This chapter is most relevant to Section F2(i) from the 2017 CICM Primary Syllabus, which expects the exam candidates to be able to "describe the control of breathing". This seems to be a popular topic. It has appeared multiple times in the CICM Part I exam, and is sure to appear again. 

To "describe the control of breathing", one would be reasonably safe to start by reading Control of breathing, the chapter from Nunn's (Chapter 4 in the 8th edition, p.51-72). If that level of depth is for whatever reason insufficient, the next best resource is the somewhat dated but insanely detailed 1992 monograph by Christopher B. Wolff from the department of physiology at Kings' College.  A more recent and less detailed overview is offered by UpToDate.  It is of course paywalled. Of the freely available literature on this subject, Prabhakar & Peng (2004) is probaby the most thorough overview.

In short, the respiratory system: it respires. Gases are exchanged between the air and blood; CO2 is eliminated and O2 is absorbed; that's its main function. Side benefits include the fact that a normal pH is maintained in the body fluids. Therefore, if one wanted to determine whether or not the respiratory system was doing its job, one would naturally want to use arterial oxygen pH and carbon dioxide tension as the most solid quality assurance indicators. Naturally, minimising wear and tear is a part of safely operating this machinery, which means some sort of regulatory stretch receptors and proprioceptive sensors would be helpful to make sure it's not flying apart in the course of routine operation. A central integrator of these inputs would probably be required, ideally with a completely automated backup rate but allowing for some voluntary control. And it would need to exert its regulatory control by means of effector organs. In this fashion, one can describe the control of respiration in terms of "sensor-controller-effector" relationships, which - judging from the college examiners' comments for the abovelisted SAQs- is exactly what they wanted. 

In summary:

Sensor Organs involved in the Control of Respiratory Function
Sensor Stimulus Afferent nerve

Carotid body glomus
(Type I cells) - sited at the bifurcation of the common carotid

  • PaO2
  • PaCO2
  • pH
  • Temperature
  • Glucose (hypoglycaemia)
Glossopharyngeal
Aortic glomus cells - in the aortic arch, subclavian arteries and pulmonary trunk
  • PaO2
  • Changes in O2 delivery (anaemia, carboxyhaemoglobin, hypotension)
  • PaCO2
Aortic nerve
(branch of the vagus)
Central chemoreceptors
  • pH
-
Mechanoreceptors in bronchial and lung tissue
  • Inflation and deflation (i.e. stretch)
Vagus
Respiratory Control Centres
Controller Role Efferents and effectors
Nucleus retroambigualis Expiratory function

Upper motor neuron axons to contralateral expiratory muscles

Nucleus paraambigualis Inspiratory function

Upper motor neuron axons to contralateral inspiratory muscles

Nucleus ambiguous Airway dilator function

Vagus nerve: to (larynx, pharynx and muscularis uvulae)

Glossopharyngeus muscle to stylopharyngeus muscle

Pre-Bötzinger complex Respiratory pacemaker ("central pattern generator") Interneurons connecting to other respiratory control regions
Bötzinger complex Expiratory function

Inhibitory interneurons to phrenic motor neurons and other respiratory control regions

Pontine respiratory group

Integrates descending control of respiration from the CNS

Interneurons connecting to other respiratory control regions
Cerebral cortex Volitional and behavioural  respiratory control Pontine respiratory group

Sensory organs of respiratory control

Of the freely available literature on this subject, Prabhakar & Peng (2004) is probably the most thorough overview. In summary, these sensory organs consist of the following:

  • Peripheral chemoreceptors
    • Carotid body (glomus cells)
    • Aortic body
  • Central chemoreceptors
    • Ventral medullary sensing body
  • Stretch and proprioception receptors

Carotid body chemoreceptors

The carotid bodies are a set of round little organs stationed on either side of the neck at the bifurcation of the common carotid.  They are quite small, about 20mmin volume, embedded in the blood vessel adventitia and roughly pea-shaped (etymologically, glomus apparently means "ball-shaped lump").  Here's a picture of a human carotid body from Ortega‐Sáenz et al (2013), who acquired about sixteen of them from organ donors. With dissection, everything looks like pale tan tissue, so the authors helpfully pointed a black arrow at it. 

carotid body gross structure and histology
As can be seen from the histological crossection (misappropriated from Junqueira's Basic Histogy, 12th ed), a large number of capillaries (labelled "C") runs between the glomus cells. The carotid bodies are suitably well supplied with arterial blood, which is logical for an organ expected to sample and analyse it.  
 
This thing consists mainly of two cell types:
  • Type I cells, also referred to as "glomus" cells, which are neuronal in origin
  • Type II cells, also called "sustentacular" cells, which are functionally glial

In addition, there are also a few neural crest-derived progenitor cells which are probably irrelevant to the chemosensory function of this organ. They are stimulated by hypoxia to reproduce, with the result that chronically hypoxic individuals (eg. dwellers of high-altitude residences) tend to have hypertrophied carotid bodies. 

The Type I cells sense oxygen, and - without going into too much detail - potassium channels are involved in this, but the mechanism by which oxygen affects them does not seem to be particularly clear to anybody. A recent entry on this topic (Lopez-Barneo, 2018) reports that some oxygen-sensitive potassium channels are inhibited by hypoxia, which leads to cell depolarisation and synaptic neurotransmitter release. The Type I cells synapse with axons of the glossopharyngeal nerve, extending from the neuron cell bodies in the petrosal ganglion. Apart from hypoxia, these cells also depolarise in response to a number of other stimuli:

  • pH changes
  • Temperature 
  • PaCO2 
  • Glucose (specifically, hypoglycaemia)

The peripheral chemoreceptor response to PaCO2 is actually a submaximal response, but occurs much faster than the response from the central chemoreceptors. An elegant experiment to support this was performed by Smith et al (2006). The authors took a dog, denervated one carotid body, and perfused the other with a controlled blood flow in which the PaCO2 was carefully adjusted. The increased delivery of PaCO2 to peripheral chemoreceptors alone produced a rapid increase in ventilation, but the increase was only about 37% of the total possible increase (where both central and peripheral receptors were perfused with similarly hypercapnic blood). However, the carotid body receptors produced a response within 1-3 seconds of the initiation of hypercapnia (i.e. within the space of a single breath), whereas central chemoreceptors took a relatively sluggish 11 seconds to produce a response. In summary, carotid body chemoreceptors are responsible for the immediate responses to changes in CO2 over short timeframes, and central chemoreceptors are responsible for most of the steady-state response to sustained hypercapnia.

 Aortic body chemoreceptors

These are seldom spoken of in physiology textbooks, and frequently lumped together with the carotid bodies as "peripheral chemoreceptors". Fortunately, Nanduri Prabhakar has dedicated an entire ection of a chapter from Chemosensory Transduction (2016) to discussing them. First of all, they are not just aortic. Coleridge et al (1967) went through the entire cat circulatory system looking for chemosensory tissues and found them scattered throughout the aorta pulmonary trunk and subclavian arteries, being most prominent in the latter. In comparative biology, their location and function are not guaranteed-  some mammals (eg. rabbits and mice) don't have any aortic body chemoreceptors whatsoever, and appear to be quite undisturbed by their absence. They are supplied by the aortic nerve (a branch of the vagus), with the cell bodies of these axons sitting in the stellate ganglion.

Though histologically these structures are identical to the carotid glomus (type I cells and everything), they receive one-sixths of the blood supply compared to the carotid body, and are scattered in small groups of cells rather than collecting in one specific pea-shaped lump. Functionally, they seem rather redundant. In the presence of a normal working set of carotid chemoreceptors, they contribute minimally to the control of ventilation. Their role becomes more prominent when the carotid chemoreceptors are bilaterally destroyed. Honda (1992) suggested that they may be responsible for the restoration of some weak peripheral chemoreceptor activity among humans who have undergone bilateral carotid body resection, a procedure historically performed to relieve the chronic dyspnoea in COPD.

From the perspective of the exam candidate ("if they are useless, why study them at all?") the aortic bodies have one notable characteristic worth knowing about. They sense oxygen content rather than oxygen tension, though they also respond weakly to the latter. Lahiri et al (1981) demonstrated this by subjecting some anaesthetised cats to carbon monoxide under conditions of a constant PaO2. With a carboxyhaemoglobin concentration in excess of 70%, while the oxygen tension remained normal, carotid body chemoreceptors completely neglected the fact that the blood had lost most of its oxygen-carrying capacity, whereas the aortic bodies increased their firing rate thirty-fold. Similarly, these sensors respond to anaemia and hypotension. The graphics below are mashed together from two studies by Lahiri (the other, from 1980, looked at the aortic body response to changes in blood pressure).

aortic body chemoreceptor response to carboxyhaemoglobin and hypotension

In addition to sensing changes to oxygen delivery, aortic chemoreceptors respond to changes to CO2, but apparently not to pH, or temperature, or glucose; or rather, nothing appears to be written on the matter. One might surmise that the investigation of these minutiae awaits a suitably motivated doctoral candidate.

Central chemoreceptors

As mentioned above, these are the receptors responsible for the slow adjustments of ventilation to steady-state conditions. Nattie & Li (2012) give an excellent overview, which is free via PubMed. To call it generously detailed would be an understatement; by the time you get to page 17 you're only just finished with the anatomy section. 

Anatomically, the chemoreceptor areas are usually described as being localised to the ventrolateral medulla (around the origin of the 9th and 10th cranial nerves). If one had to give these areas names, retrotrapezoid nucleus and caudal medullary raphe are sufficiently clever-sounding and may be enough to bamboozle a tired CICM viva examiner.  In reality, the central chemoreceptor areas are spread widely around the brain. By the use of local injections of acetazolamide directly into cat brains, mapping pH-sensitive areas revealed patches in the cerebellum, hypothalamus, pons and midbrain. 

These receptors are mainly sensitive to changes in their intracellular pH, which is related to the pH of the interstitial fluid in the CNS. Therefore, similar responses occur to increasing PaCO2 as occur to any other proportionally acidifying stimulus, be it hydrochloric acid or lactate. Wang et al (2002) stimulated the medullary raphe cells of rats with both carbon dioxide and HCl - the firing rate tripled at a pH of 7.17 irrespective of how that pH was achieved. The same responses were seen with hypercapnic acidosis at a constant bicarbonate level, acidosis with reduced bicarbonate at constant CO2, increased CO2 with lowered bicarbonate to maintain a constant extracellular pH, and by HEPES buffer which acidified the cell culture without any CO2 or bicarbonate. Clearly, intracellular pH must be the stimulus to central chemoreceptor activity, as it was the unifying change in all of these manipulations. The precise molecular mechanism which transforms intracellular pH changes into the modulation of neuron firing remains to be determined. Acid-sensitive ion channels, probably potassium channels, are implicated, but then so are a dozen others.

Unknown mechanisms of central respiratory rhythm control

Independently of central chemosensitivity to CO2 and pH, the rate of metabolic CO2 production itself is somehow linked to respiratory drive, and nobody knows how. Phillipson, Duffin and Cooper (1981) took some sheep, piped their mixed venous blood into an ECMO circuit, removed all of the excess CO2 produced by metabolism, and returned the blood into the pulmonary circulation. With this, when the rate of CO2 removal by the extracorporeal circuit equalled the rate of CO2 production by the sheep, the systemic arterial CO2 remained normal (around 40 mmHg) but the awake animals stopped breathing completely. This state of apnoea was maintained for up to an hour at a time, and could have carried on indefinitely. The mechanical act of taking a breath was completely undisturbed- "during apnea the sheep was clearly capable of breathing, particularly in response to extraneous prodding, noises, or other stimuli", the authors pointed out. 

Stretch receptors and the Hering-Breuer Reflex

Mechanoreceptors in the lung monitor mechanical forces acting on lung tissue. Specifically, they stimulate respiratory activity where the lung is deflated, and depress it when the tissues are overstretched. This reflex was discovered by Ewald Hering and Joseph Breuer in 1868. The original papers are probably available somewhere for the reader fluent in German, but are apparently written in such a way as to be almost intentionally difficult to understand, such that Elizabeth Ullmann, in translating them for the Hering-Breuer Centennary Symposium, had to take considerable liberties with the original to make it human-readable ("Without much compunction I have chopped up many of Breuer’s long, convoluted sentences into several shorter ones, often changing the sequence of statements contained in his complex clauses and sub-clauses, where this helped to clarify the sense"). Anyway, without further digressions, one last credit to Hering and Breuer is to note that they also determined that the afferent nerve for this reflex is the vagus, insofar as the reflex was completely abolished in vagotomised animals. This reflex plays a role in feedback even in normal tidal respiration, and is depressed in chronically overinflated people, for example COPD patients (Tryfon et al, 2002).

Control of ventilation by the central nervous system

Question 13 from the second paper of 2015, the examiners asked for "a description of central control ... rather than listing nuclei or areas". This is of course quite difficult; Nunn's takes about four pages to explain it. A time-poor exam candidate would need to have a succinct way to describe this complex topic, perhaps in bullet points or a table. As an example, here is a list nuclei and areas with descriptions of their functions:

Respiratory Control Centres
Controller Role Efferents
Nucleus retroambigualis Expiratory function

Upper motor neuron axons to contralateral expiratory muscles

Nucleus paraambigualis Inspiratory function

Upper motor neuron axons to contralateral inspiratory muscles

Nucleus ambiguous Airway dilator function

Vagus nerve: to (larynx, pharynx and muscularis uvulae)

Glossopharyngeus muscle to stylopharyngeus muscle

Pre-Bötzinger complex Respiratory pacemaker ("central pattern generator") Interneurons connecting to other respiratory control regions
Bötzinger complex Expiratory function

Inhibitory interneurons to phrenic motor neurons and other respiratory control regions

Pontine respiratory group

Integrates descending control of respiration from the CNS

Interneurons connecting to other respiratory control regions
Cerebral cortex Volitional and behavioural  respiratory control Pontine respiratory group

The means of their discovery lie amid piles of dead cats with mangled hindbrains. These piles are weighed and measured in an excellent retrospective by Remmers (2005), in case anybody needs to become familiar with the history of respiratory control research. It's a long article, with minimal exam relevance. In summary, most of the twentieth century was dominated by investigators who tried to produce respiratory arrest by selectively damaging small groups of cells in the brainstem. "A clear view of the area of the medulla involved was obtained, ...more usually by removing the central portion of the occipital bone with a rongeur and the central portion of the cerebellum with a scoop" report Henderson & Cragie (1936). This sort of thing went on until the 1970s, when action potentials from individual groups of respiratory neurons were measured, alleviating the need for further cat attrition.

References

Wolff, Christopher B. "The physiological control of respiration." Molecular aspects of medicine 13.6 (1992): 445-567.

Henderson, V. E., and E. Horne Craigie. "On the respiratory centre." American Journal of Physiology-Legacy Content115.3 (1936): 520-529.

Remmers, John E. "A century of control of breathing." American journal of respiratory and critical care medicine172.1 (2005): 6-11.

 Richter, D. W., F. Heyde, and M. Gabriel. "Intracellular recordings from different types of medullary respiratory neurons of the cat." Journal of neurophysiology 38.5 (1975): 1162-1171.

López-Barneo, J., et al. "Carotid body oxygen sensing." European Respiratory Journal 32.5 (2008): 1386-1398.

Prabhakar, Nanduri R., and Ying-Jie Peng. "Peripheral chemoreceptors in health and disease." Journal of Applied Physiology 96.1 (2004): 359-366.

Atanasova, Dimitrinka Y., Michail E. Iliev, and Nikolai E. Lazarov. "Morphology of the rat carotid body." Biomedical Reviews 22 (2011): 41-55.

Ortega‐Sáenz, Patricia, et al. "Cellular properties and chemosensory responses of the human carotid body." The Journal of physiology 591.24 (2013): 6157-6173.

López-Barneo, José. "Oxygen sensing and stem cell activation in the hypoxic carotid body." Cell and tissue research 372.2 (2018): 417-425.

Nattie, Eugene. "Why do we have both peripheral and central chemoreceptors?." Journal of Applied Physiology 100.1 (2006): 9-10.

Smith, Curtis A., et al. "Response time and sensitivity of the ventilatory response to CO2 in unanesthetized intact dogs: central vs. peripheral chemoreceptors." Journal of Applied Physiology 100.1 (2006): 13-19.

Lahiri, S., et al. "Relative responses of aortic body and carotid body chemoreceptors to carboxyhemoglobinemia." Journal of Applied Physiology 50.3 (1981): 580-586.

Lahiri, S., et al. "Relative responses of aortic body and carotid body chemoreceptors to hypotension." Journal of Applied Physiology 48.5 (1980): 781-788.

Prabhakar, Nanduri R. "O2 and CO2 detection by the carotid and aortic bodies." Chemosensory Transduction. Academic Press, 2016. 321-338.

Coleridge, Hazel, J. C. G. Coleridge, and A. Howe. "A search for pulmonary arterial chemoreceptors in the cat, with a comparison of the blood supply of the aortic bodies in the new‐born and adult animal." The Journal of physiology 191.2 (1967): 353-374.

Honda, Yoshiuki. "Respiratory and circulatory activities in carotid body-resected humans." Journal of Applied Physiology 73.1 (1992): 1-8.

Nattie, Eugene, and Aihua Li. "Central chemoreceptors: locations and functions.Comprehensive Physiology 2.1 (2011): 221-254.

Li, Aihua, Shawn Zhou, and Eugene Nattie. "Simultaneous inhibition of caudal medullary raphe and retrotrapezoid nucleus decreases breathing and the CO2 response in conscious rats.The Journal of physiology 577.1 (2006): 307-318.

Phillipson, ELIOT A., James Duffin, and Joel D. Cooper. "Critical dependence of respiratory rhythmicity on metabolic CO2 load." Journal of Applied Physiology 50.1 (1981): 45-54.

Wang, Wengang, Stefania Risso Bradley, and George B. Richerson. "Quantification of the response of rat medullary raphe neurones to independent changes in pHo and PCO2." The Journal of Physiology 540.3 (2002): 951-970.

Ullmann, Elisabeth. "The two original papers by Hering and Breuer submitted by Hering to the KK Akademie der Wissenschaften zu Wien in 1868." Ciba Foundation Symposium‐Breathing: Hering‐Breuer Centenary Symposium. Chichester, UK: John Wiley & Sons, Ltd., 1970

Tryfon, S., et al. "Hering-Breuer reflex in normal adults and in patients with chronic obstructive pulmonary disease and interstitial fibrosis." Respiration 68.2 (2001): 140-144.