Quantitative Biology

It has been classically conjectured that the brain compresses data by assigning probabilistic models to sequences of stimuli. An important issue associated to this conjecture is what class of models is used by the brain to perform its compression task. We address this issue by introducing a new statistical model selection procedure aiming to study the manner by which the brain performs data compression. Our procedure uses context tree models to represent sequences of stimuli and a new projective method for clustering EEG segments. The starting point is an experimental protocol in which EEG data is recorded while a participant is exposed to auditory stimuli generated by a stochastic chain. A simulation study using sequences of stimuli generated by two different context tree models with EEG segments generated by two distinct algorithms concludes this article.

We compute the firing rate of a leaky integrate-and-fire (LIF) neuron with stochastic conductance-based inputs in the limit when synaptic decay times are much shorter than the membrane time constant. A comparison of our analytical results to numeric simulations is presented for a range of biophysically-realistic parameters.

Previous research has shown a clear relationship between sleep and memory, examining the impact of sleep deprivation on key cognitive processes over very short durations or in special populations. Here, we show, in a longitudinal 16 week study, that naturalistic, unfettered sleep modulations in healthy adults have significant impacts on the brain. Using a dynamic networks approach combined with hierarchical statistical modelling, we show that the flexibility of particular brain regions that span a large network including regions in occipital, temporal, and frontal cortex increased when participants performed a working memory task following low sleep episodes. Critically, performance itself did not change as a function of sleep, implying adaptability in brain networks to compensate for having a poor night's sleep by recruiting the necessary resources to complete the task. We further explore whether this compensatory effect is driven by a (i) increase in the recruitment of network resources over time and/or (ii) an expansion of the network itself. Our results add to the literature linking sleep and memory, provide an analytical framework in which to investigate compensatory modulations in the brain, and highlight the brain's resilience to day-to-day fluctuations of external pressures to performance.

Epilepsy is recognised as a dynamic disease, where susceptibility to seizures and seizure characteristics change over time. Specifically, we recently found variable seizure dynamics within individual patients. Additionally, the variability appeared to follow subject-specific circadian or longer timescale modulations. However, whether signatures of these modulations over different timescales can be captured on continuous (interictal) EEG remains unclear. In this work, we analyse continuous interictal intracranial electroencephalographic (iEEG) recordings from video-telemetry units and find fluctuations in iEEG band power over different timescales ranging from minutes up to twelve days. We find that all subjects show not only an approximately-circadian fluctuation in their EEG band power, but also many other fluctuations on subject-specific timescales. Importantly, we find that a combination of fluctuations on different timescales can explain changes in seizure network evolution in a regression model in most subjects above chance level. These results suggest that subject-specific fluctuations in iEEG band power over timescales of minutes to days are associated with how seizures are modulated over time. Future work is needed to link the detected fluctuations to the exact biological time-varying processes. Understanding seizure modulating factors enables development of novel treatment strategies that minimise the seizure spread, duration, or severity and therefore clinical impact of seizures.

Objective: To identify if whole-brain structural network alterations in patients with temporal lobe epilepsy (TLE) and focal to bilateral tonic-clonic seizures (FBTCS) differ from alterations in patients without FBTCS. Methods: We dichotomized a cohort of 83 drug-resistant patients with TLE into those with and without FBTCS and compared each group to 29 healthy controls. For each subject, we used diffusion MRI to construct whole-brain structural networks. First, we measured the extent of alterations by performing FBTCS-negative (FBTCS-) versus control and FBTCS-positive (FBTCS+) versus control comparisons, thereby delineating altered sub-networks of the whole-brain structural network. Second, by standardising networks of each patient using control networks, we measured the subject-specific abnormality at every brain region in the network, thereby quantifying the spatial localisation and the amount of abnormality in every patient. Results: Both FBTCS+ and FBTCS- patient groups had altered sub-networks with reduced fractional anisotropy (FA) and increased mean diffusivity (MD) compared to controls. The altered subnetwork in FBTCS+ patients was more widespread than in FBTCS- patients (441 connections altered at t>3, p<0.001 in FBTCS+ compared to 21 connections altered at t>3, p=0.01 in FBTCS-). Significantly greater abnormalities-aggregated over the entire brain network as well as assessed at the resolution of individual brain areas-were present in FBTCS+ patients (p<0.001, d=0.82). In contrast, the fewer abnormalities present in FBTCS- patients were mainly localised to the temporal and frontal areas. Significance: The whole-brain structural network is altered to a greater and more widespread extent in patients with TLE and FBTCS. We suggest that these abnormal networks may serve as an underlying structural basis or consequence of the greater seizure spread observed in FBTCS.

We investigate how activation functions can be used to describe neural firing in an abstract way, and in turn, why they work well in artificial neural networks. We discuss how a spike in a biological neurone belongs to a particular universality class of phase transitions in statistical physics. We then show that the artificial neurone is, mathematically, a mean field model of biological neural membrane dynamics, which arises from modelling spiking as a phase transition. This allows us to treat selective neural firing in an abstract way, and formalise the role of the activation function in perceptron learning. Along with deriving this model and specifying the analogous neural case, we analyse the phase transition to understand the physics of neural network learning. Together, it is show that there is not only a biological meaning, but a physical justification, for the emergence and performance of canonical activation functions; implications for neural learning and inference are also discussed.

We propose a biologically plausible computational model of working memory (WM) implemented by the spiking neuron network (SNN) interacting with a network of astrocytes. SNN is modelled by the synaptically coupled Izhikevich neurons with a non-specific architecture connection topology. Astrocytes generating calcium signals are connected by local gap junction diffusive couplings and interact with neurons by chemicals diffused in the extracellular space. Calcium elevations occur in response to the increase of concentration of a neurotransmitter released by spiking neurons when a group of them fire coherently. In turn, gliotransmitters are released by activated astrocytes modulating the strengths of synaptic connections in the corresponding neuronal group. Input information is encoded as two-dimensional patterns of short applied current pulses stimulating neurons. The output is taken from frequencies of transient discharges of corresponding neurons. We show how a set of information patterns with quite significant overlapping areas can be uploaded into the neuron-astrocyte network and stored for several seconds. Information retrieval is organised by the application of a cue pattern representing the one from the memory set distorted by noise. We found that successful retrieval with level of the correlation between recalled pattern and ideal pattern more than 90% is possible for multi-item WM task. Having analysed the dynamical mechanism of WM formation, we discovered that astrocytes operating at a time scale of a dozen of seconds can successfully store traces of neuronal activations corresponding to information patterns. In the retrieval stage, the astrocytic network selectively modulates synaptic connections in SNN leading to the successful recall. Information and dynamical characteristics of the proposed WM model agrees with classical concepts and other WM models.

Neurons are connected to other neurons by axons and dendrites that conduct signals with finite velocities, resulting in delays between the firing of a neuron and the arrival of the resultant impulse at other neurons. Since delays greatly complicate the analytical treatment and interpretation of models, they are usually neglected or taken to be uniform, leading to a lack in the comprehension of the effects of delays in neural systems. This paper shows that heterogeneous transmission delays make small groups of neurons respond selectively to inputs with differing frequency spectra. By studying a single integrate-and-fire neuron receiving correlated time-shifted inputs, it is shown how the frequency response is linked to both the strengths and delay times of the afferent connections. The results show that incorporating delays alters the functioning of neural networks, and changes the effect that neural connections and synaptic strengths have.

Recent work in cognitive science has uncovered a diversity of explanatory values, or dimensions along which we judge explanations as better or worse. We propose a Bayesian account of how these values fit together to guide explanation. The resulting taxonomy provides a set of predictors for which explanations people prefer and shows how core values from psychology, statistics, and the philosophy of science emerge from a common mathematical framework. In addition to operationalizing the explanatory virtues associated with, for example, scientific argument-making, this framework also enables us to reinterpret the explanatory vices that drive conspiracy theories, delusions, and extremist ideologies.

This paper proposes a methodology to extract a low-dimensional integrate-and-fire model from an arbitrarily detailed single-compartment biophysical model. The method aims at relating the modulation of maximal conductance parameters in the biophysical model to the modulation of parameters in the proposed integrate-and-fire model. The approach is illustrated on two well-documented examples of cellular neuromodulation: the transition between Type I and Type II excitability and the transition between spiking and bursting.