activity

# What is activity?

activity (wn, noun)  
: - (the state of being **active**;)  
: - (the trait of being active; **moving or acting rapidly** and energetically;)

active (wn, adj)  
: - (disposed to take action or effectuate change;)  
: - (exerting influence or producing a change or effect;)

Note:

`wn activity -over`

Overview of noun activity

The noun activity has 6 senses (first 3 from tagged texts)

1. (43) activity -- (any specific behavior; "they avoided all recreational activity")
2. (36) action, activity, activeness -- (the state of being active; "his sphere of activity"; "he is out of action")
3. (13) bodily process, body process, bodily function, activity -- (an organic process that takes place in the body; "respiratory activity")
4. activity -- ((chemistry) the capacity of a substance to take part in a chemical reaction; "catalytic activity")
5. natural process, natural action, action, activity -- (a process existing in or produced by nature (rather than by the intent of human beings); "the action of natural forces"; "volcanic activity")
6. activeness, activity -- (the trait of being active; moving or acting rapidly and energetically; "the level of activity declines with age")

`wn active -over`

Overview of adj active

The adj active has 14 senses (first 8 from tagged texts)

active (wn, adj)  
: - (disposed to take action or effectuate change;)  
: - (exerting influence or producing a change or effect;)

---

## Bacterial behavior

<div><img src="figs/IMG_0222_ecoli_flagella_7d8b573.jpg" width="400px"><figcaption>E. Coli in 'tumble' mode, six flagella motors</figcaption></div>

<div><img src="figs/IMG_0223_ecoli_activity_7989a2e.jpg" width="400px"><figcaption>E. Coli behavior, J. Allman *Evolving Brains*</figcaption></div>

Note:

Evolving Brains. J. Allman
p. 6,7
> A bacterium, Escherichia coli.

> During a run the six flagella of E. coli are gathered togehter to form a propeller. When the receptors detect a decreasing concentration of the sugar resource, they signal the flagellar motors to revese, causing the flagella to flail about uselessly in a tumble and the bacterium to change its course. The bacterium then reverses its motors again and begins a run in a different direction.

The E. coli flagella motor  
: 1 micro inch diam  
 speed 6000 rpm  
: power output 1.10 micro-micro-micro hp  
: power per unit weight 10 hp per pound  
: power source proton current  
: cylinders 8  
: number of different parts 30  
: gears, 2-- forward (run)  and reverse (tumble)

---

## Paramecium behavior

Eckert, *Animal Physiology* 1997 p. 407  
[JA, CC0](https://creativecommons.org/share-your-work/public-domain/cc0/)  
</figcaption></figure>

Note:

Animal Physiology
p. 407
> A paramecium avoids objects with which it has collided by changing its direction and rat of swimming. A, After it collides with an object a Paramedium backus up , changes direction, and swims away in a new direction. The passage of time is indicated by sequential numbers. Mechanical stimulatin of the anterior and end opens Ca2+ selective channels (righ) increasing the internal free Ca2+ concentration which in turn reverse the ciliary beat. B, When the calcium channels are opended by mechanical stim, the anterior end, the membrane depolarized an produces a graded but weakly regnerative change in the membrane potential that is associated with reversal of the ciliary beat. C, Mechanical stimulatio of the posterior end opens K+ slective channels producing a graded hyperpolarizqation of the membarne that accelerates the ciliary beat by an unknown mechnaims (part A adapted from Grell 1973; parts B and C adapted from Eckert, 1972)

---

## Innate animal behaviors

Note:

Animal Physiology
p. 424
>Fig 11-16 Fixed action patterns can be observed in most species.  mating behaivor in 1 octopus, 2 Helix pomatitia; 3 male sepia officinalis in sexual display; 4 european wildcat strking iwth it spaw; 5, a digger wasp capturing its prey; 6 male three spined stickeback quivering to stimulate a female to spwan; 7 the mouse jmm by a domestic dog. B; the courtship behavior of a male liddler crab

part A 2,3,5,6 adaptied from Tinbergen 1951; 1 adapted from Buddenbrock 1956; 4 adapted from Lindemann 1955; 7 adapted from Lorenz 1954; part B adapted from Lorenz and Tinbergen 1938

p. 426
> Fig 11-18 Sensory input can change behavior. A , A cockroach runs away from light, a negative phototaxis. B, A tethered locust flying in the dark tends to roll about its longitudninal axis. An artifical horizon stabilized the insetcts body postition because visual input modulates the motor output to the flight muscles.

---

## Structure of muscle tissue

<div><img src="figs/IMG_0230_skeletal_muscle_structure_20cfb17.jpg" height="400px"><figcaption>Eckert, *Animal Physiology* p.352 </figcaption></div>

<div><img src="figs/IMG_0233_muscle_troponin_actin_calcium_function_c152240.jpg" height="400px"><figcaption>Eckert, *Animal Physiology* p.367 </figcaption></div>

Note:

Animal Physiology
p. 352
> All vertebrate skeletal muscles are organized in a sterotyped hierarchy. The organ called a muscle constists o fparallel multinucleate fibers, each of which contains many myofibrils. Muscles are attached to bones or other anchor points through toucgh connetive tissue bands called tendons. Each muscle fiber is derived embryonically from a group of myoblasts that fuse to form myotubes.

p. 367
> Fig. 10-16 Tropoonin and tropomyosin regulate binding betwen myosin cross bridges and actin thin filaments. (A) Three dim model depticing the association of tropmyosin (TM) and the troponin complex containing subunits C, I , and T with the actiin filament. (B) Mechanism of Ca2+ mediated regulation of actin myosin interaction. When the concentrion of Ca2+ is low the toponiin complex bindss with actin and tropmyosin sterically preventing myosin cross bridges from bining to actin. If the conentraitn of cytoplasmic Ca2+ increases toponin C binds Ca2+ changing the subunit affinities and causing thr tropomysoin molecule to move away from the myosin binding stie on actin. Cross bridges can then bind cyclically and the thick and thin filaments can slide past one another until Ca2+ is removed from the troponin complex (adapted from Phillips at al 1986, part B adapted from Ebashi 1980).

---

## Calcium and the protoplasmic unit of life

<div><img src="figs/IMG_0232_calcium_calmodulin_IP3_Gprotein_signals_558b554.jpg" height="400px"><figcaption> Eckert, *Animal Physiology* fig 9-14</figcaption></div>

<div><img src="figs/IMG_0231_calcium_calmodulin_signal_overview_4c56b2a.jpg" width="400px"><figcaption>Eckert, *Animal Physiology* fig 9-18</figcaption></div>

Note:

Animal Physilogy
p. 320
> Fig 9-14 Biding of homrones by some G protein-linked receptors induces formation of the phospholipid dereived second messengers diacylglyercol (DAG) and inositol triphosphate (InsP3)  (A) Generic schem of inositol phopholipid pathway, which is nearly identical with that of the cAMP pathway (B) Condensed outline of the inosoitol phosophlipid second messenger system. The amplifer enzyme in this pathway is phophoinosditede specific phopholpase C (PLC). The direct activation of guanylate cyclase by PLC (dashed pathway) is not fully establishe. Note that Ca2+ mobilized from intracellular stores may activate troponin C (TnC) form a complex with calmdulin (CaM) that activates Ca2+/calmodulin depedent kinase (Ca2+/CaM kinase) promate actiation of protein kinsase C or increase cGMP production by stimulating membrane bound guanylate cyclase

>Fig 9-18 Calcium/calmosuine regualtes many processes or enzymes within cells. Among these are adeynlate cyclase and guanylate cyclase, which catyze formation of the nucleotide secon messengers (Adapted from Cheung 1979)

---

## Metal ion function in cells

Note:

Animal Physiology. Eckert, 4th ed. 1978, 1997
Molecules, energy, and biosynthesis
p. 72
> Metal ions that function as cofactors. Source Lehninger, 1975

---

## Cellular activity and energy flow

Note:

Animal Physiology. Eckert, 4th ed. 1978, 1997
Molecules, energy, and biosynthesis

p. 79
> Fig. 3-55. The hydrolysis of ATP powers numerous energy-requiring processin biological systems. The ADP produced by hydrolysis is recycled to ATP by rephosphorylation energized by the oxidation of foodstuff molecules to CO2 and H20

> Fig 3-56 Carbohydrates, lipids, and proteins all can be degraded by cells to yield usable energy in the form of ATP. All three classes of foodstuffs are interlinked in intermediary metabolishm and feed intermediates in to the citric acid cycle whici is linked to the electron-transport chain. During aerobic metabolism, complete oxidation to CO2 and H2O occurs. During anaerobic metabolism, however, cellular respiration is impossible and lactate accumulates.

* Complex organic molecule breakdown results in free energy liberation, increasing entropy of the living matter. e.g. glucose oxidation to CO2 and H2O by combustion, respiration.
* Change in Gibb's free energy during glucose oxication, for one mol of glucose plus 6 mol O2 returns 6 mol CO2 and 6 mol H2O giving `delta-G=> -686 kcal*mol^-1`. This is the difference in free energy into forming glucose molecule during photosynthesis and the total free energy contained in the produced CO2 and H2O. This would be 686 kcal of heat produced in a isolated combustion chamber. For cellular respiration some of this energy is conserved as chemical energy by phosphorylating ADP into ATP for doing useful work.
* For cells delta-G is -420 kcal as heat, and thus 266 kcal is incorporated into 38 mol of ATP
* Recall that oxidation is transfer of electrons from a molecule to another; convesely ris reduction.

---

## Electrical current

Pump pressure ~ Voltage (volts) = `V`

Pipe diameter ~ Resistance (ohms) = `R`

Flow rate ~ Current (amperes) = `I`

`V = IR` **Ohm’s law**

`I = V/R`

</div>

<div style="margin:0 15px"><img src="figs/ScreenShot2016-01-10at3.49.52PM_f9a9f96.png" height="300px"><figcaption>M. Banzi Fig. 4-4, *Getting Started with Arduino* isbn:9781449363338</figcaption></div>

Note:

Recall from physics that voltage is related to the resistance and current in an electrical circuit as described by Ohm’s law. This analogy of a water pump/water wheel circuit helps us understand these relationships better.

Voltage  
: is the potential difference, or electromotive force measured across the conductor in units of volts.  
: So imagine a hand pump that you use to do some work and introduce pressure in a water system, that pressure or potential difference is the voltage.

*Volt is defined as the difference in electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points*  
*voltmeter, ammeter*

Current  
: measured in amperes is the flow of electric charge across a surface at the rate of one coulomb per second. Used to express the flow rate of electric charge.  
: So imagine the rate of water flow in this water pump as the the flow of electric charge across a cell membrane. What is the charge that is moving for a cell? Monovalent and divalent atoms like Na⁺, K⁺, Cl⁻, and Ca²⁺.

*1A equivalent to one coulomb (roughly 6.241×10^18 times the elementary charge) per second*  
*coulomb = charge (symbol: Q or q) transported by a constant current of one ampere in one second. 1C equivalent to a charge of approximately 6.242×10^18 protons or electrons.*  
*elementary positive charge: This charge has a measured value of approximately 1.6021766208×10^−19 coulombs*

Resistance  
: is the difficulty to pass a current through a conductor measured in ohms.  
: Image the diameter of a pipe or a valve that you can regulate to be the resistance  
: inverse of resistance is conducance *g* measured in siemens (S)  
: for studying neuronal excitability rewriting Ohm's law as I = g(Vm-Ex) is most useful. g = conductance, no. of open channels. (Vm-Ex) = driving force causing either positive or negative current.

**Ohm’s law** from physics class relates these quantities together as V = IR, and rearranging this equation and reading it as I = V/R or Current = Voltage divided by Resistance gives you a better intuitive feel for these relations. **Notice that when you have 0 voltage or potential difference you have no current.**

Avogadro constant  
: (symbols: L, NA)  
: is the number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by one mole.  
: Avogadro’s constant = 6.022×10^23 and is dimensionless.

mole  
: it is defined as the amount of any chemical substance that contains as many elementary entities, e.g., atoms, molecules, ions, electrons, or photons, as there are atoms in 12 grams of pure carbon-12 (12C).  
: this number is expressed by the Avogadro constant

electricity  
: movement of charged carriers through a medium in presence of electric field
: duality of electromagnetic waves as wave or particle  
: AC (oscillation of electrons in place) vs DC (movment of electrons)

100 m/s == 360K m/hr == 223 mph

---

## Na⁺–K⁺ pump

* 3 Na⁺ out for every 2 K⁺ in
* Pumps against concentration gradient
* Requires ATP
* Helps set up the ion concentration gradients and resting membrane potential

<div><img src="figs/alberts_fig11-10-NaKatpase_f8e7b70.png" height="300px"><figcaption>Alberts *Mol Biol of the Cell* 3e Fig. 11-10</figcaption></div>

Note:

Here is one these ion transporters— the Na-K pump that moves 3 Na out of the cell for every 2 K in.  This is an active process, requiring ATP. Moving 3 positively charged Na out for every 2 potassiums in leaving a net negative charge just across the membrane.

---

## Ion channels

* Membrane bound
* Open and closed states
* Show ion selectivity
* Can be gated by different mechanisms

Note:

Ion channels span the membrane and act as pores. They can open and close, often in a voltage-dependent fashion as we will learn thursday. And ion channels even show selectively such that there are different types of Na, K channels as well as others.

And they can be additionally regulated or ‘gated’ by different mechanisms including voltage or binding of ligands such as neurotransmitters. We will learn much more about the selectivity and function of ion channels a couple lectures from now.

---

## Electrochemical equilibrium

<figure><figcaption class="big">orange dots K⁺, green dots Cl⁻. This simulated membrane is **only permeable to K⁺**</figcaption><img src="figs/Neuroscience5e-Fig-02.05-1R-2_163131c.png" height="500px"><figcaption>Neuroscience 5e/6e Fig. 2.5</figcaption></figure>

Note:

First let’s discuss **electrochemical** equilibrium, which is the balance of two driving forces— electrical AND chemical diffusion– across a cell membrane.

Imagine the following experiment. We have a cell and record intracellular membrane potential with electrodes and a voltmeter.

If this membrane is only permeable to K⁺, and KCl concentration is the same inside and outside the cell, there is no net flux of K⁺

If KCl is more concentrated inside the cell, initially there is a net flux of positively charged K⁺ from inside to outside the cell due to the chemical concentration driving force which leaves the membrane hyperpolarized because of the net movement of postive charge to the outside until the this chemical force is balanced by the electrical driving force from the positively charged K⁺ being repelled by the more positive environment now outside the cell. This is called electrochemical equilibrium, and the potential at which this occurs is called the equilibrium potential for that ion.

---

## Nernst equation

* Statement of the equilibrium condition for a single ion species across a membrane that is permeable only to that ionic species:
    * *Ex* = equilibrium potential (V) for ion *x*
    * *R* = the gas constant (8.3 J mol<sup>-1</sup> K<sup>-1</sup>)
    * *T* = absolute temperature (K)
    * *F* = faraday constant (9.6x10<sup>4</sup> J mol<sup>-1</sup> V<sup>-1</sup>)
    * *z* = valence of the ion, including sign.
    * ln = natural logarithm (base *e*)
    * [*x*]<sub>out</sub> extracellular concentration of an ion; [*x*]<sub>in</sub> intracellular concentration

*  RT/F can be a constant at room temperature to give a simplified equation

</div>

<div><figcaption class="big">Nernst equation</figcaption><img src="figs/ScreenShot2016-01-12at12.35.02PM_cfc06b6.png" height="100px"><figcaption>For calculations at any temperature, E<sub>x</sub> in volts (V)</figcaption></div>

<div><figcaption class="big">Simplified Nernst equation</figcaption><img src="figs/ScreenShot2016-01-12at12.35.07PM_dc81a98.png" height="100px"><figcaption>For calculations at room temperature (68ºF = 20ºC = 20+273 = 293ºK), E<sub>x</sub> in millivolts (mV)</figcaption></div>

Note:

So I stated that the Nernst equation is how we can calculate the equilibrium potential for a cell membrane permeable to one type of ion.

And here is the Nernst equation is:

Where Ex is...

Gas constant R  
: equivalent to the Boltzmann constant but expressed in units of energy.  
: The physical significance of R is work per degree per mole.  
: R = 8.3144598 J mol−1 K−1 == R = work / amount x temperature.  
: Relates the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered. Joules/mol/K

Temperature  
: absolute temperature expressed in degrees Kelvin

Faraday constant  
: magnitude of electric charge per mole of electrons = 96485.33289 C/mol. Expressed in C/mol or J/mol/V

z  
: the valence of the ion in question

ln  
: the natural logarithm which has the mathematical constant *e* =~2.718 as it’s base (Euler's number)
: ln(e) = 1, where e =~ 2.718

Now many of the classical experiments recording membrane potential in squid axon or other preparations were conducted at room temperature, which is 20ºC or about 68ºF.

Thus to make calculations simpler in the classic scientific papers (often from the 1930s and 1940s before computers) this equation for experiments carried out at room temperature (20ºC = 68ºF = 20ºC+273ºK = 293ºK) is often simplified to the following of:

which uses the base10 logarithm. Since —>

ln(x) / log10(x) = 2.30

—> 2.30 * log10(x) = ln(x)

logarithm slope example:

```r
x = seq(0,10,0.10);
plot(x,log(x), asp=1);
plot(x,log10(x), asp=1);
```

R = 8.3 J/K∙mol, T = 37ºC + 273ºC = 310 K, F = 9.6∙10^4 J/mol∙V

E =

log(7) / log10(7)

Goldman-Hodgkin-Katz constant field equation (Hille 1992) as applied to calcium dependent depolarization currents sensitive to gap junction
https://physoc.onlinelibrary.wiley.com/doi/10.1111/j.1469-7793.1998.763bp.x

## Obtaining the simplified Nerst equation

Open up your browser's web developer javascript console (shift-ctrl-k (Firefox) or cmd-alt-j (Chrome)). Copy/paste the following lines:

```javascript
R = 8.3 //Gas constant
F = 9.6 * 10**4 //Faraday constant
T = 20+273 //Room temperature in Kelvins
```

Relation of the natural logarithm (base *e* 2.718...) to the base 10 logarithm is always `ln(x) = 2.30 * log10(x)` or `ln(x) / log10(x) = 2.30`. ln() is `Math.log()` and log10() is `Math.log10()` in javascript. Copy/paste the following lines. Try varying *x* a few times and re-calculate:

```javascript
x = 5
Math.log(x) / Math.log10(x)
```

Now use our constants defined above, convert to base10 log, and adjust the voltage from V to mV. We get 58 mV for our answer:

```javascript
(R*T / F) * 2.3 * 1000
```

=>58.26427 mV

</div>

Note:

```
var a = [2,5,7,10,1000]
a.forEach(el => console.log( Math.log(el) / Math.log10(el) ))
```

---

# Sodium, potassium, chloride, calcium

---

## Extracellular and intracellular ion concentrations

| ion | intracellular conc. (mM) | extracellular conc. (mM) | ratio [x]<sub>out</sub>/[x]<sub>in</sub> |
| --- | --- | --- | --- |
| potassium (K<sup>+</sup>), squid | 400 | 20 | ~0.05 |
| potassium (K<sup>+</sup>), mammal | 140 | 5 | ~0.04 |
| sodium (Na<sup>+</sup>), squid | 50 | 440 | ~9 |
| sodium (Na<sup>+</sup>), mammal | 5–15 | 145 | ~9 |
| chloride (Cl<sup>-</sup>), squid | 40–150 | 560 | ~3.7 |
| chloride (Cl<sup>-</sup>), mammal | 4–30 | 110 | ~3.7 |
| calcium (Ca<sup>2+</sup>), squid | 0.0001 | 10 | 100000 |
| calcium (Ca<sup>2+</sup>), mammal | 0.0001 | 1–2 | 10000 |

</div>

Note:

Table of physiological relevant intracellular and extracellular ion concentrations in squid neurons and mammalian neurons. Though the values are scaled about 4 times higher in squid, note that K is more concentrated inside, and sodium and chloride are more concentrated outside for both invertebrate and vertebrate neurons. The relevant ratios of different ion species inside and outside are similar.

---

## Cells are protoplasmic containers

* Semi permeable membranes
* Concentration gradients of ions across membranes
* Concentration of Na⁺ and Cl⁻ higher outside than inside, while K⁺ is higher inside
* The resting membrane potential is close to the equilibrium potential for K⁺, suggesting that at rest a cell is permeable mostly to K⁺

Note:

Cells are a bit like a semipermeable bag of electrolytes with different concentrations of ionic species inside and outside.

---

## The action potential as measured by Hodgkin, Huxley, and Katz

<figure><img src="figs/hodkin-huxley-nature-1939-AP_d30dfee.png" height="400px"><figcaption>Adapted from Hodgkin and Huxley *Nature* 1939</figcaption></figure>

Note:

Hodgkin and Huxley, Nature 1939 squid giant axon

Image adapted from Principles of Neurobiology, L. Luo Garland Fig 2-19 which in turn adapted from Nature 1939.

Capacitance (farads) is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. Dielectric materials. Storage of electrical energy temporarily in an electric field. **Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates.**

---

## Hodgkin and Huxley AP model simulation

https://ackmanlab.com/2017-06-30-hodgkin-huxley-model.html

---

## Calcium spikes and unicellular behavior

<figure><img src="figs/IMG_0227_paramecium_behavior_calcium_9d1dc72.jpg" height="500px"><figcaption>Eckert, *Animal Physiology* 1997 p. 407</figcaption></figure>

Note:

- unicellular
- paramecium calcium spike example
- muscle cell example from earlier
- vesicle and organelle (e.g mitochondira) transport along cytoskeletal networks inside cells (axons)
- fundamental for vesicle fusion and signal release (e.g. neurotransmitter release at synapses)
- cell-cell adhesion, tissue structure (integrins etc)
- neural cell neurotransmitter differentiation, N. Spitzer work

---

## Functional calcium flux in xenopus

* Jelly surrounding frog egg contains more than 5mM diffusible Ca2+, and Ca2+ is required for fertilization https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5256882/

* The four dimensions of calcium signalling in Xenopus oocytes https://doi.org/10.1016/0143-4160(91)90022-7

* Parker I, Yao Y. Regenerative release of calcium from functionally discrete subcellular stores by inositol trisphosphate. Proc R Soc Lond B Biol Sci. 1991;246:269–274.  https://www.ncbi.nlm.nih.gov/pubmed/1686093

* Parker I, Choi J, Yao Y. Elementary events of InsP3-induced Ca2+ liberation in Xenopus oocytes: Hot spots, puffs and blips. Cell Calcium. 1996;20:105–121. https://www.ncbi.nlm.nih.gov/pubmed/8889202

</div>

Note:

* xenopus oocytes express a single predominant intracellular Ca2+ channel, a InsP3 coupled receptor. Has endogenous Ca2+ activated chloride currents (Miledi and Parker 1984; Schroeder et al 2008) TMEM16A
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4017334/

* The Xenopus Oocyte: A Single-Cell Model for Studying Ca2+ Signaling. Cold Spring Harb Protoc. 2013 Mar 1; 2013(3): 10.1101/pdb.top066308 https://dx.doi.org/10.1101%2Fpdb.top066308

Miledi R, Parker I. Chloride current induced by injection of calcium into Xenopus oocytes. J Physiol (Lond) 1984;357:173–183. https://www.ncbi.nlm.nih.gov/pubmed/6096530

Schroeder BC, Cheng T, Jan YN, Jan LY. Expression cloning of TMEM16A as a calcium-activated chloride channel subunit. Cell. 2008;134:1019–1029. https://www.ncbi.nlm.nih.gov/pubmed/18805094

Lechleiter JD, Girard S, Clapham D, Peralta E. Subcellular patterns of calcium release determined by G protein-specific residues of muscarinic receptors. Nature. 1991a;350:505–508. https://www.ncbi.nlm.nih.gov/pubmed/1849616

Lechleiter JD, Girard S, Peralta E, Clapham D. Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. Science. 1991b;252:123–126. https://www.ncbi.nlm.nih.gov/pubmed/2011747

Model org comparison for developmental embryology Wheeler & Brändli 2009 Dev Dyn 238:1287-1308