soldiers in the 24 h preceding their suicide attempts, with emotional distress being the most common. Trauma-related thoughts were much less frequently reported in the 24 h preceding suicide attempts. Emotional experiences were directly associated with suicidal intent, and explained the relationship between external events and suicidal intent. Lethality was unrelated to any external events, emotional experiences, or trauma-related thoughts. Greater emotional distress and trauma-related thoughts were associated with shorter deliberation about whether or not to attempt suicide. Soldiers experience multiple sources of distress in the period immediately preceding their suicide attempts. Soldiers who experience more negative emotional experiences have a stronger desire for suicide and spend less time deliberating before an attempt.

Exploring models of associative memory via cavity quantum electrodynamics

Photons in multimode optical cavities can be used to mediate tailored interactions between atoms confined in the cavities. For atoms possessing multiple internal (i.e., “spin”) states, the spin–spin interactions mediated by the cavity are analogous in structure to the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between localized spins in metals. Thus, in particular, it is possible to use atoms in cavities to realize models of frustrated and/or disordered spin systems, including models that can be mapped on to the Hopfield network model and related models of associative memory. We explain how this realization of models of associative memory comes about and discuss ways in which the properties of these models can be probed in a cavity-based setting.

Regulatory Dynamics of Synthetic Gene Networks with Positive Feedback

Biological processes are governed by complex networks ranging from gene regulation to signal transduction. Positive feedback is a key element in such networks. The regulation enables cells to adopt multiple internal expression states in response to a single external input signal. However, past works lacked a dynamical aspect of this system. To address the dynamical property of the positive feedback system, we employ synthetic gene circuits in Escherichia coli to measure the rise-time of both the no-feedback system and the positive feedback system. We show that the kinetics of gene expression is slowed down if the gene regulatory system includes positive feedback. We also report that the transition of gene switching behaviors from the hysteretic one to the graded one occurs. A mathematical model based on the chemical reactions shows that the response delay is an inherited property of the positive feedback system. Furthermore, with the aid of the phase diagram, we demonstrate the decline of the feedback activation causes the transition of switching behaviors. Our findings provide a further understanding of a positive feedback system in a living cell from a dynamical point of view.

Single Neurons Can Induce Phase Transitions of Cortical Recurrent Networks with Multiple Internal States

Fluctuations of membrane potential of cortical neurons, referred to here as internal states, are essential for brain function, but little is known about how these internal states emerge and are maintained, or what determines transitions between these states. We performed intracellular recordings from hippocampal CA3 pyramidal cells ex vivo and found that neurons display multiple and hierarchical internal states, which are linked to cholinergic activity and are characterized by several power law structures in membrane potential dynamics. Multiple recordings from adjacent neurons revealed that the internal states were coherent between neurons, indicating that the internal state of any given cell in a local network could represent the network activity state. Repeated stimulation of single neurons led over time to transitions to different internal states in both the stimulated neuron and neighboring neurons. Thus, single-cell activation is sufficient to shift the state of the entire local network. As the states shift to more active levels, theta- and gamma-frequency components developed in the form of subthreshold oscillations. State transitions were associated with changes in membrane conductance but were not accompanied by a change in reversal potential. These data suggest that the recurrent network organizes the internal states of individual neurons into synchronization through network activity with balanced excitation and inhibition, and that this organization is discrete, heterogeneous and dynamic in nature. Thus, neuronal states reflect the 'phase' of an active network, a novel demonstration of the dynamics and flexibility of cortical microcircuitry.