Abstract: The transport of organelles and proteins is of vital importance for living cells. Besides passive transport by diffusion, active transport by molecular motors hopping over the cytoskeleton network is crucial for the survival of cells. We performed simulations using the Totally Asymmetric Exclusion Process (TASEP), a paradigmatic model for nonequilibrium transport, to model the dynamics along the complex microtubule network. We found that the rules at the intersection of the network seem to be the key factor for the formation of traffic jams along the microtubule segments. The rate at which motors at crossing continue along the same microtubule or switch to the other microtubule appears to determine for the transport along the network. Our simulations of the microtubule network reveal surprisingly rich behavior of the transport current with respect to the global density and exit rate ratio. We found four different regimes of motor propagation through network depending on the average motor density. For example, for low densities the current/density distribution through the network can be linearized and solved exactly. In contrast, for medium global densities the motor distribution through the network becomes highly inhomogeneous and non-linear leading to a huge reduction of the transport current through the system, when larger part of the network will be in ‘virtual’ traffic jam. We have also found a broad plateau of the current at the intermediate motor densities leading to stabilization of transport properties within such networks [1]. Due to the generality of the exclusion process in modeling transport and arrest phenomena, our results may provide generic insights into traffic jams and transport capacities of highway networks, biological networks, and other systems with similar unidirectional topology. [1] D. V. Denisov, D. M. Miedema, B. Nienhuis, and P. Schall, Phys. Rev. E 92, 052714 (2015).

Abstract: Competition for resources in biological context bears a resemblance to auction mechanisms, many agents compete but only a few (or only one) get the reward. But contrary to the well-studied auction models in economy, a reasonable assumption in this context is that everybody (not only the winner) pays their bid, e.g. time/energy invested to endure a conflict or foraging food. Following the work of Chatterjee et al. 2012, we look at the k-player all pay auctions searching for the states evolution might favour. We analyse these systems with an associated birth-death process governed by agent’s strategy success in the repeated interactions modeled as k-player all-pay auctions. In the large population limit, when the stochasticity can be neglected, we derive replicator equations whose fixed points are previously found Evolutionary Stable Strategies for these games. However, in previous works cycles were also noted that could not be explained at the level of deterministic description. We thus introduce back the stochasticity (the diffusion approximation) and the intrinsic noise, as we show, gives rise to the cyclic dynamics. We observe that the cycles are more present when the bidding strategy space is smaller, and when the number of participants in an auction (k) is small. As this description can be extended to the continuous strategy space, we find out that except for the 2-player auctions, cycles are property of games with discrete strategy space. Chatterjee, K., Reiter, J. G., Nowak, M. A., 2012. Evolutionary dynamics of biological auctions. Theoretical Population Biology, 81: 69-80.

Abstract: Neurodegenerative diseases, such as Alzheimer and Parkinson, are more common in western countries due to the longer expectation of life and the design of reliable tests for their early detection is becoming a pressing challenge. Several neurological disorders are associated with the aggregation of aberrant proteins, often localized in intracellular organelles such as the endoplasmic reticulum. We have studied protein aggregation kinetics and developed a model to follow the evolution of the aggregation and the critical role played by the cell endoplasmic reticulum. Moreover, since another important question is to be able to analyze protein aggregation in micron-scale samples but reproducible results are still hard to achieve, we have developed a strategy to quantify in silico the statistical errors associated to the detection of aggregation-prone samples. Alltogether, our work opens a new perspective on the understanding of these pathologies and on the forecasting of protein aggregation in asymptomatic subjects.

Abstract: The mesoscopic structure of complex brain networks is the key intermediate level of organisation bridging the microscopic dynamics of individual neurons with the macroscopic dynamics of the brain as a whole. At this mesoscopic level, brain activity tends to be organized in a modular way, with functionally related units being positively correlated with each other, while at the same time being relatively less (or even negatively) correlated with dissimilar ones. Such emergent organisation is mainly detected through the measurement of cross-correlations among time series of brain activity, the projection (usually via an arbitrary threshold) of these correlations to a network, and the subsequent search for denser modules (or so-called communities) in the network. It is well known that this approach suffers from an unavoidable information loss induced by the thresholding procedure. Another, less realized, limitation is the bias introduced by the use of network-based (as opposed to correlation-based) community detection methods. Here we discuss an improved method for the identification of functional brain modules based on random matrix theory. Our method is threshold-free, correlation-based, and very powerful in filtering out both local unit-specific noise and global system-wide dependencies. The approach is guaranteed to identify mesoscopic functional modules that, relative to the global signal, have an overall positive internal correlation and negative mutual correlation. We apply our method to time series of individual neurons in several samples of the suprachiasmatic nucleus (SCN) of mice, a small pacemaker region where strong spatial and temporal dependencies make the identification of substructure particularly challenging. We systematically detect two main functional modules, core and periphery, which are perfectly anti-correlated once the strong global signal is filtered out. These modules turn out to largely correspond to neuron populations with true biological differences, e.g. in the neurotransmitters used and in their coupling and synchronisation properties.

Abstract: The circadian clock in the suprachiasmatic nucleus (SCN), located in the hypothalamus in the brain, is important for the regulation of our daily and seasonal rhythms. It has been shown that the neuronal network organization of the SCN changes in different seasons, however, the mechanisms behind these changes are far from elusive. Furthermore, only a subset of neurons within the SCN network are directly responsive to light, which poses the question how encoding for seasons is achieved in the SCN network. Currently, not much is known about the function of the regional heterogeneity in the SCN in seasonal adaptation. Using time series of single cells we have applied a new community detection method to identify communities of cells in winter and summer conditions. This impartial method detected mostly two communities which we mapped to the SCN neuronal network and further characterized in their functional significance. Anterior regions encode for more phase dispersion, while posterior regions encode for more phase synchrony. Within the anterior SCN, the cells in the dorso-lateral region show more variability in their oscillatory periods in summer conditions, which means that these cells are more weakly coupled, enabling higher phase dispersion among the cells. Ventro-medially located cells in the anterior SCN and cells in the posterior SCN are more rigid in their oscillatory behaviour. This suggests that the cells in the dorso-lateral anterior region of the SCN play an active role in the phase adjustments of the SCN cells in different seasons. Our new network analysis approach enhances the identification and the subsequent functional characterization of neuronal clusters in the SCN, possibly paving the way for more elaborate network analysis on the level of single-cells in other brain regions.

Abstract: BrainX3 is a large-scale simulation of human brain activity with real-time interaction, rendered in 3D in a virtual reality environment, which combines computational power with human intuition for the exploration and analysis of complex dynamical networks. We ground this simulation on structural connectivity obtained from diffusion spectrum imaging data and model it on neuronal population dynamics. Users can interact with BrainX3 in real-time by perturbing brain regions with transient stimulations to observe reverberating network activity, simulate lesion dynamics or implement network analysis functions from a library of graph theoretic measures. BrainX3 can thus be used as a novel immersive platform for exploration and analysis of dynamical activity patterns in brain networks, both at rest or in a task-related state, for discovery of signaling pathways associated to brain function and/or dysfunction and as a tool for virtual neurosurgery. Our results demonstrate these functionalities and shed insight on the dynamics of the resting-state attractor. Specifically, we found that a noisy network seems to favor a low firing attractor state. We also found that the dynamics of a noisy network is less resilient to lesions. Our simulations on TMS perturbations show that even though TMS inhibits most of the network, it also sparsely excites a few regions. This is presumably due to anti-correlations in the dynamics and suggests that even a lesioned network can show sparsely distributed increased activity compared to healthy resting-state, over specific brain areas.