title: Predicting and identifying signs of criticality near neuronal phase transition

authors: Chandrasiri, Malithi Eranga

abstract: This thesis examines the critical transitions between distinct neural states associated with the transition to neuron spiking and with the induction of anaesthesia. First, mathematical and electronic models of a single spiking neuron are investigated, focusing on stochastic subthreshold dynamics on close approach to spiking and to depolarisation-blocked quiescence (spiking death) transition points. Theoretical analysis of subthreshold neural behaviour then shifts to the anaesthetic-induced phase transition into unconsciousness using a mean-field model for interacting populations of excitatory and inhibitory neurons. The anaesthetic-induced changes are validated experimentally using published electrophysiological data recorded in anaesthetised rats. The criticality hypothesis associated with brain state change is examined using neuronal avalanches for experimentally recorded rat local field potential (LFP) data and mean-field pseudoLFP simulation data.

We compare three different implementations of the FitzHugh--Nagumo single spiking neuron model: a mathematical model by H. R. Wilson, an alternative due to Keener and Sneyd, and an op-amp based nonlinear oscillator circuit. Although all three models can produce nonlinear ``spiking" oscillations, our focus is on the altering characteristics of noise-induced fluctuations near spiking onset and death via Hopf bifurcation. We introduce small-amplitude white noise to enable a linearised stochastic analyses using Ornstein--Uhlenbeck theory to predict variance, power spectrum and correlation of voltage fluctuations during close approach to the critical point, identified as the point at which the real part of the dominant eigenvalue becomes zero. We validate the theoretical predictions with numerical simulations and show that the fluctuations exhibit critical slowing down divergences when approaching the critical point: power-law increases in the variance of the fluctuations simultaneous with prolongation of the system response.

We expand the study of stochastic behaviour to two spatial dimensions using the Waikato mean-field model operating near phase transition points controlled by the infusion or elimination of anaesthetic inhibition. Specifically, we investigate close approach to the critical point (CP), and to the points of loss of consciousness (LOC) and recovery of consciousness (ROC). We select the equilibrium states using $\lambda$ anaesthetic inhibition and $\Delta V^{\text{rest}}_e$ cortical excitation as control parameters, then analyse the voltage fluctuations evoked by small-amplitude spatiotemporal white noise. We predict the variance and power spectrum of voltage fluctuations near the marginally stable LOC and ROC transition points, then validate via numerical simulation. The results demonstrate a marked increase in voltage fluctuations and spectral power near transition points. This increased susceptibility to low-intensity white noise stimulation provides an early warning of impending phase transition. 

Effects of anaesthetic agents on cortical activity are reflected in local field potentials (LFPs) by the variation of amplitude and frequency in voltage fluctuations. To explore these changes, we investigate LFPs acquired from published electrophysiological experiments of anaesthetised rats to extract amplitude distribution, variance and time-correlation statistics. The analysis is broadened by applying detrended fluctuation analysis (DFA) to detect long-range dependencies in the time-series, and we compare DFA results with power spectral density (PSD). We find that the DFA exponent increases with anaesthetic concentration, but is always close to 1.

The penultimate chapter investigates the evidence of criticality in anaesthetic induced phase-transitions using avalanche analysis. Rat LFP data reveal an avalanche power-law exponent close to $\alpha = 1.5$, but this value depends on both the time-bin width chosen to separate the events and the \textit{z}-score threshold used to detect these events. Power-law behaviour is only evident at lower anaesthetic concentrations; at higher concentrations the avalanche size distribution fails to align with a power-law nature. Criticality behaviour is also indicated in the Waikato mean-field model for anaesthetic-induced phase-transition using avalanches detected from the pseudoLFP time-series, but only at the critical point (CP) and at the secondary phase-transition points of LOC and ROC.   

In summary, this thesis unveils evidence of characteristic changes near phase transition points using computer-based mathematical modelling and electrophysiological data analysis. We find that noise-driven fluctuations become larger and persist for longer as the critical point is closely approached, with similar properties being seen not only in single-neuron and neural population models, but also in biological LFP signals. These results consistent with an increase of susceptibility to noise perturbations near phase transition point. Identification of neuronal avalanches in rat LFP data for low anaesthetic concentrations provides further support for the criticality hypothesis.

text: Predicting and identifying signs of criticality near neuronal phase transition This thesis examines the critical transitions between distinct neural states associated with the transition to neuron spiking and with the induction of anaesthesia. First, mathematical and electronic models of a single spiking neuron are investigated, focusing on stochastic subthreshold dynamics on close approach to spiking and to depolarisation-blocked quiescence (spiking death) transition points. Theoretical analysis of subthreshold neural behaviour then shifts to the anaesthetic-induced phase transition into unconsciousness using a mean-field model for interacting populations of excitatory and inhibitory neurons. The anaesthetic-induced changes are validated experimentally using published electrophysiological data recorded in anaesthetised rats. The criticality hypothesis associated with brain state change is examined using neuronal avalanches for experimentally recorded rat local field potential (LFP) data and mean-field pseudoLFP simulation data.

We compare three different implementations of the FitzHugh--Nagumo single spiking neuron model: a mathematical model by H. R. Wilson, an alternative due to Keener and Sneyd, and an op-amp based nonlinear oscillator circuit. Although all three models can produce nonlinear ``spiking" oscillations, our focus is on the altering characteristics of noise-induced fluctuations near spiking onset and death via Hopf bifurcation. We introduce small-amplitude white noise to enable a linearised stochastic analyses using Ornstein--Uhlenbeck theory to predict variance, power spectrum and correlation of voltage fluctuations during close approach to the critical point, identified as the point at which the real part of the dominant eigenvalue becomes zero. We validate the theoretical predictions with numerical simulations and show that the fluctuations exhibit critical slowing down divergences when approaching the critical point: power-law increases in the variance of the fluctuations simultaneous with prolongation of the system response.

We expand the study of stochastic behaviour to two spatial dimensions using the Waikato mean-field model operating near phase transition points controlled by the infusion or elimination of anaesthetic inhibition. Specifically, we investigate close approach to the critical point (CP), and to the points of loss of consciousness (LOC) and recovery of consciousness (ROC). We select the equilibrium states using $\lambda$ anaesthetic inhibition and $\Delta V^{\text{rest}}_e$ cortical excitation as control parameters, then analyse the voltage fluctuations evoked by small-amplitude spatiotemporal white noise. We predict the variance and power spectrum of voltage fluctuations near the marginally stable LOC and ROC transition points, then validate via numerical simulation. The results demonstrate a marked increase in voltage fluctuations and spectral power near transition points. This increased susceptibility to low-intensity white noise stimulation provides an early warning of impending phase transition. 

Effects of anaesthetic agents on cortical activity are reflected in local field potentials (LFPs) by the variation of amplitude and frequency in voltage fluctuations. To explore these changes, we investigate LFPs acquired from published electrophysiological experiments of anaesthetised rats to extract amplitude distribution, variance and time-correlation statistics. The analysis is broadened by applying detrended fluctuation analysis (DFA) to detect long-range dependencies in the time-series, and we compare DFA results with power spectral density (PSD). We find that the DFA exponent increases with anaesthetic concentration, but is always close to 1.

The penultimate chapter investigates the evidence of criticality in anaesthetic induced phase-transitions using avalanche analysis. Rat LFP data reveal an avalanche power-law exponent close to $\alpha = 1.5$, but this value depends on both the time-bin width chosen to separate the events and the \textit{z}-score threshold used to detect these events. Power-law behaviour is only evident at lower anaesthetic concentrations; at higher concentrations the avalanche size distribution fails to align with a power-law nature. Criticality behaviour is also indicated in the Waikato mean-field model for anaesthetic-induced phase-transition using avalanches detected from the pseudoLFP time-series, but only at the critical point (CP) and at the secondary phase-transition points of LOC and ROC.   

In summary, this thesis unveils evidence of characteristic changes near phase transition points using computer-based mathematical modelling and electrophysiological data analysis. We find that noise-driven fluctuations become larger and persist for longer as the critical point is closely approached, with similar properties being seen not only in single-neuron and neural population models, but also in biological LFP signals. These results consistent with an increase of susceptibility to noise perturbations near phase transition point. Identification of neuronal avalanches in rat LFP data for low anaesthetic concentrations provides further support for the criticality hypothesis.

year: 2020

title: Analysis of Nucleosides and Nucleotides in Milk and Infant Formula

authors: Gill, Brendon D.

subjects: Nucleotide

abstract: Nucleotides have been routinely supplemented to infant formulas due to the important roles they play in metabolism and to replicate the higher concentrations typically found in human milk.  A method utilising anion exchange solid-phase extraction clean-up and liquid chromatography was developed for the rapid, routine determination of supplemented cytidine 5′ monophosphate, uridine 5′ monophosphate, inosine 5′ monophosphate, guanosine 5′ monophosphate, and adenosine 5′ monophosphate in bovine milk-based infant formula.  Chromatographic analyses were performed using a C18 stationary phase with gradient elution, UV detection, and quantitation by an internal standard technique.  A single-laboratory validation was performed, with recoveries of 92–101% and repeatability of 1.0–2.3%.  An extension study demonstrated the expansion in scope to a wider range of different infant formula products including milk protein and hydrolysate-based products, low and high fat products, soy protein-based and elemental products, adult nutritional and infant formulations, in both ready-to-feed and powder forms.
The development of a method to measure the total potentially available nucleosides (TPAN) in human milk has made an important contribution to further understanding the distribution of nucleosides and nucleotides.  This method was applied in a lactation study of bovine milk with colostrum and milk samples collected from two herds over the course of the first month post-partum, pooled within each herd by stage of lactation and the TPAN concentrations were determined.  Sample analysis consisted of parallel enzymatic treatments, phenylboronate affinity gel extraction, and liquid chromatography to quantify contributions of nucleosides, monomeric nucleotides, nucleotide adducts, and polymeric nucleotides to the nutritionally available nucleoside pool.  Bovine colostrum contained high levels of nucleosides and monomeric nucleotides, which rapidly decreased as lactation progressed into transitional milk.  Mature milk was relatively consistent in nucleoside and monomeric nucleotide concentrations from approximately the tenth day post-partum.  Differences in concentrations between summer-milk and winter-milk herds were largely attributable to variability in uridine and monomeric nucleotide concentrations.
The TPAN method was subsequently applied to the analysis of mature bovine, caprine, and ovine milk.  The contributions to TPAN from polymeric nucleotides, monomeric nucleotides, and nucleotide adducts were then calculated.  Ovine milk contained the highest concentration of TPAN (374.1 µmol dL-1), with lower concentrations in caprine milk (97.4 µmol dL-1) and bovine milk (7.9 µmol dL-1).  Ovine milk contained the highest concentrations of each of the different nucleoside and nucleotide forms, and bovine milk contained the lowest.
A method for the simultaneous analysis of nucleosides and nucleotides in infant formula using reversed-phase liquid chromatography-tandem mass spectrometry was developed.  Following sample dissolution, protein was removed by centrifugal ultrafiltration.  Chromatographic analyses were performed using a C18 stationary phase and gradient elution, with mass spectrometric detection, and quantitation by stable isotope labelled internal standard technique.  A single laboratory validation study was performed with recoveries of 80.1–112.9% and repeatability relative standard deviations of 1.9–7.2%.  The method was validated for the analysis of bovine milk-based, soy-based, caprine milk-based and hydrolysate-based infant formula.

text: Analysis of Nucleosides and Nucleotides in Milk and Infant Formula Nucleotides have been routinely supplemented to infant formulas due to the important roles they play in metabolism and to replicate the higher concentrations typically found in human milk.  A method utilising anion exchange solid-phase extraction clean-up and liquid chromatography was developed for the rapid, routine determination of supplemented cytidine 5′ monophosphate, uridine 5′ monophosphate, inosine 5′ monophosphate, guanosine 5′ monophosphate, and adenosine 5′ monophosphate in bovine milk-based infant formula.  Chromatographic analyses were performed using a C18 stationary phase with gradient elution, UV detection, and quantitation by an internal standard technique.  A single-laboratory validation was performed, with recoveries of 92–101% and repeatability of 1.0–2.3%.  An extension study demonstrated the expansion in scope to a wider range of different infant formula products including milk protein and hydrolysate-based products, low and high fat products, soy protein-based and elemental products, adult nutritional and infant formulations, in both ready-to-feed and powder forms.
The development of a method to measure the total potentially available nucleosides (TPAN) in human milk has made an important contribution to further understanding the distribution of nucleosides and nucleotides.  This method was applied in a lactation study of bovine milk with colostrum and milk samples collected from two herds over the course of the first month post-partum, pooled within each herd by stage of lactation and the TPAN concentrations were determined.  Sample analysis consisted of parallel enzymatic treatments, phenylboronate affinity gel extraction, and liquid chromatography to quantify contributions of nucleosides, monomeric nucleotides, nucleotide adducts, and polymeric nucleotides to the nutritionally available nucleoside pool.  Bovine colostrum contained high levels of nucleosides and monomeric nucleotides, which rapidly decreased as lactation progressed into transitional milk.  Mature milk was relatively consistent in nucleoside and monomeric nucleotide concentrations from approximately the tenth day post-partum.  Differences in concentrations between summer-milk and winter-milk herds were largely attributable to variability in uridine and monomeric nucleotide concentrations.
The TPAN method was subsequently applied to the analysis of mature bovine, caprine, and ovine milk.  The contributions to TPAN from polymeric nucleotides, monomeric nucleotides, and nucleotide adducts were then calculated.  Ovine milk contained the highest concentration of TPAN (374.1 µmol dL-1), with lower concentrations in caprine milk (97.4 µmol dL-1) and bovine milk (7.9 µmol dL-1).  Ovine milk contained the highest concentrations of each of the different nucleoside and nucleotide forms, and bovine milk contained the lowest.
A method for the simultaneous analysis of nucleosides and nucleotides in infant formula using reversed-phase liquid chromatography-tandem mass spectrometry was developed.  Following sample dissolution, protein was removed by centrifugal ultrafiltration.  Chromatographic analyses were performed using a C18 stationary phase and gradient elution, with mass spectrometric detection, and quantitation by stable isotope labelled internal standard technique.  A single laboratory validation study was performed with recoveries of 80.1–112.9% and repeatability relative standard deviations of 1.9–7.2%.  The method was validated for the analysis of bovine milk-based, soy-based, caprine milk-based and hydrolysate-based infant formula.

year: 2013

title: Birds vs. Clams: Assessing the impacts of South Island pied oystercatcher predation on Toheroa at Ripiro Beach, New Zealand

authors: Vallyon, Lolita-Maria Dolores

abstract: Managing the recovery of interacting species, such as predator and prey, is one of the most challenging factors of an ecosystem-based conservation approach. The actions taken to protect one species may be in conflict with the actions necessary to protect another. For example, the recovery of a predator in an ecosystem can lead to a significant conservation conflict between the protected predator and its protected prey. In these instances, research is required to determine whether a perceived conflict is in fact happening in order to inform proper management decisions. In New Zealand, a conservation conflict exists between an endemic, recovering shorebird, the South Island pied oystercatcher (Haematopus ostralegus finschi), and an endemic surf clam, the toheroa (Paphies ventricosa) at Ripiro Beach, Northland. The toheroa was overharvested until the populations collapsed, with commercial and recreational harvesting bans put in place by the 1970s. The toheroa has continued to decline, and the cause is currently unknown. Oystercatcher predation has been implicated as the reason toheroa populations have not recovered. There have even been calls to cull the birds to protect the clams. Currently, there is no information that would facilitate conservation management in determining the appropriate action to take. My thesis aimed to investigate the claims surrounding this perceived interspecific conflict. It sought to examine the predator-prey interactions between the two species by answering the following three questions: 1) what are the spatio-temporal associations between oystercatchers and toheroa, 2) what is the composition of the oystercatcher’s diet, and 3) what size toheroa are the birds taking? 
Bird surveys were conducted to examine the distribution of oystercatchers monthly from March 2019 to February 2020. Oystercatcher foraging behaviour was observed to collect information on prey type and prey location. Feeding holes left by oystercatcher bills at predation sites were examined to determine oystercatcher predation success. A population survey was conducted on toheroa beds exposed to oystercatcher predation versus control beds to assess if there were differences in the density and size structure between toheroa populations. 

Results did not support the hypothesis that the oystercatchers are the cause behind the limited recovery of the toheroa, but they did indicate that the birds may be having localised impacts. There was limited overlap with toheroa, as the birds were found predominantly at the southern half of Ripiro Beach and were only associated with two major toheroa beds. Observations found that bivalves are a significant food resource for oystercatchers and the birds have a high predation success rate. There was a significant difference in the density and size structure between toheroa populations in beds that were oystercatcher predation sites and those at no-predation sites. However, even in the areas with the most intense oystercatcher predation, toheroa have persisted over time. While there potentially is a small local impact, overall, the South Island pied oystercatcher is not responsible for the continuing decline of the toheroa across the whole of Ripiro Beach and are not causing devastation as claimed. 
The perceived conservation conflict between the two endemic species is likely incorrect. This research demonstrates the importance of acquiring information on interacting species prior to management action to protect one of those species. Information presented in this thesis can be used to support conservation managers in making informed decisions to protect both the toheroa and the South Island pied oystercatcher.

text: Birds vs. Clams: Assessing the impacts of South Island pied oystercatcher predation on Toheroa at Ripiro Beach, New Zealand Managing the recovery of interacting species, such as predator and prey, is one of the most challenging factors of an ecosystem-based conservation approach. The actions taken to protect one species may be in conflict with the actions necessary to protect another. For example, the recovery of a predator in an ecosystem can lead to a significant conservation conflict between the protected predator and its protected prey. In these instances, research is required to determine whether a perceived conflict is in fact happening in order to inform proper management decisions. In New Zealand, a conservation conflict exists between an endemic, recovering shorebird, the South Island pied oystercatcher (Haematopus ostralegus finschi), and an endemic surf clam, the toheroa (Paphies ventricosa) at Ripiro Beach, Northland. The toheroa was overharvested until the populations collapsed, with commercial and recreational harvesting bans put in place by the 1970s. The toheroa has continued to decline, and the cause is currently unknown. Oystercatcher predation has been implicated as the reason toheroa populations have not recovered. There have even been calls to cull the birds to protect the clams. Currently, there is no information that would facilitate conservation management in determining the appropriate action to take. My thesis aimed to investigate the claims surrounding this perceived interspecific conflict. It sought to examine the predator-prey interactions between the two species by answering the following three questions: 1) what are the spatio-temporal associations between oystercatchers and toheroa, 2) what is the composition of the oystercatcher’s diet, and 3) what size toheroa are the birds taking? 
Bird surveys were conducted to examine the distribution of oystercatchers monthly from March 2019 to February 2020. Oystercatcher foraging behaviour was observed to collect information on prey type and prey location. Feeding holes left by oystercatcher bills at predation sites were examined to determine oystercatcher predation success. A population survey was conducted on toheroa beds exposed to oystercatcher predation versus control beds to assess if there were differences in the density and size structure between toheroa populations. 

Results did not support the hypothesis that the oystercatchers are the cause behind the limited recovery of the toheroa, but they did indicate that the birds may be having localised impacts. There was limited overlap with toheroa, as the birds were found predominantly at the southern half of Ripiro Beach and were only associated with two major toheroa beds. Observations found that bivalves are a significant food resource for oystercatchers and the birds have a high predation success rate. There was a significant difference in the density and size structure between toheroa populations in beds that were oystercatcher predation sites and those at no-predation sites. However, even in the areas with the most intense oystercatcher predation, toheroa have persisted over time. While there potentially is a small local impact, overall, the South Island pied oystercatcher is not responsible for the continuing decline of the toheroa across the whole of Ripiro Beach and are not causing devastation as claimed. 
The perceived conservation conflict between the two endemic species is likely incorrect. This research demonstrates the importance of acquiring information on interacting species prior to management action to protect one of those species. Information presented in this thesis can be used to support conservation managers in making informed decisions to protect both the toheroa and the South Island pied oystercatcher.

year: 2020