Keeping the neurons cool

Name: Keeping the neurons cool
Uploaded: 2017-08-14T07:47:20+00:00
Duration: PTM29S26
Channel: Homer Baker
Description: Keeping the neurons cool

Keeping the neurons cool
Part II Homeostatic Plasticity Processes in the Brain

Homeostatic Plasticity
Adjust the inhibitory input accordingly Inhibitory plasticity Change neuronal response properties Intrinsic plasticity Inhibitory Neuron Delete old and create new synapses Structural plasticity Constrain the dynamics of synaptic plasticity Maximum/minimum weight values Normalization Consider counterbalancing synaptic dynamics Synaptic scaling Change directly the synaptic dynamics Metaplasticity

Summary Part I Maximum/minimum weight values stable
Normalization Synaptic Scaling Metaplasticity Intrinsic Plasticity stable Binary weight distribution 𝑤= 𝑤 𝑚𝑎𝑥 , if 𝑤> 𝑤 𝑚𝑎𝑥 Biologically unrealistic 𝑤= 𝑤 𝑚𝑖𝑛 , if 𝑤< 𝑤 𝑚𝑖𝑛 stable Weak experimental evidence 𝑤 𝑘 ← 𝑤 𝑘 𝑗 𝑤 𝑗 Requires global knowledge stable Biologically realistic Enables the formation of memory 𝑤 = γ 𝑣 𝑇 −𝑣 𝑤 𝑛 Limited dynamics (no further learning) (un)stable Biologically realistic Unlimited dynamics τ Θ Θ =𝐹(𝑣,Θ) With biological parameter values unstable (un)stable Biologically realistic 𝑓= 1 1+exp⁡ − 𝑎𝐼+𝑏 Optimal input-output relation Dynamics depend on timescale Δ𝑎=𝐺(𝑎,𝑓,𝐼) Days: homeostatic Min.: ‘Hebbian’ Δ𝑏=𝐻(𝑏,𝑓,𝐼)

The structure of neuronal activity
Even during the performance of a task neuronal spiking is highly irregular The system has a distribution of firing rates O’Connor et al., 2010

Detour: Balanced state
Each neuron 𝑖 from 𝐸, 𝐼 receives 𝐾 excitatory and 𝐾 inhibitory connections. Excitatory 𝑁 𝐸 𝐽 𝐸𝐸 1≪ 𝐾≪ 𝑁 𝑙 , 𝑙 ∈𝐸,𝐼 𝐽 𝐼𝐸 𝐽 𝐸𝐼 Excitatory and inhibitory inputs to a neuron follow a Gaussian distribution (central limit theorem) with mean μ 𝑙 =𝐾 𝑘 𝐽 𝑙𝑘 𝑚 𝑘 and variance σ 𝑙 2 =𝐾 𝑘 𝐽 𝑘𝑙 2 𝑚 𝑘 . Inhibitory 𝐽 𝐼𝐼 𝑁 𝐼 The total input is the sum of two Gaussians: μ 𝐸 μ 𝐼 σ 𝐸 σ 𝑙 Van Vreeswijk and Sompolinsky, 1996 Vogels and Abbott, 2009

Each neuron 𝑖 from 𝐸, 𝐼 receives 𝐾 excitatory and 𝐾 inhibitory connections. Excitatory 𝑁 𝐸 𝐽 𝐸𝐸 1≪ 𝐾≪ 𝑁 𝑙 , 𝑙 ∈𝐸,𝐼 𝐽 𝐼𝐸 𝐽 𝐸𝐼 Excitatory and inhibitory inputs to a neuron follow a Gaussian distribution (central limit theorem) with mean μ 𝑙 =𝐾 𝑘 𝐽 𝑙𝑘 𝑚 𝑘 and variance σ 𝑙 2 =𝐾 𝑘 𝐽 𝑘𝑙 2 𝑚 𝑘 . Inhibitory 𝐽 𝐼𝐼 𝑁 𝐼 The total input is the sum of two Gaussians: σ 𝐸 σ 𝐼 2 fluctuations Balanced state Θ~ 𝐾 μ 𝐸 + μ 𝐼 Van Vreeswijk and Sompolinsky, 1996 Vogels and Abbott, 2009 firing threshold

excitatory input Excitatory 𝑁 𝐸 𝐽 𝐸𝐸 sum 𝐽 𝐼𝐸 𝐽 𝐸𝐼 inhibitory input Inhibitory 𝐽 𝐼𝐼 𝑁 𝐼 Irregular (chaotic) spiking activity Van Vreeswijk and Sompolinsky, 1996 Vogels and Abbott, 2009 Biological distribution of firing rates

Synaptic Plasticity excitatory neurons inhibitory neurons Although the system’s activity is chaotic it shows a linear relation between population response and strength of constant input Excitatory 𝑁 𝐸 𝐽 𝐸𝐸 Ext 𝐽 𝐼𝐸 𝐽 𝐸𝐼 Inhibitory 𝐽 𝐼𝐼 𝑁 𝐼 Ext The balanced state is very sensitive to the ratio between excitatory and inhibitory connections unbalanced fast unbalanced balanced The balanced network responds very fast according to changes in the input Van Vreeswijk and Sompolinsky, 1996 Vogels and Abbott, 2009

Inhibitory Plasticity
Exc Inh Exc D’Amour and Froemke, 2015

Exc post pre target rate 𝑤 =η 𝑢𝑣− 𝑣 𝑇 𝑢 Vogels et al., 2011 D’Amour and Froemke, 2015

In feedforward networks inhibitory plasticity leads to the balanced state. Vogels et al., 2011

Neuron 𝑖𝑗 Neuron 𝑖𝑘 Neuron 𝑙𝑗 Inhibitory Plasticity cluster of strongly interconnected neurons exc inh In recurrent networks inhibitory plasticity leads to the balanced state. Vogels et al., 2011

Sensory tuning curves in the rat’s auditory cortex Artificial readjustment stimulation original tuning Froemke et al., 2007 Experiment Sound Model Vogels et al., 2011

But… 𝑤 =η 𝑢𝑣− 𝑣 𝑇 𝑢 (mainly used in literature) The exact form of inhibitory plasticity depends various factors as brain area, animal age, brain state, etc. Vogels et al., 2013

Inhibitory plasticity drives a neural system to the balanced state. In the balanced state spiking activity is irregular and most neurons have a low firing rate (comparable to experiments). The response of the network to changes in the input are very fast. Inhibitory plasticity explains the readjustment of tuning curves of sensory neurons. ? -> stable dynamics There are many different forms of inhibitory plasticity. The (dynamic) interaction between excitatory and inhibitory plasticity is still under investigation.

Structure of a synapse dendrite axon
dendritic spine axonal bouton dendrite axon The majority of synapses is realized by close-by dendritic (spine) and axonal (bouton) protrusions. Kalisman et al., 2005

Structural Plasticity: Axons
In-vivo two-photon microscopy from the cortex of living mice reveals a permanent axonal remodelling even in the adult brain leading to synaptic rewiring. Axonal outgrowth/retraction Red: Outgrowth Yellow: Stable Blue: Retracts Rewiring Blue: Retracts and looses synapses Red: Grows and creates new synapses The tips of axonal branches are permanently remodeled. De Paola et al., 2006

Structural Plasticity: Dendrites
In-vivo imaging of dendritic structures shows stable and transient dendritic spines: stable transient semi-stable Dendritic spines are very dynamic structures determining the existence of synapses. Trachtenberg et al., 2002

Structural Plasticity: Activity-dependency
Monocular deprivation (decreased activity) Adult mouse visual cortex: Hofer et al., 2009 Red: spine gain Blue: spine loss low activity high activity Homeostatic regulation of neuronal structure. Dendritic Outgrowth/more Spines Dendritic Regression/less Spines Kater et al., 1989; Mattson and Kater, 1989

Structural Plasticity
Computational model with circular neurites (dendritic and axonal trees) overlap ≈ # synapses ( 𝐴 𝑖𝑗 ) 𝑟 𝑖 𝑟 𝑗 Neurite of neuron 𝑖 Neurite of neuron 𝑗 Overlap: 𝐴 𝑖𝑗 =𝐺( 𝑟 𝑖 , 𝑟 𝑗 ) Neuronal Activity 𝐹 𝑖 𝑟 𝑖 =ρ− 2ρ 1+exp⁡ 𝐹 𝑇 − 𝐹 𝑖 /β Radius: 𝐹 𝑇 Van Ooyen and Van Pelt, 1994

Computational model with circular neurites (dendritic and axonal trees) overlap ≈ # synapses ( 𝐴 𝑖𝑗 ) 𝐹 𝑖 < 𝐹 𝑇 𝐹 𝑗 > 𝐹 𝑇 𝑟 𝑖 𝑟 𝑗 Neurite of neuron 𝑖 Neurite of neuron 𝑗 𝐴 𝑖𝑗 =𝐺( 𝑟 𝑖 , 𝑟 𝑗 ) Neuronal Activity 𝐹 𝑖 Overlap: 𝑟 𝑖 =ρ− 2ρ 1+exp⁡ 𝐹 𝑇 − 𝐹 𝑖 /β Radius: 𝐹 𝑇 Van Ooyen and Van Pelt, 1994

Total overlap Mean activity Mean radius Structural plasticity enables the self-organized development of a neural network. Van Ooyen and Van Pelt, 1994

Days in vitro Mean number of synapses overshoot Total overlap Mean activity Mean radius Van Huizen, 1986 Van Ooyen and Van Pelt, 1994

Distinguish neurites between axonal and dendritic trees: Axonal tree Dendritic tree Overlap between axonal tree of neuron 𝑖 and dendritic tree 𝑗 determines the number of synapses ( 𝐴 𝑖𝑗 ). How does the neuronal activity change during development? Each tree has its own dynamics: 𝐹 𝑑 𝑎 𝐹 𝑇 𝑑 𝑖 ≈ 𝐹 𝑇 − 𝐹 𝑖 𝑎 𝑖 ≈ 𝐹 𝑖 − 𝐹 𝑇 Tetzlaff et al., 2010

Detour: Self-organized criticality
Bak et al., 1987 A system is self-organized if it develops to an overall, coordinated state by its own intrinsic, local rules. A system is critical if it is between two phases (phase transition). ferromagnetic critical paramagnetic TC Curie temperature e.g., the Ising model of magnetism Chialvo, 2007 How to quantify the critical state?

Avalanches: Bak, 1996, How Nature works: The Science of Self-Organized Criticality An avalanche is an object of spatial-temporal linked events. Size – number of events within one avalanche Duration – time between first and last event of the avalanche 29 29

An avalanche is an object of spatial-temporal linked events. Size – number of events within one avalanche Duration – time between first and last event of the avalanche If a system is in the critical state, the size and duration of its avalanches are power-law distributed. -> linear in a log-log plot log(size) log(P(size)) Many small avalanches Many large avalanches Levina et al., 2007

A system is self-organized if it develops to an overall, coordinated state by its own intrinsic, local rules. A system is critical if it is between two phases (phase transition). If a system is in the critical state, the size and duration of its avalanches are power-law distributed. -> scale-free General concept in nature? Examples from geophysics (plate tectonics), economy (stock market), evolution, transport sector (traffic jams), quantum gravity, sociology, solar physics, plasma physics, etc. and neuroscience

Self-organized criticality in neural systems
Slices from adult rat cortex indicate criticality. Activity at electrode 𝑖𝑗 Beggs and Plenz, 2003

Criticality during development in cell culture
20 cell cultures between day 11 and 95 in vitro have been analyzed Poisson supercritical subcritical critical The structure of the neuronal activity indicates that during development the system passes several different phases. Tetzlaff et al., 2010

Distinguish neurites between axonal and dendritic trees: Axonal tree Dendritic tree Overlap between axonal tree of neuron 𝑖 and dendritic tree 𝑗 determines the number of synapses ( 𝐴 𝑖𝑗 ). Each tree has its own dynamics: 𝐹 𝑑 𝑎 𝐹 𝑇 𝑑 𝑖 ≈ 𝐹 𝑇 − 𝐹 𝑖 𝑎 𝑖 ≈ 𝐹 𝑖 − 𝐹 𝑇 Tetzlaff et al., 2010

Total overlap Mean activity Van Ooyen and Van Pelt, 1994 ≈Mean activity Phase 1 – Outgrowth phase Phase 2 – Overshoot/Pruning phase Phase 3 – Equilibrium phase Tetzlaff et al., 2010

Outgrowth phase Overshoot/Pruning phase Equilibrium phase Cell Culture Eplileptiform Activity Remains supercritical This state does not exist Model Tetzlaff et al., 2010

Inhibition Hedner et al., 1984 Jiang et al., 2005 Sutor and Luhmann, 1995 Tetzlaff et al., 2010

Outgrowth phase Overshoot/Pruning phase Equilibrium phase Structural plasticity and inhibition can explain the development of neuronal networks into their matured state. Tetzlaff et al., 2010

Synapse Formation Synapse Deletion Axonal tree dendritic element axonal element Randomly link free axonal and dendritic elements Randomly assign synapses to be deleted Dendritic tree Tetzlaff et al., 2010 Butz et al., 2008

Synapse Formation Synapse Deletion The number of elements is homeostatically regulated: dendritic element Δ 𝐷 𝑖 =𝐺 𝐹 𝑖 Δ 𝐴 𝑖 =𝐻 𝐹 𝑖 Change in number of elements Activity 𝐹 Δ𝐴 Δ𝐷 axonal element Randomly link free axonal and dendritic elements Randomly assign synapses to be deleted 𝐹 𝑇 𝐹 𝑑 𝑎 𝐹 𝑇 Butz et al., 2008

Detour: Lesion studies
Visual Stimulation Visual Cortex Lesion Projection Zone (LPZ) Keck et al., 2008

The number of elements is homeostatically regulated: Synapse Formation Synapse Deletion dendritic element Δ 𝐷 𝑖 =𝐺 𝐹 𝑖 Δ 𝐴 𝑖 =𝐻 𝐹 𝑖 Change in number of elements Activity 𝐹 Δ𝐴 Δ𝐷 axonal element 𝐹 𝑇 Randomly link free axonal and dendritic elements Randomly assign synapses to be deleted Distance-dependent synapse formation Butz et al., 2008

Lesion study in a model of structural plasticity
Connectivity The homeostatic process of structural plasticity brings the network step by step back into an operational regime. Activity 𝐹 𝑇 𝐹 𝑇 𝐹 𝑇 Activity Activity Activity Butz and Van Ooyen, 2013

Each zone shows a different dynamic in dendritic elements/spines: control border Model center Experiment Keck et al., 2008; Butz and Van Ooyen, 2013

Structural plasticity drives the system into a homeostatic state. Furthermore, models of structural plasticity reproduce the development of neuronal systems into their matured state. -> overshoot (connectivity) -> criticality (activity) Also the self-organization of neuronal networks after lesion can be explained by the dynamics of homeostatic structural plasticity. BUT… “Hebbian-like” structural plasticity Engert and Bonhoeffer, 1999

Structural Plasticity and Learning
before training after camera poor mice structural changes Xu et al., 2009; Yang et al., 2009

new spine formation old spine elimination training duration new training task Xu et al., 2009; Yang et al., 2009

Early training No Training Late training Control Late only Retraining 30d 16d 74d 8d Experiment Xu et al., 2009 Spine / synapse formation Übergang Spine / synapse removal

Early training No Training Late training Control Late only Retraining 30d 16d 74d 8d Experiment Xu et al., 2009 Spine / synapse formation Model of Hebbian structural plasticity Fauth et al., 2015 Spine / synapse removal

Structural plasticity drives the system into a homeostatic state. Furthermore, models of structural plasticity reproduce the development of neuronal systems into their matured state. -> overshoot (connectivity) -> criticality (activity) Also the self-organization of neuronal networks after lesion can be explained by the dynamics of homeostatic structural plasticity. The dynamics of structural plasticity are different on shorter timescales (learning).

Interaction of different plasticity processes
Spike-timing dependent plasticity Normalization Synaptic scaling Metaplasticity Inhibitory plasticity Short-term plasticity Stable memory formation in the balanced state. Zenke et al., 2015

Interaction of different plasticity processes
About 20 differential equations to describe the dynamics of 5,120 neurons and ≈2,6 million synapses ≈25 million coupled differential equations Zenke et al., 2015

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