Transient oscillations in excitable cells and Spike-adding Mechanism in Transient Bursts Krasimira Tsaneva-Atanasova University of Exeter 2016 NZMRI Summer School Lecture 2

Mechanisms of intrinsic plasticity in the hippocampus Methods CA3 pyramidal neurons CA3 pyramidal neurons P14 wistar rats P14 wistar rats ºC ºC Kgluconate-based internal solution Kgluconate-based internal solution Whole-cell current clamp recordings Whole-cell current clamp recordings Resting membrane potential held constant by automatic slow somatic current injection Resting membrane potential held constant by automatic slow somatic current injection Experiments performed in blockers of fast excitatory (AMPA/kainate & NMDA receptors) and inhibitory transmission (GABA A receptors) Experiments performed in blockers of fast excitatory (AMPA/kainate & NMDA receptors) and inhibitory transmission (GABA A receptors)Methods CA3 pyramidal neurons CA3 pyramidal neurons P14 wistar rats P14 wistar rats ºC ºC Kgluconate-based internal solution Kgluconate-based internal solution Whole-cell current clamp recordings Whole-cell current clamp recordings Resting membrane potential held constant by automatic slow somatic current injection Resting membrane potential held constant by automatic slow somatic current injection Experiments performed in blockers of fast excitatory (AMPA/kainate & NMDA receptors) and inhibitory transmission (GABA A receptors) Experiments performed in blockers of fast excitatory (AMPA/kainate & NMDA receptors) and inhibitory transmission (GABA A receptors) 200 pA -100 pA 20 mV 200 ms CA1 CA3 DG

Current injection responses of 36 CA3 pyramidal neurones at V rest 1 s 100 mV

CA3 CA1 ADP +200 pA & -100 pA 500 ms +200 pA & -100 pA 500 ms 2 nA 2 ms 2 nA 2 ms CA3 pyramids exhibit more profound bursts and larger ADP

The model: Slow-Fast dynamical system J. Nowacki, H.M. Osinga, J.T. Brown, A.D. Randall, and K.T. Tsaneva-Atanasova, A unified model of CA1/3 pyramidal cells: An investigation into excitability, Progr. Biophysics and Molecular Biology, 105(1-2), (2011)

A unified pyramidal cell model CA3 vs CA1 neurons A unified pyramidal cell model CA3 vs CA1 neurons J. Nowacki, H.M. Osinga, J.T. Brown, A.D. Randall, and K.T. Tsaneva-Atanasova, A unified model of CA1/3 pyramidal cells: An investigation into excitability, Progr. Biophysics and Molecular Biology, 105(1-2), (2011)

WTPSAPP Instantaneous frequency (Hz) Spike pair # 100 pA P< pA P< Higher burst frequency WT PSAPP ADP amplitude (mV) * PSAPP WT 10 ms 10 mV 2. Larger ADP * * * Increased burstyness and ADP in aged PSAPP CA1 neurones Increased burstyness and ADP in aged PSAPP CA1 neurones J.T. Brown, J. Chin, S.C. Leiser, M.N. Pangalos, and A.D. Randall. Altered intrinsic neuronal excitability and reduced Na+ currents in a mouse model of Alzheimer's disease. Neurobiology of Aging, 32(11), (2011)

1 μA.cm -2 2 μA.cm Inst. frequency (Hz) Spike pair # 3. Enhanced burstiness 4. Enhanced ADP Short stimulus responses in experiments J.T. Brown, J. Chin, S.C. Leiser, M.N. Pangalos, and A.D. Randall. Altered intrinsic neuronal excitability and reduced Na+ currents in a mouse model of Alzheimer's disease. Neurobiology of Aging, 32(11), (2011)

The ADP drives high frequency burst firing Vm (mV) 20 ms AP threshold 2 nA, 2 ms 20 mV 10 ms 2 nA step 2 ms Action potential ADP I mem V mem Brown JT, Randall AD. Activity-dependent depression of the spike after-depolarization generates long-lasting intrinsic plasticity in hippocampal CA3 pyramidal neurons. J Physiol. 587: (2009)

A unified pyramidal cell model Short stimulus responses of CA3 and CA1 neurons A unified pyramidal cell model Short stimulus responses of CA3 and CA1 neurons J. Nowacki, H.M. Osinga, J.T. Brown, A.D. Randall, and K.T. Tsaneva-Atanasova, A unified model of CA1/3 pyramidal cells: An investigation into excitability, Progr. Biophysics and Molecular Biology, 105(1-2), (2011)

Definition of the ADP Local minimum and local maximum Definition of the ADP Local minimum and local maximum

Definition of the ADP using the first and second derivative of the membrane potential Definition of the ADP using the first and second derivative of the membrane potential

So far…  We could define the transient phenomenon of after- depolarization using the derivatives of the membrane potential;  We show that the nullclines of the membrane potential play a role of a bursting-threshold in the model;  Transitions between no ADP, ADP and a burst can be studied in a parameter-dependent setting.  We could define the transient phenomenon of after- depolarization using the derivatives of the membrane potential;  We show that the nullclines of the membrane potential play a role of a bursting-threshold in the model;  Transitions between no ADP, ADP and a burst can be studied in a parameter-dependent setting.

Excitability threshold as a two-point boundary value problem (reduced model) (2.1)

Short stimulus responses in the model J. Nowacki, H.M. Osinga, and K.T. Tsaneva-Atanasova, Continuation-based numerical detection of after- depolarisation and spike-adding threshold, Neural Computation, 25(4): , (2013)

The definition of the after-depolarization allows us to systematically investigate its onset and the generation of a burst 20 mV 10 ms 2 nA step 2 ms Action potential ADP I mem V mem Excitability threshold as a two-point boundary value problem (2PBVP) Krauskopf B, Osinga HM: Computing invariant manifolds via the continuation of orbit segments. In Numerical Continuation Methods for Dynamical Systems: Path Following and Boundary Value Problems. Edited by Krauskopf B, Osinga HM, Galán-Vioque J. Dordrecht: Springer; 2007:

J. Nowacki, H.M. Osinga, and K.T. Tsaneva-Atanasova, Continuation-based numerical detection of after-depolarisation and spike-adding threshold, Neural Computation, 25(4): , (2013) Excitability threshold as a 2PBVP

Identifying the onset of ADP in a transient burst P B

Identifying spike adding mechanism J. Nowacki, H.M. Osinga, and K.T. Tsaneva-Atanasova, Dynamical systems analysis of spike-adding mechanisms in transient bursts, J. Mathematical Neuroscience 2, 7 (2012)

Identifying spike adding mechanism

Onset of the transient busts J. Nowacki, H.M. Osinga, and K.T. Tsaneva-Atanasova, Dynamical systems analysis of spike-adding mechanisms in transient bursts, J. Mathematical Neuroscience 2, 7 (2012)

Can we observe transient spike adding in a three dimensional system?

Transient busts in 3D Osinga, Hinke M. and Tsaneva-Atanasova, Krasimira T., 2013, Geometric analysis of transient bursts, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23,

Onset of the ADP and transient busts in 3D Osinga, Hinke M. and Tsaneva-Atanasova, Krasimira T., 2013, Geometric analysis of transient bursts, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23,

Spike onset along saddle-type slow manifold

Two-parameter curves of spike-adding onsets Osinga, Hinke M. and Tsaneva-Atanasova, Krasimira T., 2013, Geometric analysis of transient bursts, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23,

Onset of the ADP and transient busts J. Nowacki, H.M. Osinga, and K.T. Tsaneva-Atanasova, Continuation-based numerical detection of after- depolarisation and spike-adding threshold, Neural Computation, 25(4): , (2013)