Biological fundamentals

Signal generation

On a coarse scale, a typical neuron can be separated into cell body (soma), the axon which transfers signals to other neurons, and the dendrites which receive signals from other neurons (cf. Figure 2.2). The morphological features of a neuron, e.g., the number of dendritic and axonal branches or the length of these outgrowths varies strongly between different neuron types (cf.

also Figure 2.1C). The axon of a neuron might form “connections” to other neurons (the contact points are called synapses) that allow the transfer of an electrical signal from one neuron to

another by the usage of chemical messengers (neurotransmitters). If two neurons are coupled, the cell receiving inputs is called postsynaptic to the sending neuron, and the sending neuron is termed presynaptic with respect to the neuron receiving signals.

Neurons are cells that are highly specialized to generate and transfer electrical signals. In particular, the membrane (separating the neuron from the extracellular fluid) contains a wide variety of ion-channels. These channels control the flow of ions, predominantly sodium (Na⁺), potassium (K⁺), calcium (Ca²⁺) and chloride (Cl⁻), between inside and outside the cell. The channels may open and close in response to voltage changes or due to other external or internal signals.

Under resting conditions, there is a difference in the electrical potential between the interior of a neuron and the extracellular medium of about −70mV (by convention the potential of the surrounding of the cell is defined as 0mV). This difference is termed membrane potential and is maintained by “ion pumps”, integral membrane proteins, that actively transport charged particles over the membrane. For example, there is typically much more potassium (K⁺) inside a cell than outside, and much more sodium (Na⁺) outside the cell than inside. The electrical as well as concentration gradients cause a flow of charged particles, if the channels (which may be permeable for only a subset of ions) open. If the membrane potential inside the neuron is reduced in response to opening of some channels (e.g., by the outflux of positively charged ions or the influx of negatively charged ions), the neuron is said to be hyperpolarized. Likewise the increase of the membrane potential is called depolarization.

sub−threshold

stimulation supra−threshold stimulation

−62 mV 0 mV

10 mV spiking threshold 1 ms

resting potential

Figure 2.3: Anatomy of an action potential recorded from a pyramidal neuron in CA1 (modified with permission from Bean, 2007).

Communication between neurons is mainly mediated by the generation of action poten-tial (also called “spikes”, “nerve impulses” or

“neuronal discharges”). This is a brief, but large depolarization of the membrane poten-tial of roughly 100mV (cf. Figure 2.3). It is generated in the axon initial segment (adja-cent to the axon hillock where the axon leaves the soma; cf. Figure 2.2), if the membrane po-tential becomes sufficiently strong depolarized (i.e., exceeding a “threshold potential”). Sub-threshold depolarization does not elicit an ac-tion potential and thus such (sub-threshold) fluctuations in the membrane potential are typically not transmitted to subsequent neu-rons.

Action potentials result from a complex interplay of different voltage-gated ion channels (Bear et al., 2006; Bean, 2007; Dayan and Abbott, 2001): Neuronal discharges are initiated, if the membrane potential is sufficiently depolarized by, e.g., the influx of sodium ions in response to a presynaptic action potential. If the depolarization exceeds a threshold potential (typically

≈ −55mV), more and more voltage gated sodium channels open in a positive feed-back cascade (the opening of channels results in an influx of sodium ions that depolarizes the neuron even more

and thus opens more sodium channels, etc.). The opening (activation) of the channels is typically very fast (hundreds of microseconds) and thus cause a very rapid rise of the membrane potential up to a value close to the reversal potential of sodium (E_Na ≈ 55mV). The sodium channels typically stay open for up to one millisecond and become impermeable to sodium afterwards.

Simultaneously to the opening of sodium channels, other voltage-gated channels, in particular potassium channels, open. When the maximal permeability for sodium is achieved and the ion channels are closing, the dynamics of the flow of potassium ions start to govern the change of the membrane potential. The strong depolarization of the neuron cause a strong driving force on (positively charged) potassium ions to leave the neuron. The membrane potential decreases towards the reversal potential of potassium (E_K≈ −80mV) causing a hyperpolarization relative to the resting potential. Finally, also the voltage gated potassium channels close and the neuron reverses to the resting potential. After generation of an action potential, the ion channels are in an “inactivated” state that makes it impossible to elicit another action potential. The time period for which no further spikes can be generated or require a substantially larger depolarization to elicit a spike is called (absolute/relative) refractory period.

We note that the above description of action potential generation is very basic, e.g., we consider only two type of ion channels. Neurons in the brain might express a plethora of such channels, thus generating action potentials with widely varying amplitudes and timescales. However, the basic mechanism as outlined above still holds. More detailed descriptions of action potential generation can be found in recent textbooks or review articles (e.g., Bear et al., 2006; Bean, 2007; Dayan and Abbott, 2001).

Axonal transmission

Once an action potential is initiated, it is actively transmitted along the axonal tree. The depolarization caused by an action potential activates the voltage gated ion channels downstream the axon and thereby “refresh” the signal.

nodes of Ranvier

myelin sheaths

axon terminals soma

Figure 2.4: Sketch of a myelinated axon (modi-fied from Wikimedia, 2009, published under CC-BY-SA-3.0).

In vertebrates most axons are myelinated, which drastically increases the speed and de-creases the energetic cost of signal transmis-sion. Parts of the axon are sheath by myelin cells that isolate the axon from the surround-ing intercellular plasma and therefore allow the direct electromagnetical transmission of an action potential (which would not be pos-sible in uninsulated axons due to the leak over the membrane and the resulting strong atten-uation). The myelin sheaths are interrupted by so called “nodes of Ranvier”, where the membrane contains a large amount of voltage

gated ion channels that refresh the action potential (see also description of generation of action potentials above).

Chemical transmission

At the axonal terminals (the synapses) the chemical signal transmission to other neurons takes place. These terminals contain synaptic vesicles filled with neurotransmitters (cf. Figure 2.2).

The neurotransmitters are amino acids, amines or peptides which are synthesized in specialized fabrication units and/or by the support of enzymes in the soma or directly at the axonal terminal (see, e.g., Bear et al., 2006, for detailed description). An arriving action potential causes opening of voltage-gated calcium channels that are found within the membrane in the “active zones” of the axonic terminal. At resting conditions the concentration of calcium within the cell is very low such that an opening of the calcium channels causes an influx of calcium to the cell.

In a process termed exocytosis, the calcium influx triggers a fusion of the vesicles with the membrane and thus causes the release of the contained neurotransmitters. The exocytosis can happen remarkably rapid within tens of microseconds after the onset of the calcium influx (Sabatini and Regehr, 1996) allowing for a fast signal transmission. After the release of the neurotransmitters, the vesicle membrane is recovered in a process called endocytosis (Sudhof, 2004; Bear et al., 2006). The precise mechanism by which calcium stimulates exocytosis and the cellular mechanisms underlying endocytosis are not completely understood, but are currently under intensive investigation (see, e.g., Sudhof, 2004; Jahn and Fasshauer, 2012, for recent reviews).

Figure 2.5: Chemically gated ion channel(modified from Wikimedia, 2013, published under CC-BY-3.0).

After being released, the neurotransmitters diffuse across the synaptic cleft (separating the pre- and post-synaptic terminal) and bind to specific receptor pro-teins embedded in the postsynaptic membrane. The binding causes conformational changes in the receptor protein and induce a signal either by the opening of ion channels (cf. Figure 2.5) or by triggering the release of secondary messengers to the cytosol of the postsy-naptic neuron (Bear et al., 2006). In the final step of synaptic transmission, the released neurotransmitters are removed from the synaptic cleft. This removal may happen by re-uptake through specialized proteins (neu-rotransmitter pumps) in the membrane of the presy-naptic terminal (or other surrounding non-neural cells, called glia cells), simple diffusion away from the synapse or enzymatic destruction of the transmitter.

On the postsynaptic side the opening of channels cause an influx or efflux of ions. Depending whether the mem-brane potential is depolarized or hyperpolarised (post-synaptic potential), the effect of the (post-synaptic transmis-sion is called excitatory or inhibitory. There is a wide variety of neurotransmitters and -receptors present in

the nervous system. However, the most abundant receptors mediating (fast) excitatory sig-nals in the mammalian brain areα-amino-3-hydroxy-5-methyl-4-isocazoleprpionic acid receptors (AMPA receptors) which open channels permeable to potassium and sodium. Inhibitory signals are mainly mediated by receptors responding to gamma-aminobutric acid (GABA receptors) that allow an influx of chloride to the cell. We note that depending on the concentration of the single ions within the cell and in the intercellular medium a synapse might act excitatory or inhibitory. For example it has been shown that the chloride level inside a cell decreases during development of the brain and thus GABA acts excitatory in the immature brain and inhibitory in later development stages (Ben-Ari et al., 1997).

Dendritic transmission and signal integration

The induced (excitatory or inhibitory) postsynaptic potential is transmitted from the synaptic terminal to the soma of the postsynaptic cell by the dendrites (cf. Figure 2.2). The dendritic tree gathers signals from thousands of presynaptic inputs and this bombardment causes fluctuations of the membrane potential of the postsynaptic cell, and if the cell is sufficiently depolarized an ac-tion potential might be elicited. The transfer of signals by the dendrites is typically passive, i.e., the electrical signal is conducted like in a (dendritic) cable. The amplitude decays over distance and the contribution of a single presynaptic input to the total depolarization/hyperpolarization at the soma is comparably weak. In this thesis, we refer to this type of dendritic signal trans-mission and integration as “linear”, appreciating the fact that multiple presynaptic inputs are summed approximately linearly. This, however, does not mean that all postsynaptic quantities are just a linear summation of single responses: For example, a second identical presynaptic input might double the (total) amount of presynaptic transmitter release and thus double the number of open ion channels (i.e., the total conductance change is a linear superposition of single responses). Yet, the depolarization at the soma is not the arithmetic sum of the single responses as it also depends on the reversal potential of involved ion channels (cf. also Section 2.1.2 below), and thus single postsynaptic potentials are typically summed sublinearly.

However, recent neurophysiological experiments have shown that neuronal dendrites are capable of actively integrating synchronous presynaptic inputs (e.g., Ariav et al., 2003; Gasparini et al., 2004; Gasparini and Magee, 2006; Nevian et al., 2007; Losonczy et al., 2008; Remy et al., 2009;

Branco et al., 2010; M¨uller et al., 2012; Makara and Magee, 2013). Temporally and spatially simultaneous presynaptic stimulation might elicit dendritic spikes (similiar to somatic spikes described above), that are actively (by voltage gated channels along the dendrite) or passively transmitted to the soma, and cause somatic depolarizations of the postsynaptic neuron much stronger than expected from linear transmission of signals. In this thesis, we study the impact of such nonlinear amplification on the dynamics of neuronal networks. Appreciating the great importance of active dendrites to this thesis, we discuss them separately in Section 2.2.

Synaptic plasticity

The connections between neurons, i.e., the underlying network that gives birth to the fascinating computing capabilities of our brain, are far from being static. Our brain restructures perma-nently by creating new neurons (which was recently shown to happen even in adult mammals, cf. Kempermann et al., 2004; Lledo et al., 2006, for reviews), building new connections be-tween them or abolishing existing ones (Bear et al., 2006). Additionally, also existing synapses undergo changes of their efficiencies in an activity dependent manner on different timescales (Tetzlaff et al., 2012).

On a short time scale (up to some minutes) the repetitive activation of a synapse, might lead to a facilitation or depression of consecutive postsynaptic responses (see, e.g., Zucker and Regehr, 2002, for a comprehensive review on underlying biochemical mechanisms): Facilitation is mostly attributed to enhanced calcium influx or an increased residual level of calcium concentration inside the presynaptic terminal after multiple stimulation. Depression might arise from depletion of release-ready pool of vesicles, release of modulatory messengers from presynaptic, postsynaptic or glia cells, and/or a desensitization of postsynaptic receptors. However, after short recovery periods postsynaptic responses return to the initial amplitude.

In contrast, a coordinated pre- and postsynaptic activity might induce changes that are “per-manent”, i.e., lasting for days, weeks or even months (Sj¨ostr¨om et al., 2008, and references therein). Synaptic efficiencies might be enhanced (“long term potentiation”; LTP) or decreased (“long term depression”; LTD) and this adaptation is assumed to be controlled by calcium influx to the postsynaptic terminal (Bear et al., 2006): A high calcium concentration may activate dif-ferent protein kinases which then enhance the efficiency of AMPA receptors by phosphorylation or — on a longer time scale — trigger the insertion of entirely new AMPA receptors in the postsynaptic membrane. In contrast, modest and prolonged elevations in calcium concentration activate protein phosphatases, which by dephosphorylasation weaken the efficiency of AMPA receptors.

Figure 2.6: NMDA receptors are opened by binding of presynaptic glutamate and removal of Mg²⁺-block by postsynaptic depolarization (modified from Sj¨ostr¨om et al., 2008, with permis-sion).

The level of calcium influx itself is dominantly controlled by N-methyl-D-aspartate (NMDA) receptors (cf. Figure 2.6) which are integrated in the postsynaptic membrane. These work as coincidence detectors between pre- and post-synaptic stimulation (see also Section 2.2):

The channel opens by binding of presynaptic released glutamate, however, ion conduction is minimized by a Mg²⁺ion blocking the channel and only moderate amounts of ions (mainly calcium and sodium) pass through the chan-nel. Yet, a sufficient postsynaptic depolariza-tion removes the Mg²⁺ block, thus opens the channel completely and causes strong calcium fluxes. The depolarization might arise from

back propagating action potentials

(originat-ing from the soma) and thus provide a mechanism for coincidence detection of pre- and post-synaptic activity. Thus the timing of the action potentials of pre- and postpost-synaptic neurons intimately control the depression or potentiation of the synaptic efficiencies (more detailed de-scription, additional mechanisms are discussed in Sj¨ostr¨om et al., 2008).

We note that the above description of the biophysical foundations of signal generation, transmis-sion and processing outlines some of the basic principles, but is by no means complete. Further informations can be found in recent textbooks (e.g., Dayan and Abbott, 2001; Bear et al., 2006;

Purves et al., 2008).