Optimal decision making for sperm chemotaxis in the presence of noise

For navigation, microscopic agents such as biological cells rely on noisy sensory input. In cells performing chemotaxis, such noise arises from the stochastic binding of signaling molecules at low concentrations. Using chemotaxis of sperm cells as application example, we address the classic problem of chemotaxis towards a single target. 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 the chemical input signal. This relation implies a trade-off between slow, but reliable, and fast, but less reliable, steering. By formulating the problem of optimal navigation in the presence of noise as a Markov decision process, we show that dynamic switching between reliable and fast steering substantially increases the probability to find a target, such as the egg. Intriguingly, this decision making would provide no benefit in the absence of noise. Instead, decision making is most beneficial, if chemical signals are above detection threshold, yet signal-to-noise ratios of gradient measurements are low. This situation generically arises at intermediate distances from a target, where signaling molecules emitted by the target are diluted, thus defining a `noise zone' that cells have to cross. Our work addresses the intermediate case between well-studied perfect chemotaxis at high signal-to-noise ratios close to a target, and random search strategies in the absence of navigation cues, e.g. far away from a target. Our specific results provide a rational for the surprising observation of decision making in recent experiments on sea urchin sperm chemotaxis. The general theory demonstrates how decision making enables chemotactic agents to cope with high levels of noise in gradient measurements by dynamically adjusting the persistence length of a biased persistent random walk.Comment: 9 pages, 5 figure

Weighted-ensemble Brownian dynamics simulation: Sampling of rare events in non-equilibrium systems

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 to calculate steady state probabilities of order $10^{-300}$ and reproduce Arrhenius law for rates of order $10^{-280}$. Special attention is payed to the simulation of non-potential 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 algorithms efficiency with standard Brownian dynamics simulations and other WE methods

Synaptic network structure shapes cortically evoked spatio-temporal responses of STN and GPe neurons in a computational model

IntroductionThe 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.MethodsWe 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.ResultsOur 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.Discussion/conclusionThe 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

Noise-induced dynamics of coupled excitable systems with slow positive feedback

In excitable systems, superthreshold stimuli can cause strong responses—events. Event generation is often modulated by slow feedback processes. The interplay of noise and a positive (upregulating) event-triggered feedback mechanism in excitable systems is studied using the active rotator (AR) model. First, recent results on the dynamics of a single AR with positive feedback are reviewed. Feedback may lead to bursting that results from stochastic switching between a subthreshold and a superthreshold regime. Both regimes coexist in a limited range of noise intensities. Second, novel results on all-to-all coupled ARs in the presence of positive feedback are presented. The interplay of noise, feedback, and input from other ARs can lead to asynchronous bursting of individual elements and collective bursting of the entire network. Collective event generation is strongly shaped by the network size. For a fixed noise intensity, sparse collective event generation is observed in large networks, while small networks exhibit rapid collective event generation. Collective bursting occurs for intermediate network sizes. The presented results contribute to a deeper understanding of the complex interplay of noise and slow feedback processes in interacting excitable systems

Phason-induced dynamics of colloidal particles on quasicrystalline substrates

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

Chemotactic success with decision making.

<p>Success probability <i>P</i>(<i>R</i>₀) for the optimal decision strategy, resulting from switching between ‘low-gain’ and ‘high-gain’ steering, as function of initial distance <i>R</i>₀ to the egg for the case of noise-free concentration measurements (A), and physiological levels of sensing noise (B) (red squares). For comparison, success probabilities for strategies without decision making are shown (circles). (C,D) Optimal decision strategies for the cases shown in panel A and B. Greyscale represents prediction frequency of ‘high-gain’ steering, using a cohort of MDPs obtained by bootstrapping, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006109#pcbi.1006109.s001" target="_blank">S1 Appendix</a> for details. Arrows and dashed lines indicate zone boundaries as introduced in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006109#pcbi.1006109.g002" target="_blank">Fig 2</a>. (E,F) Spatial sensitivity analysis of optimal strategies: Shown is the change in chemotactic range as function of cut-off distance <i>R</i>_<i>c</i> for hybrid strategies that employ the optimal strategy for <i>R</i> < <i>R</i>_<i>c</i>, and either ‘low-gain’ steering (white circles) or ‘high-gain’ steering (black circles) else. Positive values indicate a benefit of decision making at the respective distance to the egg. Parameters, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006109#pcbi.1006109.s001" target="_blank">S1 Appendix</a>.</p