brijeshm39/HH_exercise_solution_openworm.rtf

## HH_exercise_solution_openworm.rtf
=================
Section 1
=================

1.1 What is the minimum current you can inject that will cause at least one spike?
A: 2.4 uA/cm^2

1.2 Adjust the input current duration to stimulate the cell for the full duration of the simulation. What is the minimum curent you need to inject to get the cell to fire for the full duration?
A: 6.3 uA/cm^2

1.3 How much does a 10-fold increase in injected current from the repetitive firing current increase the firing rate?
Answer:
Setting I_inj to 100 uA/cm^2 throughout the course of time.
31 spikes to 67 spikes per 450 ms

1.4 What happens for a 100-fold increase? Why does this happen?
Answer:
Setting I_inj to 1000 uA/cm^2 throughout the course of time.
In this situation, only one incomplete spike is observed. The probable reason why this occurs can be understood by considering the gating dynamics of Voltage Gated Sodium channel. We can see that, the sodium channel never enters deactivation mode after the first spike. Thus, it becomes impossible for a neuron to spike without sodium channel.

1.5 Is there any current you can inject to get a half height action potential?
Answer:
Not possible without any alteration in properties of core elements like Voltage gates sodium channel. The height of action potential is directly proportional to amount of sodium ions entering the neuron during depolarization phase. Thus, inorder to achieve the half height, sodium gates must be closed at 20mV, that is reversal potential of sodium must be shifted to 20mV.
However, sodium gates that are present in nature shuts down at 40mV.

1.6 Single action potentials can also be elicited by transient current pulses, even when the duration of the current pulse is shorter than the action potential. What is the effect of pulse duration on threshold current for eliciting a single action potential? Generate a plot of threshold current vs. pulse duration for pulse widths between 0.1 ms and 5 ms. Is there a simple relationship between pulse width and threshold current?
Answer:
It seems like threshold current remains 2.3 uA/cm^2 irrespective of pulse width.


=================
Section 2
=================

2.1 Return the input current injection to the original values. Reduce the conductance densities of Na and K. What is the impact on the AP?
Answer:
+ Frequency reduces. In fact, when g_K is reduced beyond 23 mS/cm^2 (keeping everything else untouched), the model starts firing without any external current.
+ Reduction in g_K  leads to lesser refractory period and hence increases the frequency
+ After reduction of g_Na, the model require more current to fire. Net frequency is reduced

2.2 Restore the original conductance densities. Reduce the reversal potential (e.g. to 20mV) of Na to simulate a decrease in the extracellular Na concentration (i.e. external [Na+] is closer to internal [Na+]). What is the impact on the height/waveform of the action potential? Can a change in the conductance density of Na compensate for this (i.e. increase the height of the AP)? If not, why not?

Answer:
+ During 10 uA/cm^2 - Only one spike is produced. Sodium concentration outside the membrane and input current I_inj are not sufficient to trigger the adjacent channels in the neuron.

+ During 100 uA/cm^2 - It is observed that first spike hits ~ 14 mV bar, but as there is less sodium outside(E_Na = 20 mV) the cell compared to original case(E_NA = 50 mV), less sodium enters the neuron during depolarisation and thus it is in adequate to open all the gates in the neighbour. Thus for next spike, fewer gates are opened. This is demonstrated by decrease in value of "m" - activation constant for sodium channels which also represents the fraction of gates that are open(active) at any given time.

+ An increase in conduction density of voltage gated sodium channels can help to regain the spike "shape", however the amplitude of the spike cannot be achieved unless the external concentration of sodium is increased to its original value. This is because, the height of the spike is determined by the amount of sodium that enters the neuron during depolarisation. Less Sodium outside = Less height.

=================
Section 3
=================

3.1 What happens for hyperpolarizing current injections (set the pulse amplitude to –5 and the pulse duration to 5 ms)?
Answer:
+ The potential across the membrane and threshold required for action potential continues to decrease as long as the hyperpolarising current is applied. As soon as the current is stopped, the potential returns to its resting state, however the threshold is still below its original value. This leads to a state in neuron where potential across membrane is greater than threshold required for action potential. Thus an spike is triggered. One should note that the sodium gates do not open and thus the amplitude of spike is not as high as 40 mV. Amplitude reaches the value of -60 mV. Spike of amplitude 40 mV is triggered only when the potential required to open the voltage gated sodium channels is reached.

3.2 What is the threshold, in terms of current magnitude and pulse duration, for eliciting this so called anode break excitation?
Answer:
-12 uA/cm2 for 2 ms
or -6 uA/cm2 for 5ms

3.3 What mechanisms in the model are responsible for this behaviour? Look at the time course of the activation and inactivation variables n, m and h.
Answer:
3.1 covers the discussion
	=================
	Section 1
	=================

	1.1 What is the minimum current you can inject that will cause at least one spike?
	A: 2.4 uA/cm^2

	1.2 Adjust the input current duration to stimulate the cell for the full duration of the simulation. What is the minimum curent you need to inject to get the cell to fire for the full duration?
	A: 6.3 uA/cm^2

	1.3 How much does a 10-fold increase in injected current from the repetitive firing current increase the firing rate?
	Answer:
	Setting I_inj to 100 uA/cm^2 throughout the course of time.
	31 spikes to 67 spikes per 450 ms

	1.4 What happens for a 100-fold increase? Why does this happen?
	Answer:
	Setting I_inj to 1000 uA/cm^2 throughout the course of time.
	In this situation, only one incomplete spike is observed. The probable reason why this occurs can be understood by considering the gating dynamics of Voltage Gated Sodium channel. We can see that, the sodium channel never enters deactivation mode after the first spike. Thus, it becomes impossible for a neuron to spike without sodium channel.

	1.5 Is there any current you can inject to get a half height action potential?
	Answer:
	Not possible without any alteration in properties of core elements like Voltage gates sodium channel. The height of action potential is directly proportional to amount of sodium ions entering the neuron during depolarization phase. Thus, inorder to achieve the half height, sodium gates must be closed at 20mV, that is reversal potential of sodium must be shifted to 20mV.
	However, sodium gates that are present in nature shuts down at 40mV.

	1.6 Single action potentials can also be elicited by transient current pulses, even when the duration of the current pulse is shorter than the action potential. What is the effect of pulse duration on threshold current for eliciting a single action potential? Generate a plot of threshold current vs. pulse duration for pulse widths between 0.1 ms and 5 ms. Is there a simple relationship between pulse width and threshold current?
	Answer:
	It seems like threshold current remains 2.3 uA/cm^2 irrespective of pulse width.


	=================
	Section 2
	=================

	2.1 Return the input current injection to the original values. Reduce the conductance densities of Na and K. What is the impact on the AP?
	Answer:
	+ Frequency reduces. In fact, when g_K is reduced beyond 23 mS/cm^2 (keeping everything else untouched), the model starts firing without any external current.
	+ Reduction in g_K leads to lesser refractory period and hence increases the frequency
	+ After reduction of g_Na, the model require more current to fire. Net frequency is reduced

	2.2 Restore the original conductance densities. Reduce the reversal potential (e.g. to 20mV) of Na to simulate a decrease in the extracellular Na concentration (i.e. external [Na+] is closer to internal [Na+]). What is the impact on the height/waveform of the action potential? Can a change in the conductance density of Na compensate for this (i.e. increase the height of the AP)? If not, why not?

	Answer:
	+ During 10 uA/cm^2 - Only one spike is produced. Sodium concentration outside the membrane and input current I_inj are not sufficient to trigger the adjacent channels in the neuron.

	+ During 100 uA/cm^2 - It is observed that first spike hits ~ 14 mV bar, but as there is less sodium outside(E_Na = 20 mV) the cell compared to original case(E_NA = 50 mV), less sodium enters the neuron during depolarisation and thus it is in adequate to open all the gates in the neighbour. Thus for next spike, fewer gates are opened. This is demonstrated by decrease in value of "m" - activation constant for sodium channels which also represents the fraction of gates that are open(active) at any given time.

	+ An increase in conduction density of voltage gated sodium channels can help to regain the spike "shape", however the amplitude of the spike cannot be achieved unless the external concentration of sodium is increased to its original value. This is because, the height of the spike is determined by the amount of sodium that enters the neuron during depolarisation. Less Sodium outside = Less height.

	=================
	Section 3
	=================

	3.1 What happens for hyperpolarizing current injections (set the pulse amplitude to –5 and the pulse duration to 5 ms)?
	Answer:
	+ The potential across the membrane and threshold required for action potential continues to decrease as long as the hyperpolarising current is applied. As soon as the current is stopped, the potential returns to its resting state, however the threshold is still below its original value. This leads to a state in neuron where potential across membrane is greater than threshold required for action potential. Thus an spike is triggered. One should note that the sodium gates do not open and thus the amplitude of spike is not as high as 40 mV. Amplitude reaches the value of -60 mV. Spike of amplitude 40 mV is triggered only when the potential required to open the voltage gated sodium channels is reached.

	3.2 What is the threshold, in terms of current magnitude and pulse duration, for eliciting this so called anode break excitation?
	Answer:
	-12 uA/cm2 for 2 ms
	or -6 uA/cm2 for 5ms

	3.3 What mechanisms in the model are responsible for this behaviour? Look at the time course of the activation and inactivation variables n, m and h.
	Answer:
	3.1 covers the discussion