Keeping the neurons cool Homeostatic Plasticity Processes in the Brain

What is homeostasis? Homeostasis (from Greek: “homoios”, “similar”; “stasis”, “standing still”) is the ability of a system to regulate its own variables to maintain the internal conditions rather stable (negative feedback loop). Sensor Controller Effector Homeostatic principles are often used in automatic control systems as thermostats. But they also occur in biological systems as “human homeostasis” (e.g., body temperature). -> also in the brain

Synaptic Plasticity Classical Hebbian Plasticity:

Synaptic Plasticity Classical Hebbian Plasticity:

Synaptic Plasticity Classical Hebbian Plasticity:

Synaptic Plasticity Classical Hebbian Plasticity: linear neuron model

Synaptic Plasticity Classical Hebbian Plasticity: Stability analysis linear neuron model Positive feedback loop between activity and synaptic changes lead to runaway dynamics.

Homeostatic Plasticity Constrain the dynamics of synaptic plasticity Maximum/minimum weight values Normalization Consider counterbalancing synaptic dynamics Synaptic scaling Change directly the synaptic dynamics Metaplasticity Change neuronal response properties Intrinsic plasticity

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

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

Maximum/minimum weight values Synaptic Plasticity: Hard boundaries: Classical Hebbian Plasticity BCM rule Hard boundaries yields binary synapses neglecting all intermediate weight values. Song et al., 2000 Song et al., 2005

Normalization Subtractive: These normalization methods require global information (info about ALL inputs or weights), which is biologically unrealistic. Global: BUT…

Normalization Time after LTP stimulation Normalization: Bourne and Harris, 2011 Stimulation Electrodes Recording Electrode Normalized Response LTP LTD Royer and Paré, 2003 Dendrite Spine (Synapse) (with EM)

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

Synaptic Scaling Long-lasting alterations of neuronal activity induces some changes of the basic properties. Block neuronal activity Increase neuronal act. Firing rate homeostasis in cultured networks Control Block or raise activity (for 2 days) After washing out After TTX After Bicuculline Response increased Response decreased Change of EPSP amplitudes Turrigiano and Co-workers, 1998, 2004, 2008,…

Synaptic Scaling Long-lasting alterations of neuronal activity induces some changes of the basic properties. Block neuronal activity Increase neuronal act. Firing rate homeostasis in cultured networks Control Block or raise activity (for 2 days) After washing out After TTX After Bicuculline Change of EPSP amplitudes Response decreased Response increased After TTX After Bicuculline Change of EPSP amplitudes Turrigiano and Co-workers, 1998, 2004, 2008,…

Synaptic Scaling After TTX After Bicuculline Change of EPSP amplitudes (after washing out) Decreased activity Increased activity Turrigiano and Co-workers, 1998, 2004, 2008,…

Synaptic Scaling (after washing out) Firing rate [v] Synaptic weight [w] Decreased activity Increased activity Turrigiano and Co-workers, 1998, 2004, 2008,…

Synaptic Scaling Firing rate [v] Synaptic weight [w] Theoretical formulation Does synaptic scaling balance the divergent dynamics of synaptic plasticity? Synaptic scaling induces stable weight dynamics

General fixed point analysis Synaptic PlasticitySynaptic Scaling w = μ G(u,v,w) + γ [v T – v] w = μ G(u,F(u,w),w) + γ [v T – F(u,w)] general function G (Hebb, STDP, etc.) general neuron model v=F(u,w) Canonical Form of G linear weight dependency of F Calculate fixed points for different n w = μ u v + γ [v T – v] w = μ (aw 2 + bw) + γ [v T – wF(u)] ω n unstable Weight dependency of synaptic scaling e.g. Hebb a=0; b=u F(u) Tetzlaff et al., 2011

Synaptic Scaling and Hebbian Plasticity Synaptic ScalingHebbian Plasticity w = μ u v + γ [v T – v] w n n=0 n=1 n=2 unstable stable Tetzlaff et al., 2011

n=1 n=2 stable unstable stable Synaptic Scaling and BCM rule Synaptic ScalingBCM rule ω = μ u v [v – θ] + γ [v T – v] ω n Tetzlaff et al., 2011

Synaptic Scaling and Plasticity in a Network Environmental Input 100 Hz 130 Hz Tetzlaff et al., 2013

Synaptic Scaling and Plasticity in a Network Environmental Input 100 Hz 130 Hz Tetzlaff et al., 2013

Detour: Groups of strongly interconnected neurons LearningRecall Pattern Completion Groups of strongly interconnected neurons serve as a model of neural memory.

Synaptic Scaling and Plasticity in a Network Environmental Input 100 Hz 130 Hz The system “uses” nearly all possible weight values Tetzlaff et al., 2013

Synaptic Scaling and Plasticity in a Network 100 Hz 130 Hz Tetzlaff et al., 2013

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

Metaplasticity BCM rule: Metaplasticity directly changes synaptic plasticity by the self-organized adaptation of the plasticity-parameters LTP LTD Abraham and Bear, 1996; Abraham, 2008

Kirkwood et al., 1996 Metaplasticity light-deprived (less activity) after two days control condition (more activity)

Metaplasticity BCM rule: Yger and Gilson, 2015 oscillations oscillations are stronger than convergence

Summary Maximum/minimum weight values Normalization Synaptic Scaling Metaplasticity Binary weight distribution Biologically unrealistic Requires global knowledge Weak experimental evidence stable Biologically realistic Enables the formation of memory Limited dynamics (no further learning) Unlimited dynamics With biological parameter values unstable (un)stable Biologically realistic

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

Intrinsic Plasticity Block neuronal activity Increase neuronal act. Firing rate homeostasis in cultured networks Control Block or raise activity (for 2 days) After washing out Reminder: Synaptic Scaling Synapse-dependent effect Control Block or raise activity (for 6 days) After washing out Firing rate homeostasis in each neuron electrode What happens at the soma?

Intrinsic Plasticity electrode Somatic input (test pulse) Output activity control activity blockage Activity blockage by TTX Control Increased activity Desai et al., 1999 van Welie et al., 2004

Intrinsic Plasticity Gründemann and Häusser, 2010 The position of the Axonal Initial Segment (AIS; initiation site of action potentials) could determine the neuronal excitability Grubb and Burrone, 2010 Kuba et al., 2010

Intrinsic Plasticity Triesch, 2007 output activity somatic input slope offset Intrinsic Plasticity rule:

Intrinsic Plasticity Triesch, 2007 adaptedafterbefore Average curve

Detour: How to encode the input optimally? frequency Input distribution noise no output “normal” input rare but strong events * * Many (input) events with many output spikes Very high output rate frequency Output distribution

Detour: How to encode the input optimally? frequency Input distribution noise no output “normal” input rare but strong events * * frequency Output distribution Many (input) events with few output spikes Lower output rate

Detour: How to encode the input optimally? frequency Input distribution noise no output “normal” input rare but strong events * * frequency Output distribution * * encode rare events by strong outputs Analytically:

Intrinsic Plasticity Stemmler and Koch, 1999 Intrinsic Plasticity Each spike should encode/transmit the maximal amount of information about the input Hodgkin-Huxley model with intrinsic plasticity: firing rate

Intrinsic Plasticity Stemmler and Koch, 1999 Intrinsic plasticity optimizes the amount of information transmitted by each spike. Intrinsic Plasticity firing rate

Intrinsic Plasticity + Synaptic Plasticity Triesch, 2007 Decreased activity LTP LTD Intrinsic plasticity acts as a sliding threshold (metaplasticity) if it is faster than synaptic plasticity

Intrinsic Plasticity on fast timescales Daoudal et al., 2002 After several minutes After several days Low activity High activity Desai et al., 1999 van Welie et al., 2004 Input

Intrinsic Plasticity + Synaptic Plasticity Triesch, 2007 Decreased activity LTP LTD Intrinsic plasticity acts as a sliding threshold (metaplasticity) if it is faster than synaptic plasticity

Intrinsic Plasticity Intrinsic plasticity stabilizes the neuronal dynamics by adapting the input-output relation. The output distribution is an exponential distribution. Thereby, the information each output spike transmits about the input distribution is optimized Intrinsic plasticity can act as a sliding threshold (metaplasticity) for synaptic plasticity. BUT… The dynamics of intrinsic plasticity are different on different timescales: Hours: homeostatic Minutes: “Hebbian” (amplifies the positive feedback loop)

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