Beyond spike timing: the role of nonlinear plasticity and unreliable synapses

 Spike-timing-dependent plasticity (STDP) strengthens synapses that are activated immediately before a postsynaptic spike, and weakens those that are activated after a spike. To prevent an uncontrolled growth of the synaptic strengths, weakening must dominate strengthening for uncorrelated spike times. However, this weight-normalization property would preclude Hebbian potentiation when the pre- and postsynaptic neurons are strongly active without specific spike-time correlations. We show that nonlinear STDP as inherent in the data of Markram et al. [(1997) Science 275:213–215] can preserve the benefits of both weight normalization and Hebbian plasticity, and hence can account for learning based on spike-time correlations and on mean firing rates. As examples we consider the moving-threshold property of the Bienenstock–Cooper–Munro rule, the development of direction-selective simple cells by changing short-term synaptic depression, and the joint adaptation of axonal and dendritic delays. Without threshold nonlinearity at low frequencies, the development of direction selectivity does not stabilize in a natural stimulation environment. Without synaptic unreliability there is no causal development of axonal and dendritic delays. Received: 22 April 2002 / Accepted: 23 May 2002 Acknowledgements. This study was supported by the Swiss National Science Foundation (grant 3152-065234.01) and the Silva-Casa foundation. The author thanks Stefano Fusi, Henry Markram, and Misha Tsodyks for helpful discussions, Nissim Buchs and Martin Schneider for their simulations, and Jan Reutimann for proof reading. Correspondence to: e-mail: wsenn@cns.unibe.ch, Tel.: +41-31-6318721, Fax: 41-31-6314611     

Self-influencing synaptic plasticity: Recurrent changes of synaptic weights can lead to specific functional properties

Recent experimental results suggest that dendritic and back-propagating spikes can influence synaptic plasticity in different ways (Holthoff, 2004; Holthoff et al., 2005). In this study we investigate how these signals could interact at dendrites in space and time leading to changing plasticity properties at local synapse clusters. Similar to a previous study (Saudargiene et al., 2004) we employ a differential Hebbian learning rule to emulate spike-timing dependent plasticity and investigate how the interaction of dendritic and back-propagating spikes, as the post-synaptic signals, could influence plasticity. Specifically, we will show that local synaptic plasticity driven by spatially confined dendritic spikes can lead to the emergence of synaptic clusters with different properties. If one of these clusters can drive the neuron into spiking, plasticity may change and the now arising global influence of a back-propagating spike can lead to a further segregation of the clusters and possibly the dying-off of some of them leading to more functional specificity. These results suggest that through plasticity being a spatial and temporal local process, the computational properties of dendrites or complete neurons can be substantially augmented. Action Editor: Wulfram Gerstner     

Mathematical formulations of Hebbian learning

 Several formulations of correlation-based Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backpropagating action potentials (BPAPs). It is shown that all of the above formulations can be derived from the point of view of an expansion. In the absence of BPAPs, it is natural to correlate presynaptic spikes with the postsynaptic membrane potential. Time windows of spike-time-dependent plasticity arise naturally if the timing of postsynaptic spikes is available at the site of the synapse, as is the case in the presence of BPAPs. With an appropriate choice of parameters, Hebbian synaptic plasticity has intrinsic normalization properties that stabilizes postsynaptic firing rates and leads to subtractive weight normalization. Received: 1 February 2002 / Accepted: 28 March 2002 Correspondence to: W. Gerstner (e-mail: wulfram.gerstner@epfl.ch, Tel.: +41-21-6936713, Fax: +41-21-6935263)     

Spike propagation synchronized by temporally asymmetric Hebbian learning

 Synchronously spiking neurons have been observed in the cerebral cortex and the hippocampus. In computer models, synchronous spike volleys may be propagated across appropriately connected neuron populations. However, it is unclear how the appropriate synaptic connectivity is set up during development and maintained during adult learning. We performed computer simulations to investigate the influence of temporally asymmetric Hebbian synaptic plasticity on the propagation of spike volleys. In addition to feedforward connections, recurrent connections were included between and within neuron populations and spike transmission delays varied due to axonal, synaptic and dendritic transmission. We found that repeated presentations of input volleys decreased the synaptic conductances of intragroup and feedback connections while synaptic conductances of feedforward connections with short delays became stronger than those of connections with longer delays. These adaptations led to the synchronization of spike volleys as they propagated across neuron populations. The findings suggests that temporally asymmetric Hebbian learning may enhance synchronized spiking within small populations of neurons in cortical and hippocampal areas and familiar stimuli may produce synchronized spike volleys that are rapidly propagated across neural tissue. Received: 28 May 2002 / Accepted: 3 June 2002 RID="*" ID="*" Correspondence to: R. E. Suri Intelligent Optical Systems (IOS), 2520 W 237th St, Torrance, CA 90505-5217, USA (e-mail: rsuri@intopsys.com, Tel.: +1-310-5307130 ext. 108, Fax: +1-210-5307417)     

Kinetics of anaerobic biodegradation of glycerol by sulfate-reducing bacteria

A kinetic model has been developed and kinetic parameters of anaerobic degradation of glycerol, an abundant by-product of biofuel manufacturing, by a consortium of sulfate reducing bacteria (SRB) in a closed system have been determined. The following main species of SRB has been identified in the consortium: Desulfovibrio baarsii, Desulfomicrobium sp., and Desufatomaculum sp. The proposed model included processes of glycerol degradation, sulfate reduction, and inhibition by metabolic products, as well as effects of pH and temperature. The suggested equation for the anaerobic glycerol degradation was based on Edward and Andrew’s equation. The following kinetic parameters of the anaerobic glycerol degradation were obtained for the initial glycerol concentration from 0.15 to 4 ml/l and sulfate concentration of 2760 mg/l at 22°C: maximum specific growth rate of SRB μ_max = 0.56 day⁻¹, economic coefficient of ashless biomass from glycerol of 0.08 mol SRB/mol COC, and yield of ashless biomass from sulfate of 0.020 mol SRB/mol SO₄. It was shown that the optimum molar ratio of $ {{C_{Gl} } \mathord{\left/ {\vphantom {{C_{Gl} } {C_{SO_4 } }}} \right. \kern-\nulldelimiterspace} {C_{SO_4 } }} $ {{C_{Gl} } \mathord{\left/ {\vphantom {{C_{Gl} } {C_{SO_4 } }}} \right. \kern-\nulldelimiterspace} {C_{SO_4 } }} for SRB growth was 0.8. Initial boundary concentration of inhibition by undissociated hydrogen sulfide was 70 mg/l. Dependence of the specific growth rate of bacteria on the temperature was approximated by the Arrhenius equation in the temperature range of 20–30°C with the goodness of fit R² = 0.99.     

In Situ pH Measurement in Partly Frozen Aqueous Solution Using the Fluorescent Probe 8-Hydroxypyrene-1,3,6-Trisulfonic Acid

A method based on the fluorescence probe 8-hydroxypyrene-1,3,6-trisulfonic acid for in situ measurement of pH in partly frozen aqueous solutions was developed using multifrequency, phase-modulated fluorescence spectroscopy inherently correcting for light scattering. The probe was determined to have pK _a = 7.72 ± 0.03 at 25.0 °C extrapolated to zero ionic strength with as derived from temperature dependence (5 to 25 °C investigated). Ionic strength dependence of pK _a determined experimentally was described using Debye–Hückel formalism for ionic strength up to 3 M. Temperature and ionic strength dependence were combined to yield for determination of pH at subzero temperatures with α experimentally determined from the ratio between fluorescence intensity after excitation at 454 and 415 nm, α = FI(454 nm)/2.5·FI(415 nm). Fluorescence could be described as a decay of a single excited state with a fluorescence life time of 5.40 ± 0.05 ns at 25 °C, and excited state acid–base equilibration was shown not to interfere with the pH measurement. Using the method, pH of a 0.25 M phosphate buffer with pH = 6.8 at 25 °C was shown to decrease gradually to pH = 4.2 in the ice slurry at −13 °C.     

Heterogeneous organ models

A theoretical study is made of three organ flow models with heterogeneity of capillary transit times. A new parametrization of Rose and Goresky's Model III facilitates in many cases a reduction to Goresky's Model II, accomplished by a special time shift. The shift parameter defined here is critical in this analysis of Model III. A new expression of the series for outflow concentration in Model III is given and proves useful in examining the model as an operator and in relating it to Models I and II. A result on parameter optimization is given: if then Model III cannot fit better than Model II. This is applied to some data from Rose and Goresky [Circulation Res. 39, 541–544 (1976)] and raises a new question about their model. A heart model of Levin and Bassingthwaighte based on regional flow measurement is shown to be a discretized generalization of Model II. This work supported in part by PHS Grant Nos. HL-19153 (SCOR for Pulmonary Vascular Disease) and HL-19370 at Vanderbilt University.     

Self-thinning lines of organs and aboveground parts based on allometric relationships in overcrowded Pinus densiflora stands

The allometric relationships of mean tree height [`(H)]( μ [`(w)]_x^q ) \bar{H}( \propto \bar{w}_{\rm {x}}^{\theta } ) and of organ mass density [`(d)]<sub>x</sub> ( μ [`(w)]_x^d ) \bar{d}_{\rm {x}} ( \propto \bar{w}_{\rm {x}}^{\delta } ) to mean organ mass [`(w)]_x \bar{w}_{\rm {x}} were studied in self-thinning Pinus densiflora Sieb. et Zucc. stands. Tree height increased significantly with increasing mean mass of organs and aboveground parts on log–log coordinates. The value of the allometric constant θ ranged from 0.2878 to 0.3349. On the other hand, the constant value δ was not significantly different from zero, except for leaves. The value of the allometric constant δ ranged from −0.2926 to 0.0120. According to Weller’s allometric model, the slope of the self-thinning line was calculated from the allometric constants θ and δ. The thinning slope was estimated to be −1.51 in stem, −1.39 in branches, −1.00 in leaf and −1.41 in aboveground parts, respectively. Mass density was high in stem, medium in branches and low in leaves. Mean leaf mass density decreased significantly with decreasing stand density on log–log coordinates, which could be interpreted as indicating the importance of the constant final leaf biomass in overcrowded P. densiflora stands. The self-thinning exponents of branch, stem and aboveground parts were not significantly different from 3/2, which indicated that the 3/2 power law of self-thinning holds for stem mass, branch mass and aboveground mass in overcrowded P. densiflora stands.     

On the derivation of a mean growth equation for cell cultures

IfN(t) is the expected number of cells in a culture at timet, the corresponding time derivative, andf(t−τ)dt the probability that a cell of aget−τ at timet will divide in the succeeding time intervaldt, then according to Hirsch and Engelberg (this issue) there obtains the integral equation for describing the dynamics of the cell population. It is the purpose of this note to give two alternative derivations of this equation, one based on the age density equation of Von Foerster, and the other based on a generalized form of the Harris-Bellman equation describing the first moment of an age dependent, branching process. In addition, a probability model is posed from which the Von Foerster equation and, hence, the Hirsch-Engelberg equation readily follows.     

Modeling Optimal Age-Specific Vaccination Strategies Against Pandemic Influenza

In the context of pandemic influenza, the prompt and effective implementation of control measures is of great concern for public health officials around the world. In particular, the role of vaccination should be considered as part of any pandemic preparedness plan. The timely production and efficient distribution of pandemic influenza vaccines are important factors to consider in mitigating the morbidity and mortality impact of an influenza pandemic, particularly for those individuals at highest risk of developing severe disease. In this paper, we use a mathematical model that incorporates age-structured transmission dynamics of influenza to evaluate optimal vaccination strategies in the epidemiological context of the Spring 2009 A (H1N1) pandemic in Mexico. We extend previous work on age-specific vaccination strategies to time-dependent optimal vaccination policies by solving an optimal control problem with the aim of minimizing the number of infected individuals over the course of a single pandemic wave. Optimal vaccination policies are computed and analyzed under different vaccination coverages (21%–77%) and different transmissibility levels (R₀\mathcal{R}_{0} in the range of 1.8–3). The results suggest that the optimal vaccination can be achieved by allocating most vaccines to young adults (20–39 yr) followed by school age children (6–12 yr) when the vaccination coverage does not exceed 30%. For higher R₀\mathcal{R}_{0} levels ($\mathcal{R}_{0}>=2.4$\mathcal{R}_{0}>=2.4), or a time delay in the implementation of vaccination (>90 days), a quick and substantial decrease in the pool of susceptibles would require the implementation of an intensive vaccination protocol within a shorter period of time. Our results indicate that optimal age-specific vaccination rates are significantly associated with R₀\mathcal{R}_{0}, the amount of vaccines available and the timing of vaccination.     

Capacity analysis in multi-state synaptic models: a retrieval probability perspective

We define the memory capacity of networks of binary neurons with finite-state synapses in terms of retrieval probabilities of learned patterns under standard asynchronous dynamics with a predetermined threshold. The threshold is set to control the proportion of non-selective neurons that fire. An optimal inhibition level is chosen to stabilize network behavior. For any local learning rule we provide a computationally efficient and highly accurate approximation to the retrieval probability of a pattern as a function of its age. The method is applied to the sequential models (Fusi and Abbott, Nat Neurosci 10:485–493, 2007) and meta-plasticity models (Fusi et al., Neuron 45(4):599–611, 2005; Leibold and Kempter, Cereb Cortex 18:67–77, 2008). We show that as the number of synaptic states increases, the capacity, as defined here, either plateaus or decreases. In the few cases where multi-state models exceed the capacity of binary synapse models the improvement is small.     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

Modification of the data-processing method for the turbidimetric bioassay of nisin

The data processing method of the turbidimetric bioassay of nisin was modified to facilitate its industrial application. The influence of the initial indicator concentration was minimized by a redefined specific dose of the bacteriocin as the quotient between the titer of the added bacteriocin and the initial population density of the indicator in the suspension. It was found that d _c = 0.125 μg ml⁻¹ was the critical dose of nisin that can cause a complete inhibition of the indicator, Pediococcus acidilactici UL5, with an initial OD of 0.135. To eliminate the interference of the cell debris, an equation, , exploiting d _c, was formulated to obtain the intrinsic survival proportion. The use of the specific dose of the bacteriocin and the intrinsic survival proportion as parameters of the dose/response curve greatly enhanced its repeatability and feasibility. A dual-dosage approach was developed to further simplify the conventional standard dose/response curve method.     

Stability of differential susceptibility and infectivity epidemic models

We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R₀ ￡ 1{\mathcal{R}_0 \leq 1} and the existence and uniqueness of an endemic equilibrium when ${\mathcal{R}_0 >1 }${\mathcal{R}_0 >1 } . We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when ${\mathcal{R}_0 >1 }${\mathcal{R}_0 >1 } . Our results encompass and generalize those of Hyman and Li (J Math Biol 50:626–644, 2005; Math Biosci Eng 3:89–100, 2006).     

The Tryptophan Fluorescence of Tetracarbidium conophorum Agglutinin II and a Solution-Based Assay for the Binding of a Biantennary Glycopeptide

The plant lectin Tetracarbidium conophorum agglutinin II binds to glycoproteins and glycopeptides in a structurally specific manner [Animashaun et al., (1994) Glycoconjugate J. 11, 299–303]. We have characterized the steady-state and time-resolved fluorescence of the tryptophan residues of this lectin. The fluorescence (_ex = 295 nm, _em = 350 nm) decay is complex and can be described by four decay times with the following values: ₁ = 7.4nsec, ₁ = 0.22; ₂ = 2.9 nsec, ₂ = 0.25; ₃ = l.0 nsec, ₃ = 0.34; ₄ = 0.2 nsec, ₄ = 0.18. The addition of a biantennary glycopeptide to the lectin results in a quench and an 8 nm blue shift of the emission spectrum. The effect is saturable, and is described by an association constant of 1.8×10⁵ M^–1. The tryptophan fluorescence of Tetracarbidium conophorum agglutinin II may therefore be utilized to characterize thermodynamically the binding interactions between this lectin and complex glycoprotein.     

Minichromosome stability induced by partial genome duplication in Arabidopsis thaliana

Two partially reconstructed karyotypes (RK1 and RK2) of Arabidopsis thaliana have been established from a transformant, in which four structurally changed chromosomes (α, β, γ, and δ) were involved. Both karyotypes are composed of 12 chromosomes, 2n = 1￠￠+ 3￠￠+ 4￠￠+ 5￠￠+ a￠￠+ g￠￠ = 12 {2}n = {1}\prime \prime + {3}\prime \prime + {4}\prime \prime + {5}\prime \prime + \alpha \prime \prime + \gamma \prime \prime = {12} for RK1 and 2n = 3￠￠+ 4￠￠+ 5￠￠+ a￠￠+ b￠￠+ g￠￠ = 12 {2}n = {3}\prime \prime + {4}\prime \prime + {5}\prime \prime + \alpha \prime \prime + \beta \prime \prime + \gamma \prime \prime = {12} for RK2, and these chromosome constitutions were relatively stable at least for three generations. Pairing at meiosis was limited to the homologues (1, 3, 4, 5, α, β, or γ), and no pairing occurred among non-homologous chromosomes in both karyotypes. For minichromosome α (mini α), precocious separation at metaphase I was frequently observed in RK2, as found for other minichromosomes, but was rare in RK1. This stable paring of mini α was possibly caused by duplication of the terminal tip of chromosome 1 that is characteristic of RK1.     

Moderate grade hyperammonemia induced concordant activation of antioxidant enzymes is associated with prevention of oxidative stress in the brain slices

Acute hyperammonemia (HA) induced oxidative stress in the brain is considered to play critical roles in the neuropathology of end stage hepatic encephalopathy (HE). Moderate grade HA led minimal/moderate type HE is more common in the patients with chronic liver failure. However, implication of oxygen free radical ( \textO ₂ ^- {\text{O}}_{ 2}^{ - } ) based oxidative mechanisms remain to be defined during moderate grade HA. This article describes profiles of all the antioxidant enzymes Vis a Vis status of oxidative stress/damage in the brain slices exposed to 0.1–1 mM ammonia, reported to exist in the brain of animals with chronic liver failure and in liver cirrhotic patients. Superoxide dismutase catalyzes the first step of antioxidant mechanism and, with concerted activity of catalase, neutralizes \textO ₂ ^- {\text{O}}_{ 2}^{ - } produced in the cells. Both these enzymes remained unchanged up to 0.2–0.3 mM ammonia, however, with significant increments (P < 0.01–0.001) in the brain slices exposed to 0.5–1 mM ammonia. This was consistent with the similar pattern of production of reactive oxygen species in the brain slices. However, level of lipid peroxidation remained unchanged throughout the ammonia treatment. Synchronized activities of glutathione peroxidase and glutathione reductase regulate the level of glutathione to maintain reducing equivalents in the cells. The activities of both these enzymes also increased significantly in the brain slices exposed to 0.5–1 mM ammonia with concomitant increments in GSH/GSSG ratio and in the levels of total and protein bound thiol. The findings suggest resistance of brain cells from ammonia induced oxidative damage during moderate grade HA due to concordant activations of antioxidant enzymes.     

Temporal profile of the singlet oxygen emission endogenously produced by photosystem II reaction centre in an aqueous buffer

The temporal profile of the phosphorescence of singlet oxygen endogenously photosensitized by photosystem II (PSII) reaction centre (RC) in an aqueous buffer has been recorded using laser excitation and a near infrared photomultiplier tube. A weak emission signal was discernible, and could be fitted to the functional form a[exp( - t/t₂ ) - exp( - t/t₁ )] a[\exp ( - t/\tau_{2} ) - \exp ( - t/\tau_{1} )] , with $ a > 0 $ a > 0 and $ \tau_{2} > \tau_{1} $ \tau_{2} > \tau_{1} . The value of t₂ \tau_{2} decreased from 11.6 ± 0.5 μs under aerobic conditions to 4.1 ± 0.2 μs in oxygen-saturated samples, due to enhanced bimolecular quenching of the donor triplet by oxygen, whereas that of t₁ \tau_{1} , identifiable with the lifetime of singlet oxygen, was close to 3 μs in both cases. Extrapolations based on the low amplitude of the emission signal of singlet oxygen formed by PSII RC in the aqueous buffer and the expected values of t₁ \tau_{1} and t₂ \tau_{2} in chloroplasts indicate that attempts to analyse the temporal profile of singlet oxygen in chloroplasts are unlikely to be rewarded with success without a significant advance in the sensitivity of the detection equipment.     

Compensatory changes in Photosystem II electron turnover rates protect photosynthesis from photoinhibition

Exposure of algae or higher plants to bright light can result in a photoinhibitory reduction in the number of functional PS II reaction centers (n) and a consequential decrease in the maximum quantum yield of photosynthesis. However, we found that light-saturated photosynthetic rates (P_max) in natural phytoplankton assemblages sampled from the south Pacific ocean were not reduced despite photoinhibitory decreases in n of up to 52%. This striking insensitivity of P_max to photoinhibition resulted from reciprocal increases in electron turnover ( )through the remaining functional PS II centers. Similar insensitivity of P_max was also observed in low light adapted cultures of Thalassiosira weissflogii (a marine diatom), but not in high light adapted cells where P_max decreased in proportion to n. This differential sensitivity to decreases in n occurred because was close to the maximum achievable rate in the high light adapted cells, whereas was initially low in the low light adapted cells and could thus increase in response to decreases in n. Our results indicate that decreases in plant productivity are not necessarily commensurate with photoinhibition, but rather will only occur if decreases in n are sufficient to maximize or incident irradiance becomes subsaturating.