All Publications

  • Sequences and their shuffling may crucially impact coordinated reset stimulation - A theoretical study. Brain stimulation Kromer, J. A., Tass, P. A. 2024

    View details for DOI 10.1016/j.brs.2024.02.004

    View details for PubMedID 38346587

  • Synaptic network structure shapes cortically evoked spatio-temporal responses of STN and GPe neurons in a computational model. Frontiers in neuroinformatics Kromer, J. A., Bokil, H., Tass, P. A. 2023; 17: 1217786


    The basal ganglia (BG) are involved in motor control and play an essential role in movement disorders such as hemiballismus, dystonia, and Parkinson's disease. Neurons in the motor part of the BG respond to passive movement or stimulation of different body parts and to stimulation of corresponding cortical regions. Experimental evidence suggests that the BG are organized somatotopically, i.e., specific areas of the body are associated with specific regions in the BG nuclei. Signals related to the same body part that propagate along different pathways converge onto the same BG neurons, leading to characteristic shapes of cortically evoked responses. This suggests the existence of functional channels that allow for the processing of different motor commands or information related to different body parts in parallel. Neurological disorders such as Parkinson's disease are associated with pathological activity in the BG and impaired synaptic connectivity, together with reorganization of somatotopic maps. One hypothesis is that motor symptoms are, at least partly, caused by an impairment of network structure perturbing the organization of functional channels.We developed a computational model of the STN-GPe circuit, a central part of the BG. By removing individual synaptic connections, we analyzed the contribution of signals propagating along different pathways to cortically evoked responses. We studied how evoked responses are affected by systematic changes in the network structure. To quantify the BG's organization in the form of functional channels, we suggested a two-site stimulation protocol.Our model reproduced the cortically evoked responses of STN and GPe neurons and the contributions of different pathways suggested by experimental studies. Cortical stimulation evokes spatio-temporal response patterns that are linked to the underlying synaptic network structure. Our two-site stimulation protocol yielded an approximate functional channel width.The presented results provide insight into the organization of BG synaptic connectivity, which is important for the development of computational models. The synaptic network structure strongly affects the processing of cortical signals and may impact the generation of pathological rhythms. Our work may motivate further experiments to analyze the network structure of BG nuclei and their organization in functional channels.

    View details for DOI 10.3389/fninf.2023.1217786

    View details for PubMedID 37675246

    View details for PubMedCentralID PMC10477454

  • Synaptic reshaping of plastic neuronal networks by periodic multichannel stimulation with single-pulse and burst stimuli. PLoS computational biology Kromer, J. A., Tass, P. A. 2022; 18 (11): e1010568


    Synaptic dysfunction is associated with several brain disorders, including Alzheimer's disease, Parkinson's disease (PD) and obsessive compulsive disorder (OCD). Utilizing synaptic plasticity, brain stimulation is capable of reshaping synaptic connectivity. This may pave the way for novel therapies that specifically counteract pathological synaptic connectivity. For instance, in PD, novel multichannel coordinated reset stimulation (CRS) was designed to counteract neuronal synchrony and down-regulate pathological synaptic connectivity. CRS was shown to entail long-lasting therapeutic aftereffects in PD patients and related animal models. This is in marked contrast to conventional deep brain stimulation (DBS) therapy, where PD symptoms return shortly after stimulation ceases. In the present paper, we study synaptic reshaping by periodic multichannel stimulation (PMCS) in networks of leaky integrate-and-fire (LIF) neurons with spike-timing-dependent plasticity (STDP). During PMCS, phase-shifted periodic stimulus trains are delivered to segregated neuronal subpopulations. Harnessing STDP, PMCS leads to changes of the synaptic network structure. We found that the PMCS-induced changes of the network structure depend on both the phase lags between stimuli and the shape of individual stimuli. Single-pulse stimuli and burst stimuli with low intraburst frequency down-regulate synapses between neurons receiving stimuli simultaneously. In contrast, burst stimuli with high intraburst frequency up-regulate these synapses. We derive theoretical approximations of the stimulation-induced network structure. This enables us to formulate stimulation strategies for inducing a variety of network structures. Our results provide testable hypotheses for future pre-clinical and clinical studies and suggest that periodic multichannel stimulation may be suitable for reshaping plastic neuronal networks to counteract pathological synaptic connectivity. Furthermore, we provide novel insight on how the stimulus type may affect the long-lasting outcome of conventional DBS. This may strongly impact parameter adjustment procedures for clinical DBS, which, so far, primarily focused on acute effects of stimulation.

    View details for DOI 10.1371/journal.pcbi.1010568

    View details for PubMedID 36327232

  • Long-Lasting Desynchronization of Plastic Neuronal Networks by Double-Random Coordinated Reset Stimulation Frontiers in Network Physiology Khaledi-Nasab, A., Kromer, J. A., Tass, P. A. 2022; 2
  • Coordinated Reset Vibrotactile Stimulation Induces Sustained Cumulative Benefits in Parkinson's Disease. Frontiers in physiology Pfeifer, K. J., Kromer, J. A., Cook, A. J., Hornbeck, T., Lim, E. A., Mortimer, B. J., Fogarty, A. S., Han, S. S., Dhall, R., Halpern, C. H., Tass, P. A. 2021; 12: 624317


    Background: Abnormal synchronization of neuronal activity in dopaminergic circuits is related to motor impairment in Parkinson's disease (PD). Vibrotactile coordinated reset (vCR) fingertip stimulation aims to counteract excessive synchronization and induce sustained unlearning of pathologic synaptic connectivity and neuronal synchrony. Here, we report two clinical feasibility studies that examine the effect of regular and noisy vCR stimulation on PD motor symptoms. Additionally, in one clinical study (study 1), we examine cortical beta band power changes in the sensorimotor cortex. Lastly, we compare these clinical results in relation to our computational findings.Methods: Study 1 examines six PD patients receiving noisy vCR stimulation and their cortical beta power changes after 3 months of daily therapy. Motor evaluations and at-rest electroencephalographic (EEG) recordings were assessed off medication pre- and post-noisy vCR. Study 2 follows three patients for 6+ months, two of whom received daily regular vCR and one patient from study 1 who received daily noisy vCR. Motor evaluations were taken at baseline, and follow-up visits were done approximately every 3 months. Computationally, in a network of leaky integrate-and-fire (LIF) neurons with spike timing-dependent plasticity, we study the differences between regular and noisy vCR by using a stimulus model that reproduces experimentally observed central neuronal phase locking.Results: Clinically, in both studies, we observed significantly improved motor ability. EEG recordings observed from study 1 indicated a significant decrease in off-medication cortical sensorimotor high beta power (21-30 Hz) at rest after 3 months of daily noisy vCR therapy. Computationally, vCR and noisy vCR cause comparable parameter-robust long-lasting synaptic decoupling and neuronal desynchronization.Conclusion: In these feasibility studies of eight PD patients, regular vCR and noisy vCR were well tolerated, produced no side effects, and delivered sustained cumulative improvement of motor performance, which is congruent with our computational findings. In study 1, reduction of high beta band power over the sensorimotor cortex may suggest noisy vCR is effectively modulating the beta band at the cortical level, which may play a role in improved motor ability. These encouraging therapeutic results enable us to properly plan a proof-of-concept study.

    View details for DOI 10.3389/fphys.2021.624317

    View details for PubMedID 33889086

  • Long-Lasting Desynchronization Effects of Coordinated Reset Stimulation Improved by Random Jitters Frontiers in physiology Khaledi-Nasab, A., Kromer , J., Tass, P. A. 2021: 1446
  • Chemokinetic Scattering, Trapping, and Avoidance of Active Brownian Particles PHYSICAL REVIEW LETTERS Kromer, J. A., de la Cruz, N., Friedrich, B. M. 2020; 124 (11)
  • Long-lasting desynchronization by decoupling stimulation PHYSICAL REVIEW RESEARCH Kromer, J. A., Tass, P. A. 2020; 2 (3)
  • Impact of number of stimulation sites on long-lasting desynchronization effects of coordinated reset stimulation CHAOS Kromer, J. A., Khaledi-Nasab, A., Tass, P. A. 2020; 30

    View details for DOI 10.1063/5.0015196

  • Long-Lasting Desynchronization of Plastic Neural Networks by Random Reset Stimulation. Frontiers in physiology Khaledi-Nasab, A. n., Kromer, J. A., Tass, P. A. 2020; 11: 622620


    Excessive neuronal synchrony is a hallmark of neurological disorders such as epilepsy and Parkinson's disease. An established treatment for medically refractory Parkinson's disease is high-frequency (HF) deep brain stimulation (DBS). However, symptoms return shortly after cessation of HF-DBS. Recently developed decoupling stimulation approaches, such as Random Reset (RR) stimulation, specifically target pathological connections to achieve long-lasting desynchronization. During RR stimulation, a temporally and spatially randomized stimulus pattern is administered. However, spatial randomization, as presented so far, may be difficult to realize in a DBS-like setup due to insufficient spatial resolution. Motivated by recently developed segmented DBS electrodes with multiple stimulation sites, we present a RR stimulation protocol that copes with the limited spatial resolution of currently available depth electrodes for DBS. Specifically, spatial randomization is realized by delivering stimuli simultaneously to L randomly selected stimulation sites out of a total of M stimulation sites, which will be called L/M-RR stimulation. We study decoupling by L/M-RR stimulation in networks of excitatory integrate-and-fire neurons with spike-timing dependent plasticity by means of theoretical and computational analysis. We find that L/M-RR stimulation yields parameter-robust decoupling and long-lasting desynchronization. Furthermore, our theory reveals that strong high-frequency stimulation is not suitable for inducing long-lasting desynchronization effects. As a consequence, low and high frequency L/M-RR stimulation affect synaptic weights in qualitatively different ways. Our simulations confirm these predictions and show that qualitative differences between low and high frequency L/M-RR stimulation are present across a wide range of stimulation parameters, rendering stimulation with intermediate frequencies most efficient. Remarkably, we find that L/M-RR stimulation does not rely on a high spatial resolution, characterized by the density of stimulation sites in a target area, corresponding to a large M. In fact, L/M-RR stimulation with low resolution performs even better at low stimulation amplitudes. Our results provide computational evidence that L/M-RR stimulation may present a way to exploit modern segmented lead electrodes for long-lasting therapeutic effects.

    View details for DOI 10.3389/fphys.2020.622620

    View details for PubMedID 33613303

    View details for PubMedCentralID PMC7893102

  • Variability of collective dynamics in random tree networks of strongly coupled stochastic excitable elements PHYSICAL REVIEW E Khaledi-Nasab, A., Kromer, J. A., Schimansky-Geier, L., Neiman, A. B. 2018; 98 (5)
  • General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks JOURNAL OF MATHEMATICAL BIOLOGY Reis, M., Kromer, J. A., Klipp, E. 2018; 77 (2): 377–419


    Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME's. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties. Given Poisson/deterministic initial conditions, we then prove the independent species to be Poisson/binomially distributed, while the dependent species exhibit generalized Poisson/Khatri Type B distributions. Generalized Poisson/Khatri Type B distributions are multimodal for an appropriate choice of parameters. We illustrate our criteria for multimodality by several basic models, as well as the well-known two-stage transcription-translation network and Bateman's model from nuclear physics. For both examples, multimodality was previously not reported.

    View details for DOI 10.1007/s00285-018-1205-2

    View details for Web of Science ID 000439442300004

    View details for PubMedID 29353313

    View details for PubMedCentralID PMC6061068

  • Decision making improves sperm chemotaxis in the presence of noise PLOS COMPUTATIONAL BIOLOGY Kromer, J. A., Maercker, S., Lange, S., Baier, C., Friedrich, B. M. 2018; 14 (4): e1006109


    To navigate their surroundings, cells rely on sensory input that is corrupted by noise. In cells performing chemotaxis, such noise arises from the stochastic binding of signalling molecules at low chemoattractant concentrations. We reveal a fundamental relationship between the speed of chemotactic steering and the strength of directional fluctuations that result from the amplification of noise in a chemical input signal. This relation implies a trade-off between steering that is slow and reliable, and steering that is fast but less reliable. We show that dynamic switching between these two modes of steering can substantially increase the probability to find a target, such as an egg to be found by sperm cells. This decision making confers no advantage in the absence of noise, but is beneficial when chemical signals are detectable, yet characterized by low signal-to-noise ratios. The latter applies at intermediate distances from a target, where signalling molecules are diluted, thus defining a 'noise zone' that cells have to cross. Our results explain decision making observed in recent experiments on sea urchin sperm chemotaxis. More generally, our theory demonstrates how decision making enables chemotactic agents to cope with high levels of noise in gradient sensing by dynamically adjusting the persistence length of a biased random walk.

    View details for DOI 10.1371/journal.pcbi.1006109

    View details for Web of Science ID 000432169600044

    View details for PubMedID 29672515

    View details for PubMedCentralID PMC5929576

  • Emergent stochastic oscillations and signal detection in tree networks of excitable elements SCIENTIFIC REPORTS Kromer, J., Khaledi-Nasab, A., Schimansky-Geier, L., Neiman, A. B. 2017; 7: 3956


    We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading to global coherent oscillations in the network. This scenario may be relevant to action potential generation in certain sensory neurons, which possess myelinated distal dendritic tree-like arbors with excitable nodes of Ranvier at peripheral and branching nodes and exhibit noisy periodic sequences of action potentials. We focus on the spiking statistics of the central node, which fires in response to a noisy input at peripheral nodes. We show that, in the strong coupling regime, relevant to myelinated dendritic trees, the spike train statistics can be predicted from an isolated excitable element with rescaled parameters according to the network topology. Furthermore, we show that by varying the network topology the spike train statistics of the central node can be tuned to have a certain firing rate and variability, or to allow for an optimal discrimination of inputs applied at the peripheral nodes.

    View details for DOI 10.1038/s41598-017-04193-8

    View details for Web of Science ID 000403840000028

    View details for PubMedID 28638071

    View details for PubMedCentralID PMC5479816

  • Emergence and coherence of oscillations in star networks of stochastic excitable elements PHYSICAL REVIEW E Kromer, J. A., Schimansky-Geier, L., Neiman, A. B. 2016; 93 (4): 042406


    We study the emergence and coherence of stochastic oscillations in star networks of excitable elements in which peripheral nodes receive independent random inputs. A biophysical model of a distal branch of sensory neuron in which peripheral nodes of Ranvier are coupled to a central node by myelinated cable segments is used along with a generic model of networked stochastic active rotators. We show that coherent oscillations can emerge due to stochastic synchronization of peripheral nodes and that the degree of coherence can be maximized by tuning the coupling strength and the size of the network. Analytical results are obtained for the strong-coupling regime of the active rotator network. In particular, we show that in the strong-coupling regime, the network dynamics can be described by an effective single active rotator with rescaled parameters and noise.

    View details for DOI 10.1103/PhysRevE.93.042406

    View details for Web of Science ID 000373586200007

    View details for PubMedID 27176328

  • Noise-controlled bistability in an excitable system with positive feedback EPL Kromer, J. A., Pinto, R. D., Lindner, B., Schimansky-Geier, L. 2014; 108 (2)
  • Event-triggered feedback in noise-driven phase oscillators PHYSICAL REVIEW E Kromer, J. A., Lindner, B., Schimansky-Geier, L. 2014; 89 (3): 032138


    Using a stochastic nonlinear phase oscillator model, we study the effect of event-triggered feedback on the statistics of interevent intervals. Events are associated with the entering of a new cycle. The feedback is modeled by an instantaneous increase (positive feedback) or decrease (negative feedback) of the oscillator frequency whenever an event occurs followed by an exponential decay on a slow time scale. In addition to the known excitable and oscillatory regimes, which are separated by a saddle node on invariant circle bifurcation, positive feedback can lead to bistable dynamics and a change of the system's excitability. The feedback has also a strong effect on noise-induced phenomena like coherence resonance or anticoherence resonance. Both positive and negative feedback can lead to more regular output for particular noise strengths. Finally, we investigate serial correlations in the sequence of interevent intervals that occur due to the additional slow dynamics. We derive approximations for the serial correlation coefficient and show that positive feedback results in extended positive interval correlations, whereas negative feedback yields short-ranging negative correlations. Investigating the interplay of feedback and the nonlinear phase dynamics close to the bifurcation, we find that correlations are most pronounced for optimal feedback strengths.

    View details for DOI 10.1103/PhysRevE.89.032138

    View details for Web of Science ID 000333702800004

    View details for PubMedID 24730820

  • Weighted-ensemble Brownian dynamics simulation: Sampling of rare events in nonequilibrium systems PHYSICAL REVIEW E Kromer, J. A., Schimansky-Geier, L., Toral, R. 2013; 87 (6): 063311


    We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed in calculating steady-state probabilities of order 10(-300) and reproduce the Arrhenius law for rates of order 10(-280). Special attention is payed to the simulation of nonpotential systems where no detailed balance assumption exists. For this large class of stochastic systems, the stationary probability distribution density is often unknown and cannot be used as preknowledge during the simulation. We compare the algorithm's efficiency with standard Brownian dynamics simulations and the original WE method.

    View details for DOI 10.1103/PhysRevE.87.063311

    View details for Web of Science ID 000321096000012

    View details for PubMedID 23848810

  • Phason-induced dynamics of colloidal particles on quasicrystalline substrates EUROPEAN PHYSICAL JOURNAL E Kromer, J. A., Schmiedeberg, M., Roth, J., Stark, H. 2013; 36 (3): 25


    Phasons are special hydrodynamic modes that occur in quasicrystals. The trajectories of particles due to a phasonic drift were recently studied by Kromer et al. (Phys. Rev. Lett. 108, 218301 (2012)) for the case where the particles stay in the minima of a quasicrystalline potential. Here, we study the mean motion of colloidal particles in quasicrystalline laser fields when a phasonic drift or displacement is applied and also consider the cases where the colloids cannot follow the potential minima. While the mean square displacement is similar to the one of particles in a random potential with randomly changing potential wells, there also is a net drift of the colloids that reverses its direction when the phasonic drift velocity is increased. Furthermore, we explore the dynamics of the structural changes in a laser-induced quasicrystal during the rearrangement process that is caused by a steady phasonic drift or an instantaneous phasonic displacement.

    View details for DOI 10.1140/epje/i2013-13025-0

    View details for Web of Science ID 000317856000006

    View details for PubMedID 23512714

  • What Phasons Look Like: Particle Trajectories in a Quasicrystalline Potential PHYSICAL REVIEW LETTERS Kromer, J. A., Schmiedeberg, M., Roth, J., Stark, H. 2012; 108 (21): 218301


    Among the distinctive features of quasicrystals-structures with long-range order but without periodicity-are phasons. Phasons are hydrodynamic modes that, like phonons, do not cost free energy in the long-wavelength limit. For light-induced colloidal quasicrystals, we analyze the collective rearrangements of the colloids that occur when the phasonic displacement of the light field is changed. The colloidal model system is employed to study the link between the continuous description of phasonic modes in quasicrystals and collective phasonic flips of atoms. We introduce characteristic areas of reduced phononic and phasonic displacements and use them to predict individual colloidal trajectories. In principle, our method can be employed with all quasicrystalline systems in order to derive collective rearrangements of particles from the continuous description of phasons.

    View details for DOI 10.1103/PhysRevLett.108.218301

    View details for Web of Science ID 000304405000012

    View details for PubMedID 23003308