17.4: Subjectivity and Revolutionary Creative Labor
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- Marwan M. Kraidy
- University of California Press
This chapter has been grappling with the extent to which different contextual environments and constraints generate different types of creative labor with different levels of precarity. From the preceding critical comparison of what I called industrial and revolutionary creative labor, we can conclude that the extreme strictures of revolutionary contexts lead to a specific relation between the individual and the social. In The Creativity of Action , Joas singles out three metaphors, which emerged between 1750 and 1850, that are central to creative action: expression, from the work of Johann Gottfried Herder; and production and revolution, both elaborated by Karl Marx. Each of these metaphors, Joas argues, “represents an attempt to anchor human creativity in at least one of the three ways of relating to the world. The idea of expression circumscribes creativity primarily in relation to the subjective world of the actor.” In contrast, “the idea of production relates creativity to the objective world, the world of material objects that are the conditions and means of actions.” “And finally,” Joas concludes, “the idea of revolution assumes that there is a potential of human creativity relative to the social world, namely that we can fundamentally reorganize the social institutions that govern human coexistence.” 36
Revolutionary creative labor, I conclude, entails the convergence of expression, production, and revolution. Revolutionary contexts are characterized by total upheaval—social and political but also economic and cultural—in which everything is up for grabs. These contexts of tremendous flux and peril require a total expenditure of resources, calling on people to mobilize to enact subjective and objective changes to the world they live in.
The definitional field delineated by expression, production, and revolution encompasses familiar axes of tension: the individual versus the social, the ideational against the material, the reformist in contrast to the radical. Such a field is a particularly apt space to grapple with the revolutionary creative labor emerging in the Arab uprisings. If, as Joas and Mayer argue, creativity entails coordinating a variety of means, responding to incentives, and working within constraints, and if, as I have already argued, revolutionaries respond to specific motivations and work within strictures distinct from the constraints of the factory floor (or, for that matter, the production studio), then revolutionary creative labor is indeed a distinct kind of creative labor. 37
Revolutionary creative labor contributes to the creation of a subjectivity that is radically different from that of industrial labor. Jasper noted that artists can “generate and regenerate the very subjectivity they pretend only to display.” 38 This echoes Lazzarato’s argument about immaterial labor, which “presupposes and results in an enlargement of productive cooperation that even includes the production and reproduction of communication and hence its most important content: subjectivity.” 39 Whereas Lazzarato argues that immaterial labor changes the relationship between producer and consumer , it is productive to think of revolutionary creative labor as changing the relationship between ruler and ruled . One important aspect of Lazzarato’s thesis is that the shift from manual to immaterial labor transforms the three elements of what he calls the aesthetic model of labor—author, reproduction, and reception—by emphasizing their social rather than individual aspects. Creativity, Lazzarato concludes by way of brief mentions of Simmel’s work on intellectual labor and Bakhtin’s focus on social creativity, is social rather than individual, a point also made by Joas and Mayer.
Ordinary people from among the hitherto ruled, having become revolutionary activists, enact revolutionary creative labor to get rid of the ruler. Revolutionary creative labor, then, occasions a shift in subjectivity from the atomized docility of subjects under dictatorship to the collective rebellion of politicized agents in revolution. In Foucauldian terms, we can describe revolutionary creative labor as a technology of revolutionary selfhood . It mobilizes expressive and affective resources alongside the material resources of “noncreative” revolutionary labor— demonstrating in the street, staffing barricades, confronting security personnel, wielding sticks, shooting guns, tending to the wounded—to effect fundamental and political change.
The body is crucial to the project of revolutionary selfhood. As I have argued elsewhere 40 (though without grappling with the conceptual minutiae of creativity and labor), the body—as instrument, metaphor, symbol, medium—is central to revolutionary creative labor. Mayer explains how creativity pertains to Joas’s concept of a “situation,” by which he means “the ability of the body to move and communicate in an innovative way. . . . [C]reativity must be enacted through both the body and the social system of meanings that recognizes the action as different from the norm. . . . Creative action unifies the mind and body in doing something perceived as different. . . . This means that thought must be materialized, but also that the material is cause for later reflection.” 41
But in revolutionary contexts of the twenty-first century, the body must be understood as a central and agentive node among a panoply of other media—from cardboard to digital video—that are harnessed by revolutionaries in an all-out campaign to change their lives. The body, then, must be understood as the animator of what I elsewhere called “hypermedia space,” a space of signification with multiple points of access created by interconnections among various media platforms. 42 In the case of the Arab uprisings, these include media that can be characterized as mainstream (television, newspapers), new (mobile devices, social media), and old (puppetry, graffiti), alongside the oldest of them all, the human body, which operates all other media.
Revolutionary creative labor, then, is an embodied, extremely precarious practice unfolding in a life-or-death situation, one among several kinds of labor (from physical struggle to mainstream media production) that challenge authoritarian leaders. Whereas, as Mayer argues, assembly-line work is a kind of creative labor that should to be situated within the broader context of media creativity, a different kind of creativity is at work in what I defined and explicated in this chapter as revolutionary creative labor. Indeed, a final distinction can be made between forms of creative labor that are embedded in localized contexts (the factory) which are otherwise not creative (the assembly line), what in this chapter I called industrial creative labor, and revolutionary creative labor, which consists of explicit and self-conscious forms of revolutionary creativity that are intended to be launched into broader trajectories of circulation. By enacting contextually new forms of political subjectivity and directing them at radical change, revolutionary creative labor seeks to find, congeal, and mobilize publics.


9.2: Introduction
Adventurously sailing the Indian Ocean in the early 1500s CE, Duarte Barbosa, a Portuguese naval officer, was confident that he was helping to forge a new, enduring era of Portuguese dominance. As he passed through several Swahili city-states on the East African coast, Barbosa noted the brisk trade and the riches of these African settlements where he saw a “great plenty of gold” that would serve Portuguese interests. 1 In his mind, God had destined these stashes of gold for the Portuguese and the local Swahili rulers acted unwisely and arrogantly to defend themselves. In the conflict that followed, the Portuguese plundered the Swahili city-states, burning buildings and enslaving African men and women. Barbosa boasted that when the Portuguese looted the settlements, they slaughtered many people and took a “great spoil of gold and silver and goods.” 2 Barbosa’s description highlights the violence of Portuguese conquest and also his expectation that he and his countrymen were creating a new Portuguese empire that would make a lasting mark in East Africa and the wider Indian Ocean world. However, less than 100 years later, Portuguese influences were noticeably absent in most of East Africa and their power in the Indian Ocean was fading rapidly. Barbosa, himself, had traveled with his brother-in-law, Ferdinand Magellan, and met an untimely end (in his early 40s) in the Philippines.
Writing about the coast of East Africa, Barbosa paid little heed to the hundreds of years of Swahili history that preceded his visit. Therefore, his narrative gives us minimal information about Swahili civilization. This chapter will fill in some of the silences in the written historical record as it describes Africa’s major contributions to World History.
Since information readily available in the U.S. tends to focus on issues like drought, famine, and war, Americans have many common misconceptions about Africa. In addition to associating Africa with extreme hardships, a plethora of western-made TV shows focus on wildlife and the rainforests. However, these popular images don’t give an accurate portrayal of the everyday experiences of most Africans or tell us much about the history of the continent.
One of the main points glossed over by these popular images is that the African continent is large and diverse. Africa is the second largest continent in the world. Today, it has over 50 independent countries. You can also find just about every imaginable environment, from savannahs, rainforests, and deserts, to glaciers and snow-capped mountains in Africa. Its over 1,000 languages (or about one-third of the world’s languages) also demonstrate the continent’s diversity. 3 Africa is home to more than a billion people, who are living, working, and raising their families.
Historically, Africans faced significant environmental challenges that limited population growth. There are exceptions, but overall, African soils are poor and rainfall has been unpredictable. Soils are comparatively unfertile, due in part to the geologic age of the continent. Also, the more temperate climates in a number of regions slows the decomposition of organic materials in the soil, meaning that the soil in many regions has few minerals and nutrients. The areas that are exceptions, such as the highlands of Ethiopia, Rwanda, and Burundi, have seen much higher population concentrations. Rainfall also tends to be concentrated in just two or three months a year, while disease has been yet another challenge.
Considering the past 5,000 years of African history, malaria, yellow fever, and trypanosomiasis (also known as sleeping sickness) have made the biggest impacts on population growth and settlement patterns. Even today, all three diseases affect the continent. Both malaria and yellow fever are spread to people by mosquitos. According to the World Health Organization (WHO), despite preventative measures and great efforts to extend the availability of treatments, malaria was responsible for almost 600,000 deaths in 2013. Children in Africa account for most of the fatalities, and the WHO estimates that currently one African child dies from malaria every minute of every day. 4 Those who have suffered through malaria multiple times as adults will attest that malaria, with the exception of its most virulent strains like plasmodium falciparum , is usually more of a nuisance than an emergency for healthy adults. It causes symptoms like headaches, fever, and chills. Even though it does not usually constitute a medical emergency for adults, malaria does decrease productivity and has significant treatment costs. On the other hand, yellow fever has a high mortality rate—about 50%—even amongst healthy adult populations. 5 While malaria and yellow fever have historically taken the largest toll on human populations, one of the main effects of trypanosomiasis (or sleeping sickness) has been to limit the practicality of keeping certain types of livestock in Africa. Horses and many breeds of cattle are especially susceptible to trypranosomiasis, which is spread by the tsetse fly and can lead to either chronic illness, characterized by weight loss, fever, anemia, cardiac lesions, and other symptoms in animals, or to a more immediate death. Until the past fifty years or so, in many parts of the continent, these noteworthy challenges with disease, alongside the low fertility of the soils and the unpredictable rainfalls, were significant constraints on human population growth. Environmental challenges and disease also affected settlement patterns as, for example, people avoided more forested and wetter areas because of the prevalence of mosquitoes. Additionally, Africans continuously adapted their herding and farming techniques to overcome these challenges.
Endnotes
1 Quoted in “The East Coast of Africa: Duarte Barbosa,” Aspects of World Civilization, vol. 1, Ed. Perry M. Rogers, (Upper Saddle River, NJ: Prentice Hall, 2003): 376.
2 Ibid, p. 377.
3 African Language Program, Department of African and African American Studies, “African Languages,” Harvard University, aaas.fas.harvard.edu/greeting...nguage-program.
4 World Health Organization Media Centre, “Malaria: Fact Sheet,” www.who.int/mediacentre/factsheets/fs094/en
5 World Health Organization Media Centre, “Yellow Fever: Fact Sheet,” www.who.int/mediacentre/factsheets/fs100/en


5.2: Simple Interest
Money is not free to borrow! We will refer to money in terms of present value P, which is an amount of money at the present time, and future value F, which is an amount of money in the future. Usually, if someone loans money to another person in present value, and are promised to be paid back in future value, then the person who loaned the money would like the future value to be more than the present value. That is because the value of money declines over time due to inflation. Therefore, when a person loans money, they will charge interest. They hope that the interest will be enough to beat inflation and make the future value more than the present value.
Simple interest is interest that is only calculated on the initial amount of the loan. This means you are paying the same amount of interest every year. An example of simple interest is when someone purchases a U.S. Treasury Bond.
Interest that is only paid on the principal.
\[F = P(1+rt) \nonumber \]
where,
- \(F\) is the Future value
- \(P\) is the Present value
- \(r\) is the Annual percentage rate (APR) changed to a decimal
- \(t\) is the Number of years
Sue borrows $2000 at 5% annual simple interest from her bank. How much does she owe after five years?
Solution
| Year | Interest Earned | Total Balance Owed |
|---|---|---|
| 1 | $2000*.05 = $100 | $2000 + $100 = $2100 |
| 2 | $2000*.05 = $100 | $2100 + $100 = $2200 |
| 3 | $2000*.05 = $100 | $2200 + $100 = $2300 |
| 4 | $2000*.05 = $100 | $2300 + $100 = $2400 |
| 5 | $2000*.05 = $100 | $2400 + $100 = $2500 |
After 5 years, Sue owes $2500.
Chad got a student loan for $10,000 at 8% annual simple interest. How much does he owe after one year? How much interest will he pay for that one year?
Solution
P = $10,000, r = 0.08, t = 1
\[F = P(1+rt) \nonumber \]
\[F = 10000(1+0.08(1)) = $10,800 \nonumber \]
Chad owes $10,800 after one year. He will pay $10800 - $10000 = $800 in interest.
Ben wants to buy a used car. He has $3000 but wants $3500 to spend. He invests his $3000 into an account earning 6% annual simple interest. How long will he need to leave his money in the account to accumulate the $3500 he wants?
Solution
F = $3500, P = $3000, r = 0.06
\[F = P(1+rt) \nonumber \]
\[\begin{align*} 3500 &= 3000(1+0.06t) \\ \dfrac{3500}{3000} &= 1 + 0.06t \\ \dfrac{3500}{3000} - 1 &= 0.06t \\ \dfrac{\dfrac{3500}{3000}-1}{0.06} &= t \end{align*} \nonumber \]
\[t\approx 2.8 \text{ years}\nonumber \]
Ben would need to invest his $3000 for about 2.8 years until he would have $3500 to spend on a used car.
Note: As shown above, wait to round your answer until the very last step so you get the most accurate answer.


30.4A: Development of Joints
Movable joints are formed at the intersection of bones and are covered by cartilage, which allows them to move freely.
- Explain the development of joints
Key Points
- Cartilage is a flexible material found between joints, initially formed by chondrification (also known as chondrogenesis).
- Following the initial chondrification, cartilage growth consists mostly of the development of immature cartilage to a more mature state.
- Remodeling of cartilage is predominantly affected by changes to the collagen matrix, which responds to tensile and compressive forces.
- Cartilage growth generally refers to collagen matrix deposition, but can include both growth and remodeling of the extracellular matrix.
- The pressure epiphyses, which take the weight of the long bones, include the head of the femur at the hip joint and the head of the humerus at the shoulder joint.
Key Terms
- Chondrogenesis : The process by which cartilage is developed.
- cartilage : A type of dense, non-vascular connective tissue, usually found at the end of joints, the rib cage, the ear, the nose, in the throat and between intervertebral disks.
- Pressure epiphysis : The region of the long bone that forms the joint.
EXAMPLES
Knowledge of joint growth and development is useful in forensic contexts. For instance, if a skeleton is found and the epiphyses are missing or unfused to the diaphyses, then the examiner knows that the skeleton is that of a juvenile or young adult: if female, probably under age 18; if male, probably under age 25. Other clues, such as dental eruption, can refine the age estimate.
Epiphyseal Plate : Image shows the location of the epiphyseal plates (or lines) and the articular surfaces of long bones.
Articular cartilage is a flexible material found between bones at movable joints. Chondrification (also known as chondrogenesis) is the process by which cartilage is formed from condensed mesenchyme tissue, which differentiates into chondroblasts and begins secreting the molecules that form the extracellular matrix. Following the initial chondrification that occurs during embryogenesis, cartilage growth consists mostly of the development of immature cartilage to a more mature state.
Cell division within cartilage occurs very slowly, so growth is not based on a mass increase of the cartilage itself. Articular cartilage function is dependent on the molecular composition of its extracellular matrix (ECM), which consists mainly of proteoglycans and collagens. Articular cartilage is maintained by embedded chondrocytes that comprise only 1% of the cartilage volume. Remodeling of cartilage is predominantly affected by changes to the collagen matrix, which responds to tensile and compressive forces. Cartilage growth generally refers to matrix deposition, but can include both growth and remodeling of the extracellular matrix.
The epiphysis is the rounded end of a long bone, at its joint with adjacent bone(s). Between the epiphysis and diaphysis (the long midsection of the long bone) lies the metaphysis, including the epiphyseal plate (growth plate). At the joint, the epiphysis is covered with articular cartilage; below that covering is a zone similar to the epiphyseal plate, known as subchondral bone. The region of the long bone that forms the joint is called pressure epiphysis. For example, the head of the femur (which is a part of the hip joint complex) is a pressure epiphyses. These epiphyses assist in transmitting the weight of the human body and are the regions of the bone that are under pressure during movement or locomotione. Another example of pressure epiphysis is the head of humorus, part of the shoulder complex.
Hyaline Cartilage : Histological image of the hyaline cartilage which coats the articular surfaces of joints.


4.A: Chapter 4 Review Questions
Complete as directed.
1. When an infirmary, clinic, hospital, or physician, is not reasonably accessible in terms of time and distance to the worksite, for the treatment of injured employees, what other option is permitted?
2. Common drinking cups are permitted for jobsite water coolers provided a means to rinse the cup after each use is provided.
a. ________ True b. ________ False
3. When employees are subjected to sound levels exceeding ________ dBA for 8 hours, feasible administrative or engineering controls shall be utilized to protect against hearing loss.
4. Only ________ and trained employees shall be assigned to install, adjust, and operate laser equipment.
5. Whenever hazardous substances such as dusts, fumes, mists, vapors, or gases exist or are produced in the course of construction work their concentrations shall not exceed the ________ of airborne contaminants for construction.
6. New construction, alteration, repair, or renovation of structures, substrates, or portions thereof, that contain Lead, or materials containing Lead are not covered by the Lead in construction standard.
a. ________ True b. ________ False
7. The Lead standard protects workers from the hazards associated with Lead by assuring that no employee is exposed to lead at concentrations greater than ________ micrograms per cubic meter of air, averaged over an ________ -hour period.
8. Toilets shall be provided at construction sites according to the number of employees on the site. For 20 or less employees ________ toilet is required.
a. ________ 1 b. ________ 2 c. ________ 3 d. ________ 4
9. The requirements of part 1910 and part 1926 of Title 29 of the Code of Federal Regulations apply pursuant to their terms to Hazardous Waste and Emergency Response Operations only if they are specifically mentioned in the Hazwopper Standard.
a. ________ True b. ________ False
General site workers engaged in hazardous substance removal or other activities which expose or potentially expose workers to hazardous substances and health hazards shall receive a minimum of hours of instruction off the site, and a minimum of _ days actual field experience under the direct supervision of a trained, experienced supervisor.


6.4: Sexual Fluidity
Sexual fluidity is a term that encompasses the many different ways that people experience desire. Contrary to the stereotypes associated with sexual orientation, bisexuality does in fact exist! In fact, there are many ways in which people express their sexual orientations (for a more detailed list, refer to the section entitled Different Types of Sexuality ). Attention was drawn to the term “sexual fluidity” in 2008 by Lisa Diamond in a book titled, Sexual Fluidity: Understanding Women's Love and Desire. In the book, Diamond describes the idea of bisexuality, and that it does not completely identify the nature of many people’s sexual identity. Sexual fluidity, one or more changes in a person’s sexuality or sexual identity, describes the idea that an individual’s sexual orientation can be ‘fluid,’ or something that can change over time.  In truth, human beings may develop relationships with individuals of different gender identifications through their lifetime, and people are not “tied” to one sexual orientation throughout the entirety of their life.
According to a study that looks at sexuality throughout the United States by the UCLA School of Law, the percentage of people who identify as lesbian, gay or bisexual is 3.5%, which translates to roughly 9 million people throughout the country (LGBT Demographic Data Interactive, 2019). It can also be argued that if there were no social stigma attached to not being heterosexual, a lot more people would openly admit to a wider variety of sexualities. In the same study, it was found that women were significantly more likely to identify as bisexual as compared to men. As an example of sexual fluidity, a pansexual identifying person, or a person who is attracted to someone regardless of their gender identity, might pursue a relationship with a male or female identifying person, whereas someone who is sexually fluid might be seek female identifying people one day, but seek male identifying people another day.
 It allows people to redefine their sexuality(ies) throughout their lives.
I’ve always said, I like who I like. Sometimes I liked them romantically, sometimes I liked them physically, and sometimes I felt deep love for them. It was never exactly the same type of like I had for each of them, they were all different. For those of you lucky enough to be coming into your sexuality in the present era, there is a lot of room for discovery and flexibility.  It didn’t make sense and it left me confused. The first time I heard the term pansexual I was blown away. That’s a thing? Yes! That’s me! I just like who I like, regardless of their label.


12.7: Hamilton Cycles
- Describe and identify Hamilton cycles.
- Compute the number of Hamilton cycles in a complete graph.
- Apply and evaluate weighted graphs.
In Euler Circuits and Euler Trails, we looked for circuits and paths that visited each edge of a graph exactly once. In this section, we will look for circuits that visit each vertex exactly once. Like many concepts in graph theory, the idea of a circuit that visits each vertex once was inspired by games and puzzles. As early as the 9th century, Indian and Islamic intellectuals wondered whether it was possible for a knight to visit every space on a chess board of a given size, which is equivalent to visiting every vertex of a graph that represents the chess board.
In 1857, a mathematician named William Rowan Hamilton invented a puzzle in which players were asked to find a route along the edges of a dodecahedron (see Figure 12.178), which visited every vertex exactly once. Let’s explore how graph theory provides insight into these games as well as practical applications such as the Traveling Salesperson Problem.
Hamilton’s Puzzle
Before we look at the solution to Hamilton's puzzle, let’s review some vocabulary we used in Figure
. It will be helpful to remember that directed cycle is a type of circuit that doesn’t repeat any edges or vertices.The goal of Hamilton's puzzle was to find a route along the edges of the dodecahedron, which visits each vertex exactly once. A dodecahedron is a three-dimensional space figure with faces that are all pentagons as we saw in Figure 12.178.
Since it is easier to visualize two dimensions rather than three, we will flatten out the dodecahedron and look at the edges and vertices on a flat surface. Graph A in Figure 12.180 shows a two-dimensional graph of the edges and vertices, and Graph B shows an untangled version of Graph A in which no edges are crossing. Graph B in Figure 12.180 is very similar to the design of the game board that Hamilton invented for his puzzle.
|
Untangle graph |
We can see that this is a planar graph because it can be “untangled.” In order to solve Hamilton’s puzzle, we need to find a circuit that visits every vertex once. A solution is shown in Figure 12.181.
.
|
In three Dimensions > |
A circuit that doesn’t repeat any vertices, like the one in Figure 12.181, is called a directed cycle. So, we can most accurately say that Hamilton’s puzzle asks us to find a directed cycle that visits every vertex in a graph exactly once. Because Hamilton created and solved this puzzle, these special circuits were named Hamilton cycles , or Hamilton circuits .
When Hamilton invented his puzzle in the 19th century, it was originally called the Icosian game. This was a reference to an icosahedron, not a dodecahedron. Why? Hamilton was actually interested in the symmetries of icosahedrons. It turns out that these two space figures are related to each other. The dodecahedron has 30 edges, 20 faces, and 12 vertices, while the icosahedron has 30 edges, 12 faces, and 20 vertices. By relating the vertices of the dodecahedron to the faces of the icosahedron, Hamilton was able to make the mathematical connections necessary to use graph theory and dodecahedrons to make discoveries about the symmetries of icosahedrons.
Hamilton Cycles vs. Euler Circuits
Let’s practice naming and identifying Hamilton cycles, as well as distinguishing them from Euler circuits. It is important to remember that Euler circuits visit all edges without repetition, while Hamilton cycles visit all vertices without repetition. Hamilton cycles are named by their vertices just like all circuits. An example is given in Figure
.
Notice that the Hamilton cycle
a
→
b
→
c
→
d
for Graph
Z
in Figure 12.182 is NOT an Euler circuit, because it does not visit edge
TIP! Sometimes students confuse Euler circuits with Hamilton cycles. To help you remember, think of the E in Euler as standing for Edge.
Use Figure
Figure 12.183 to determine whether the given circuit is a Hamilton cycle, an Euler circuit, both, or neither.- a → b → c → e → h → g → f → d → a
- g → e → h → g → f → d → a → b → d → g
- a → b → c → e → h → g → f → d → b → e → g → d → a
- Answer
-
- This circuit is a Hamilton cycle only. It visits each vertex exactly once, so, it is a Hamilton cycle. It is not an Euler circuit because it doesn’t visit all of the edges.
-
This circuit is neither Hamilton cycle nor an Euler circuit. It doesn’t visit vertex
, so, it is not a Hamilton cycle. It also doesn’t visit edges
be andbe ce , so, it is not an Euler circuit.ce - This circuit is an Euler circuit only. It visits several vertices more than once; so, it is not a Hamilton cycle. It visits every edge exactly once, so, it is an Euler circuit.
TIP! Euler circuits never skip a vertex, so, they only fail to be Hamilton cycles when they visit a vertex more than once. Hamilton cycles never visit any edges twice, so, they only fail to be Euler circuits when they skip edges.
Consider the figure shown. Is the circuit a → b → f → e → h → i → g → d → c → a an Euler circuit, a Hamilton cycle, or both?
Notice that the graph is a cycle. A cycle will always be Eulerian because all vertices are degree 2. Moreover, any circuit in the graph will always be both an Euler circuit and a Hamilton cycle. It is not always as easy to determine if a graph has a Hamilton cycle as it is to see that it has an Euler circuit, but there is a large group of graphs that we know will always have Hamilton cycles, the complete graphs. Since all vertices in a complete graph are adjacent, we can always find a directed cycle that visits all the vertices. For example, look at the directed six-cycle, n → o → p → q → r → s , in the complete graph with six vertices in Figure
.That is not the only directed six-cycle in the graph though. We could find another just be reversing the direction, and we could find even more by using different edges. So, how many Hamilton cycles are in a complete graph with vertices? Before we tackle this problem, let’s look at a shorthand notation that we use in mathematics which will be helpful to us.
Factorials
In many areas of mathematics, we must calculate products like or , products that involve multiplying all the counting numbers from a particular number down to 1. Imagine that the product happened to be all the numbers from 100 down to 1. That’s a lot of writing! Instead of writing all of that out, mathematicians came up with a shorthand notation. For example, instead of , we write , which is read “7 factorial .” In other words, the product of all the counting numbers from down to 1 is called factorial and it is written
Evaluate and for .
- Answer
-
24 n and! = 4 ! = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24
Evaluate \(n!\) and \((n - 1)!\) for \(n = 6\).
A common use for factorials is counting the number of ways to arrange objects. Suppose that there were three students, Aryana, Byron, and Carlos, who wanted to line up in a row. How many arrangements are possible? There are six possibilities: ABC, ACB, BAC, BCA, CAB, or CBA. Notice that there were three students being arranged, and the number of possible arrangements is three.
The number of ways to arrange distinct objects is .
Find the number of ways to arrange the letters a, b, c, and d.
- Answer
-
Find the number of ways to arrange the letters v, w, x, y, and z.
Counting Hamilton Cycles in Complete Graphs
Now, let’s get back to answering the question of how many Hamilton cycles are in a complete graph. In Table 12.8, we have drawn all the four cycles in a complete graph with four vertices. Remember, cycles can be named starting with any vertex in the cycle, but we will name them starting with vertex .
| Complete Graph | Cycle | Cycle | Cycle |
|---|---|---|---|
| Cycle Name Clockwise | a, b, c, d | a, b, d, c | a, c, b, d |
| Cycle Name Counterclockwise | a, d, c, b | a, c, d, b | a, d, b, c |
Table
shows that there are three unique four-cycles in a complete graph with four vertices. Notice that there were two ways to name each cycle, one reading the vertices in a clockwise direction and one reading the vertices in a counterclockwise direction. This is important to us because we are interested in Hamilton cycles, which are directed cycles. Although the cycles (a, b, c, d) and (a, d, c, b) are the same cycle, the directed cycles, a → b → c → d → a and a → d → c → b → a , which travel the same route in reverse order are considered different directed cycles, as shown in Table .| Complete Graph | Cycle | Cycle | Cycle |
|---|---|---|---|
| Clockwise Hamilton Cycle |
a → b → c → d → a |
a → b → d → c → a |
a → c → b → d → a |
| Counter-clockwise Hamilton Cycle |
a → d → c → b → a |
a → c → d → b → a |
a → d → b → c → a |
The six directed four-cycles in Table
are the only distinct Hamilton cycles in a complete graph with four vertices. Six is also the number of ways to arrange the three letters b, c, and d. (Do you see why?) The number of ways to arrange three letters is . Similarly, the number of Hamilton cycles in a graph with five vertices is the number of ways to arrange four letters, which is . In general, to find the number of Hamilton cycles in a graph, we take one less than the number of vertices and find its factorial.The number of distinct Hamilton cycles in a complete graph with vertices is
How many Hamilton cycles are in the complete graph in Figure
?- Answer
-
There are five vertices in the graph. Using , we have Hamilton cycles.
How many Hamilton cycles are in the graph?
Weighted Graphs
Suppose that an officer in the U.S. Air Force who is stationed at Vandenberg Air Force base must drive to visit three other California Air Force bases before returning to Vandenberg. The officer needs to visit each base once. The vertices in the graph in Figure
represent the four U.S. Air Force bases, Vandenberg, Edwards, Los Angeles, and Beale. The edges are labeled to with the driving distance between each pair of cities.The graph in Figure weighted graph , because each edge has been assigned a value or weight. The weights can represent quantities such as time, distance, money, or any quantity associated with the adjacent vertices joined by the edges. The total weight of any walk, trail, or path is the sum of the weights of the edges it visits.
is called aNotice that the officer’s trip can be represented as a Hamilton cycle, because each of the four vertices in the graph is visited exactly once.
Use Figure
and the given Hamilton cycles to answer the following questions.V → L → E → B → V
V → L → B → E → V
V → E → L → B → V
V → B → E → L → V
- Which of the Hamilton cycles (directed cycles) lie on the same cycle (undirected cycle) in the graph?
- Find the total weight of each cycle.
- Of the four, which of the Hamilton cycles describes the shortest trip for the officer? Describe the route.
- Answer
-
- V → L → E → B → V and V → B → E → L → V follow the same edges in reverse order.
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Any Hamilton cycles that lie on the same cycle will have the same edges and the same total weight.
V → L → E → B → V and V → B → E → L → V each have total weight .
V → L → B → E → V has a total weight .
V → E → L → B → V has a total weight .
- Hamilton cycles V → L → E → B → V and V → B → E → L → V each have the lowest total weight. The officer would take the route from Vandenberg, to Los Angeles, to Edwards, to Beale, and back to Vandenberg, or reverse that route.
Find the weight of the Hamilton cycle m → o → p → n → q → m in the given figure.
Check Your Understanding
For the following exercises, fill in the blank to make the statement true.
- A Hamilton cycle is a circuit that visits each ___________ exactly once.
- A __________ graph with \(n \geq 3\) vertices has \(\left( {n - 1} \right)!\) Hamilton cycles.
- For the following exercises, fill in the blank with is or is not to make the statement true.
- A Hamilton cycle ________ a circuit.
- A Hamilton cycle that visits every edge ________ an Euler circuit.
- A Hamilton cycle ________ different from a Hamilton circuit.
- An Euler circuit that visits every vertex ________ a Hamilton cycle.
- The total weight of a trail _______ the sum of the weights of the edges visited by the trail.
- A weighted graph _______ always a complete graph.
- The number of ways to arrange n objects _______ \(\left( {n - 1} \right)!\)
- Every cycle ____ a circuit.


9.1: Signaling Molecules and Cellular Receptors
Skills to Develop
- Describe four types of signaling found in multicellular organisms
- Compare internal receptors with cell-surface receptors
- Recognize the relationship between a ligand’s structure and its mechanism of action
There are two kinds of communication in the world of living cells. Communication between cells is called intercellular signaling , and communication within a cell is called intracellular signaling . An easy way to remember the distinction is by understanding the Latin origin of the prefixes: inter- means "between" (for example, intersecting lines are those that cross each other) and intra- means "inside" (like intravenous).
Chemical signals are released by signaling cells in the form of small, usually volatile or soluble molecules called ligands. A ligand is a molecule that binds another specific molecule, in some cases, delivering a signal in the process. Ligands can thus be thought of as signaling molecules. Ligands interact with proteins in target cells , which are cells that are affected by chemical signals; these proteins are also called receptors . Ligands and receptors exist in several varieties; however, a specific ligand will have a specific receptor that typically binds only that ligand.
Forms of Signaling
There are four categories of chemical signaling found in multicellular organisms: paracrine signaling, endocrine signaling, autocrine signaling, and direct signaling across gap junctions (Figure \(\PageIndex{1}\)). The main difference between the different categories of signaling is the distance that the signal travels through the organism to reach the target cell. Not all cells are affected by the same signals.
Paracrine Signaling
Signals that act locally between cells that are close together are called paracrine signals . Paracrine signals move by diffusion through the extracellular matrix. These types of signals usually elicit quick responses that last only a short amount of time. In order to keep the response localized, paracrine ligand molecules are normally quickly degraded by enzymes or removed by neighboring cells. Removing the signals will reestablish the concentration gradient for the signal, allowing them to quickly diffuse through the intracellular space if released again.
One example of paracrine signaling is the transfer of signals across synapses between nerve cells. A nerve cell consists of a cell body, several short, branched extensions called dendrites that receive stimuli, and a long extension called an axon, which transmits signals to other nerve cells or muscle cells. The junction between nerve cells where signal transmission occurs is called a synapse. A synaptic signal is a chemical signal that travels between nerve cells. Signals within the nerve cells are propagated by fast-moving electrical impulses. When these impulses reach the end of the axon, the signal continues on to a dendrite of the next cell by the release of chemical ligands called neurotransmitters by the presynaptic cell (the cell emitting the signal). The neurotransmitters are transported across the very small distances between nerve cells, which are called chemical synapses (Figure \(\PageIndex{2}\)). The small distance between nerve cells allows the signal to travel quickly; this enables an immediate response, such as, Take your hand off the stove!
When the neurotransmitter binds the receptor on the surface of the postsynaptic cell, the electrochemical potential of the target cell changes, and the next electrical impulse is launched. The neurotransmitters that are released into the chemical synapse are degraded quickly or get reabsorbed by the presynaptic cell so that the recipient nerve cell can recover quickly and be prepared to respond rapidly to the next synaptic signal.
Endocrine Signaling
Signals from distant cells are called endocrine signals , and they originate from endocrine cells . (In the body, many endocrine cells are located in endocrine glands, such as the thyroid gland, the hypothalamus, and the pituitary gland.) These types of signals usually produce a slower response but have a longer-lasting effect. The ligands released in endocrine signaling are called hormones, signaling molecules that are produced in one part of the body but affect other body regions some distance away.
Hormones travel the large distances between endocrine cells and their target cells via the bloodstream, which is a relatively slow way to move throughout the body. Because of their form of transport, hormones get diluted and are present in low concentrations when they act on their target cells. This is different from paracrine signaling, in which local concentrations of ligands can be very high.
Autocrine Signaling
Autocrine signals are produced by signaling cells that can also bind to the ligand that is released. This means the signaling cell and the target cell can be the same or a similar cell (the prefix auto- means self, a reminder that the signaling cell sends a signal to itself). This type of signaling often occurs during the early development of an organism to ensure that cells develop into the correct tissues and take on the proper function. Autocrine signaling also regulates pain sensation and inflammatory responses. Further, if a cell is infected with a virus, the cell can signal itself to undergo programmed cell death, killing the virus in the process. In some cases, neighboring cells of the same type are also influenced by the released ligand. In embryological development, this process of stimulating a group of neighboring cells may help to direct the differentiation of identical cells into the same cell type, thus ensuring the proper developmental outcome.
Direct Signaling Across Gap Junctions
Gap junctions in animals and plasmodesmata in plants are connections between the plasma membranes of neighboring cells. These water-filled channels allow small signaling molecules, called intracellular mediators , to diffuse between the two cells. Small molecules, such as calcium ions (Ca 2+ ), are able to move between cells, but large molecules like proteins and DNA cannot fit through the channels. The specificity of the channels ensures that the cells remain independent but can quickly and easily transmit signals. The transfer of signaling molecules communicates the current state of the cell that is directly next to the target cell; this allows a group of cells to coordinate their response to a signal that only one of them may have received. In plants, plasmodesmata are ubiquitous, making the entire plant into a giant, communication network.
Types of Receptors
Receptors are protein molecules in the target cell or on its surface that bind ligand. There are two types of receptors, internal receptors and cell-surface receptors.
Internal receptors
Internal receptors , also known as intracellular or cytoplasmic receptors, are found in the cytoplasm of the cell and respond to hydrophobic ligand molecules that are able to travel across the plasma membrane. Once inside the cell, many of these molecules bind to proteins that act as regulators of mRNA synthesis (transcription) to mediate gene expression. Gene expression is the cellular process of transforming the information in a cell's DNA into a sequence of amino acids, which ultimately forms a protein. When the ligand binds to the internal receptor, a conformational change is triggered that exposes a DNA-binding site on the protein. The ligand-receptor complex moves into the nucleus, then binds to specific regulatory regions of the chromosomal DNA and promotes the initiation of transcription (Figure \(\PageIndex{3}\)). Transcription is the process of copying the information in a cells DNA into a special form of RNA called messenger RNA (mRNA); the cell uses information in the mRNA (which moves out into the cytoplasm and associates with ribosomes) to link specific amino acids in the correct order, producing a protein. Internal receptors can directly influence gene expression without having to pass the signal on to other receptors or messengers.
Cell-Surface Receptors
Cell-surface receptors , also known as transmembrane receptors, are cell surface, membrane-anchored (integral) proteins that bind to external ligand molecules. This type of receptor spans the plasma membrane and performs signal transduction, in which an extracellular signal is converted into an intercellular signal. Ligands that interact with cell-surface receptors do not have to enter the cell that they affect. Cell-surface receptors are also called cell-specific proteins or markers because they are specific to individual cell types.
Because cell-surface receptor proteins are fundamental to normal cell functioning, it should come as no surprise that a malfunction in any one of these proteins could have severe consequences. Errors in the protein structures of certain receptor molecules have been shown to play a role in hypertension (high blood pressure), asthma, heart disease, and cancer.
Each cell-surface receptor has three main components: an external ligand-binding domain, a hydrophobic membrane-spanning region, and an intracellular domain inside the cell. The ligand-binding domain is also called the extracellular domain . The size and extent of each of these domains vary widely, depending on the type of receptor.
Evolution Connection: How Viruses Recognize a Host
Unlike living cells, many viruses do not have a plasma membrane or any of the structures necessary to sustain life. Some viruses are simply composed of an inert protein shell containing DNA or RNA. To reproduce, viruses must invade a living cell, which serves as a host, and then take over the hosts cellular apparatus. But how does a virus recognize its host?
Viruses often bind to cell-surface receptors on the host cell. For example, the virus that causes human influenza (flu) binds specifically to receptors on membranes of cells of the respiratory system. Chemical differences in the cell-surface receptors among hosts mean that a virus that infects a specific species (for example, humans) cannot infect another species (for example, chickens).
However, viruses have very small amounts of DNA or RNA compared to humans, and, as a result, viral reproduction can occur rapidly. Viral reproduction invariably produces errors that can lead to changes in newly produced viruses; these changes mean that the viral proteins that interact with cell-surface receptors may evolve in such a way that they can bind to receptors in a new host. Such changes happen randomly and quite often in the reproductive cycle of a virus, but the changes only matter if a virus with new binding properties comes into contact with a suitable host. In the case of influenza, this situation can occur in settings where animals and people are in close contact, such as poultry and swine farms. 1 Once a virus jumps to a new host, it can spread quickly. Scientists watch newly appearing viruses (called emerging viruses) closely in the hope that such monitoring can reduce the likelihood of global viral epidemics.
Cell-surface receptors are involved in most of the signaling in multicellular organisms. There are three general categories of cell-surface receptors: ion channel-linked receptors, G-protein-linked receptors, and enzyme-linked receptors.
Ion channel-linked receptors bind a ligand and open a channel through the membrane that allows specific ions to pass through. To form a channel, this type of cell-surface receptor has an extensive membrane-spanning region. In order to interact with the phospholipid fatty acid tails that form the center of the plasma membrane, many of the amino acids in the membrane-spanning region are hydrophobic in nature. Conversely, the amino acids that line the inside of the channel are hydrophilic to allow for the passage of water or ions. When a ligand binds to the extracellular region of the channel, there is a conformational change in the proteins structure that allows ions such as sodium, calcium, magnesium, and hydrogen to pass through (Figure \(\PageIndex{4}\)).
G-protein-linked receptors bind a ligand and activate a membrane protein called a G-protein. The activated G-protein then interacts with either an ion channel or an enzyme in the membrane (Figure \(\PageIndex{5}\)). All G-protein-linked receptors have seven transmembrane domains, but each receptor has its own specific extracellular domain and G-protein-binding site.
Cell signaling using G-protein-linked receptors occurs as a cyclic series of events. Before the ligand binds, the inactive G-protein can bind to a newly revealed site on the receptor specific for its binding. Once the G-protein binds to the receptor, the resultant shape change activates the G-protein, which releases GDP and picks up GTP. The subunits of the G-protein then split into the α subunit and the βγ subunit. One or both of these G-protein fragments may be able to activate other proteins as a result. After awhile, the GTP on the active α subunit of the G-protein is hydrolyzed to GDP and the βγ subunit is deactivated. The subunits reassociate to form the inactive G-protein and the cycle begins anew.
G-protein-linked receptors have been extensively studied and much has been learned about their roles in maintaining health. Bacteria that are pathogenic to humans can release poisons that interrupt specific G-protein-linked receptor function, leading to illnesses such as pertussis, botulism, and cholera. In cholera (Figure \(\PageIndex{6}\)), for example, the water-borne bacterium Vibrio cholerae produces a toxin, choleragen, that binds to cells lining the small intestine. The toxin then enters these intestinal cells, where it modifies a G-protein that controls the opening of a chloride channel and causes it to remain continuously active, resulting in large losses of fluids from the body and potentially fatal dehydration as a result.
Enzyme-linked receptors are cell-surface receptors with intracellular domains that are associated with an enzyme. In some cases, the intracellular domain of the receptor itself is an enzyme. Other enzyme-linked receptors have a small intracellular domain that interacts directly with an enzyme. The enzyme-linked receptors normally have large extracellular and intracellular domains, but the membrane-spanning region consists of a single alpha-helical region of the peptide strand. When a ligand binds to the extracellular domain, a signal is transferred through the membrane, activating the enzyme. Activation of the enzyme sets off a chain of events within the cell that eventually leads to a response. One example of this type of enzyme-linked receptor is the tyrosine kinase receptor (Figure \(\PageIndex{7}\)). A kinase is an enzyme that transfers phosphate groups from ATP to another protein. The tyrosine kinase receptor transfers phosphate groups to tyrosine molecules (tyrosine residues). First, signaling molecules bind to the extracellular domain of two nearby tyrosine kinase receptors. The two neighboring receptors then bond together, or dimerize. Phosphates are then added to tyrosine residues on the intracellular domain of the receptors (phosphorylation). The phosphorylated residues can then transmit the signal to the next messenger within the cytoplasm.
Art Connection
HER2 is a receptor tyrosine kinase. In 30 percent of human breast cancers, HER2 is permanently activated, resulting in unregulated cell division. Lapatinib, a drug used to treat breast cancer, inhibits HER2 receptor tyrosine kinase autophosphorylation (the process by which the receptor adds phosphates onto itself), thus reducing tumor growth by 50 percent. Besides autophosphorylation, which of the following steps would be inhibited by Lapatinib?
- Signaling molecule binding, dimerization, and the downstream cellular response
- Dimerization, and the downstream cellular response
- The downstream cellular response
- Phosphatase activity, dimerization, and the downsteam cellular response
Signaling Molecules
Produced by signaling cells and the subsequent binding to receptors in target cells, ligands act as chemical signals that travel to the target cells to coordinate responses. The types of molecules that serve as ligands are incredibly varied and range from small proteins to small ions like calcium (Ca 2+ ).
Small Hydrophobic Ligands
Small hydrophobic ligands can directly diffuse through the plasma membrane and interact with internal receptors. Important members of this class of ligands are the steroid hormones. Steroids are lipids that have a hydrocarbon skeleton with four fused rings; different steroids have different functional groups attached to the carbon skeleton.  Other hydrophobic hormones include thyroid hormones and vitamin D. In order to be soluble in blood, hydrophobic ligands must bind to carrier proteins while they are being transported through the bloodstream.
Water-Soluble Ligands
Water-soluble ligands are polar and therefore cannot pass through the plasma membrane unaided; sometimes, they are too large to pass through the membrane at all. Instead, most water-soluble ligands bind to the extracellular domain of cell-surface receptors. This group of ligands is quite diverse and includes small molecules, peptides, and proteins.
Other Ligands
Nitric oxide (NO) is a gas that also acts as a ligand. It is able to diffuse directly across the plasma membrane, and one of its roles is to interact with receptors in smooth muscle and induce relaxation of the tissue. NO has a very short half-life and therefore only functions over short distances. Nitroglycerin, a treatment for heart disease, acts by triggering the release of NO, which causes blood vessels to dilate (expand), thus restoring blood flow to the heart. NO has become better known recently because the pathway that it affects is targeted by prescription medications for erectile dysfunction, such as Viagra (erection involves dilated blood vessels).
Summary
Cells communicate by both inter- and intracellular signaling. Signaling cells secrete ligands that bind to target cells and initiate a chain of events within the target cell. The four categories of signaling in multicellular organisms are paracrine signaling, endocrine signaling, autocrine signaling, and direct signaling across gap junctions. Paracrine signaling takes place over short distances. Endocrine signals are carried long distances through the bloodstream by hormones, and autocrine signals are received by the same cell that sent the signal or other nearby cells of the same kind. Gap junctions allow small molecules, including signaling molecules, to flow between neighboring cells.
Internal receptors are found in the cell cytoplasm. Here, they bind ligand molecules that cross the plasma membrane; these receptor-ligand complexes move to the nucleus and interact directly with cellular DNA. Cell-surface receptors transmit a signal from outside the cell to the cytoplasm. Ion channel-linked receptors, when bound to their ligands, form a pore through the plasma membrane through which certain ions can pass. G-protein-linked receptors interact with a G-protein on the cytoplasmic side of the plasma membrane, promoting the exchange of bound GDP for GTP and interacting with other enzymes or ion channels to transmit a signal. Enzyme-linked receptors transmit a signal from outside the cell to an intracellular domain of a membrane-bound enzyme. Ligand binding causes activation of the enzyme. Small hydrophobic ligands (like steroids) are able to penetrate the plasma membrane and bind to internal receptors. Water-soluble hydrophilic ligands are unable to pass through the membrane; instead, they bind to cell-surface receptors, which transmit the signal to the inside of the cell.
Art Connections
Figure \(\PageIndex{7}\): HER2 is a receptor tyrosine kinase. In 30 percent of human breast cancers, HER2 is permanently activated, resulting in unregulated cell division. Lapatinib, a drug used to treat breast cancer, inhibits HER2 receptor tyrosine kinase autophosphorylation (the process by which the receptor adds phosphates onto itself), thus reducing tumor growth by 50 percent. Besides autophosphorylation, which of the following steps would be inhibited by Lapatinib?
- Signaling molecule binding, dimerization, and the downstream cellular response.
- Dimerization, and the downstream cellular response.
- The downstream cellular response.
- Phosphatase activity, dimerization, and the downsteam cellular response.
- Answer
-
C. The downstream cellular response would be inhibited.
Footnotes
- 1 A. B. Sigalov, The School of Nature. IV. Learning from Viruses, Self/Nonself 1, no. 4 (2010): 282-298. Y. Cao, X. Koh, L. Dong, X. Du, A. Wu, X. Ding, H. Deng, Y. Shu, J. Chen, T. Jiang, Rapid Estimation of Binding Activity of Influenza Virus Hemagglutinin to Human and Avian Receptors, PLoS One 6, no. 4 (2011): e18664.
Glossary
- autocrine signal
- signal that is sent and received by the same or similar nearby cells
- cell-surface receptor
- cell-surface protein that transmits a signal from the exterior of the cell to the interior, even though the ligand does not enter the cell
- chemical synapse
- small space between axon terminals and dendrites of nerve cells where neurotransmitters function
- endocrine cell
- cell that releases ligands involved in endocrine signaling (hormones)
- endocrine signal
- long-distance signal that is delivered by ligands (hormones) traveling through an organisms circulatory system from the signaling cell to the target cell
- enzyme-linked receptor
- cell-surface receptor with intracellular domains that are associated with membrane-bound enzymes
- extracellular domain
- region of a cell-surface receptor that is located on the cell surface
- G-protein-linked receptor
- cell-surface receptor that activates membrane-bound G-proteins to transmit a signal from the receptor to nearby membrane components
- intercellular signaling
- communication between cells
- internal receptor
- (also, intracellular receptor) receptor protein that is located in the cytosol of a cell and binds to ligands that pass through the plasma membrane
- intracellular mediator
- (also, second messenger) small molecule that transmits signals within a cell
- intracellular signaling
- communication within cells
- ion channel-linked receptor
- cell-surface receptor that forms a plasma membrane channel, which opens when a ligand binds to the extracellular domain (ligand-gated channels)
- ligand
- molecule produced by a signaling cell that binds with a specific receptor, delivering a signal in the process
- neurotransmitter
- chemical ligand that carries a signal from one nerve cell to the next
- paracrine signal
- signal between nearby cells that is delivered by ligands traveling in the liquid medium in the space between the cells
- receptor
- protein in or on a target cell that bind to ligands
- signaling cell
- cell that releases signal molecules that allow communication with another cell
- synaptic signal
- chemical signal (neurotransmitter) that travels between nerve cells
- target cell
- cell that has a receptor for a signal or ligand from a signaling cell


11.1: Introduction
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Our view of objects in the sky at night, the warm radiance of sunshine, the sting of sunburn, our cell phone conversations, and the X-rays revealing a broken bone—all are brought to us by electromagnetic waves. It would be hard to overstate the practical importance of electromagnetic waves, through their role in vision, through countless technological applications, and through their ability to transport the energy from the Sun through space to sustain life and almost all of its activities on Earth.
Theory predicted the general phenomenon of electromagnetic waves before anyone realized that light is a form of an electromagnetic wave. In the mid-nineteenth century, James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects known at that time. Maxwell’s equations, summarizing this theory, predicted the existence of electromagnetic waves that travel at the speed of light. His theory also predicted how these waves behave, and how they carry both energy and momentum. The tails of comets, such as Comet McNaught in Figure 16.1, provide a spectacular example. Energy carried by light from the Sun warms the comet to release dust and gas. The momentum carried by the light exerts a weak force that shapes the dust into a tail of the kind seen here. The flux of particles emitted by the Sun, called the solar wind, typically produces an additional, second tail, as described in detail in this chapter.
In this chapter, we explain Maxwell’s theory and show how it leads to his prediction of electromagnetic waves. We use his theory to examine what electromagnetic waves are, how they are produced, and how they transport energy and momentum. We conclude by summarizing some of the many practical applications of electromagnetic waves.


5.18: Skills Checklist- Perineal Care (Female)
- Gather Supplies: Basin, warm water, soap, four washcloths, one towel, barrier, gloves, and linen bag or hamper
-
Routine Pre-Procedure Steps:
- Knock on the resident’s door.
- Perform hand hygiene.
- Maintain respectful, courteous, and professional communication at all times.
- Introduce yourself and identify the resident.
- Provide for privacy.
- Explain the procedure to the resident.
-
Procedure Steps:
- Raise one side rail of the bed after checking the resident’s mobility and their preferred side to lie on.
- Put on gloves.
- Raise the bed height if needed.
- Fill the basin with warm water and place it on a flat surface with a barrier underneath. Have the resident check the water temperature by placing their hand in the basin or putting a wet washcloth on the back of their hand.
- Turn the resident or raise their hips and place a barrier (a towel, waterproof soaker pad, disposable pad, etc.) under their buttocks.
- Expose their perineum only.
- Separate the labia.
- Use water and a soapy washcloth.
- Clean one side of the labia from top to bottom.
- Using a clean portion of the first washcloth, clean the other side of the labia from top to bottom.
- Using a clean portion of the first washcloth, clean the vaginal area from top to bottom.
- Put the first washcloth in the linen bag.
- Using the second clean washcloth, rinse one side of the labia from top to bottom.
- Using a clean portion of the second washcloth, rinse the other side of the labia from top to bottom.
- Using a clean portion of the second washcloth, rinse the vaginal area from top to bottom.
- Put the second washcloth in the linen bag.
- Avoid overexposure throughout the procedure.
- Pat dry.
- Cover the exposed area with the bath blanket.
- Assist the resident to turn onto their side facing away from you and ask the resident to hold onto the raised side rail.
- Using the third clean washcloth, apply water and soap.
- Using a clean portion of the third washcloth, clean one side of the buttock, wiping away from vagina.
- Using a clean portion of the third washcloth, clean the other side of the buttock, wiping away from the vagina.
- Using a clean portion of the third washcloth, clean the rectal area wiping away from the vagina.
- Put the third washcloth in the linen bag.
- Using the fourth washcloth, rinse one side of the buttock wiping away from the vagina.
- Using a clean portion of the fourth washcloth, rinse the other side of the buttock wiping away from the vagina.
- Using a clean portion of the fourth washcloth, rinse the rectal area wiping away from vagina.
- Put the fourth washcloth in the linen bag.
- Pat dry.
- Safely remove the waterproof pad from under the buttocks.
- Remove the gloves, turning them inside out.
- Perform hand hygiene.
- Position the resident on her back.
- Put on clean gloves.
- Dispose of soiled linen in the designated laundry hamper.
- Empty the equipment.
- Rinse the equipment.
- Dry the equipment.
- Return the equipment to storage.
- Remove the gloves, turning them inside out.
- Dispose of the gloves in an appropriate container.
-
Post- Procedure Steps:
- Perform hand hygiene.
- Check for resident comfort and ask if anything else is needed.
- Ensure the bed is low and locked. Check the brakes.
- Place the call light or signaling device within reach of the resident.
- Open the door and privacy curtain.
- Perform hand hygiene.
-
Document and report any skin issues or changes noted with the resident.
View a YouTube video [1] of an instructor demonstrating female perineal care:
- Chippewa Valley Technical College. (2022, December 3). Perineal Care (Female). [Video]. YouTube. Video licensed under CC BY 4.0 . https://youtu.be/6Xu2Sgk1y80 ↵


3.2: Biogeochemical Cycles
Energy flows directionally through ecosystems, entering as sunlight (or inorganic molecules for chemoautotrophs) and leaving as heat during energy transformation between trophic levels. Rather than flowing through an ecosystem, the matter that makes up organisms is conserved and recycled. The six most common elements associated with organic molecules—carbon, nitrogen, hydrogen, oxygen, phosphorus, and sulfur—take a variety of chemical forms and may exist for long periods in the atmosphere, on land, in water, or beneath Earth’s surface. Geologic processes, such as weathering, erosion, water drainage, and the subduction of the continental plates, all play a role in the cycling of elements on Earth. Because geology and chemistry have major roles in the study of these processes, the recycling of inorganic matter between living organisms and their nonliving environment are called biogeochemical cycles .
The six aforementioned elements are used by organisms in a variety of ways. Hydrogen and oxygen are found in water and organic molecules, both of which are essential to life. Carbon is found in all organic molecules, whereas nitrogen is an important component of nucleic acids and proteins. Phosphorus is used to make nucleic acids and the phospholipids that comprise biological membranes. Lastly, sulfur is critical to the three-dimensional shape of proteins.
The cycling of these elements is interconnected. For example, the movement of water is critical for the leaching of sulfur and phosphorus into rivers, lakes, and oceans. Minerals cycle through the biosphere between the biotic and abiotic components and from one organism to another.
The Water Cycle
The hydrosphere is the area of Earth where water movement and storage occurs: as liquid water on the surface (rivers, lakes, oceans) and beneath the surface (groundwater) or ice, (polar ice caps and glaciers), and as water vapor in the atmosphere.The human body is about 60 percent water and human cells are more than 70 percent water. Of the stores of water on Earth, 97.5 percent is salt water (see Figure \(\PageIndex{1}\) below). Of the remaining water, more than 99 percent is groundwater or ice. Thus, less than one percent of freshwater is present in lakes and rivers. Many organisms are dependent on this small percentage, a lack of which can have negative effects on ecosystems. Humans, of course, have developed technologies to increase water availability, such as digging wells to harvest groundwater, storing rainwater, and using desalination to obtain drinkable water from the ocean. Although this pursuit of drinkable water has been ongoing throughout human history, the supply of fresh water continues to be a major issue in modern times.
The various processes that occur during the cycling of water are illustrated in Figure \(\PageIndex{2}\) below. The processes include the following:
- evaporation and sublimation
- condensation and precipitation
- subsurface water flow
- surface runoff and snowmelt
- streamflow
The water cycle is driven by the Sun’s energy as it warms the oceans and other surface waters. This leads to evaporation (liquid water to water vapor) of liquid surface water and sublimation (ice to water vapor) of frozen water, thus moving large amounts of water into the atmosphere as water vapor. Over time, this water vapor condenses into clouds as liquid or frozen droplets and eventually leads to precipitation (rain, snow, hail), which returns water to Earth’s surface. Rain reaching Earth’s surface may evaporate again, flow over the surface, or percolate into the ground. Most easily observed is surface runoff : the flow of freshwater over land either from rain or melting ice. Runoff can make its way through streams and lakes to the oceans.
In most natural terrestrial environments rain encounters vegetation before it reaches the soil surface. A significant percentage of water evaporates immediately from the surfaces of plants. What is left reaches the soil and begins to move down. Surface runoff will occur only if the soil becomes saturated with water in a heavy rainfall. Water in the soil can be taken up by plant roots. The plant will use some of this water for its own metabolism and some of that will find its way into animals that eat the plants, but much of it will be lost back to the atmosphere through a process known as transpiration: water enters the vascular system of plants through the roots and evaporates, or transpires, through the stomata (small microscope openings) of the leaves. Ecologists combine transpiration and evaporation into a single term that describes water returned to the atmosphere: evapotranspiration . Water in the soil that is not taken up by a plant and that does not evaporate is able to percolate into the subsoil and bedrock where it forms groundwater.
Groundwater is a significant, subsurface reservoir of fresh water. It exists in the pores between particles in dirt, sand, and gravel or in the fissures in rocks. Groundwater can flow slowly through these pores and fissures and eventually finds its way to a stream or lake where it becomes part of the surface water again. Many streams flow not because they are replenished from rainwater directly but because they receive a constant inflow from the groundwater below. Some groundwater is found very deep in the bedrock and can persist there for millennia. Most groundwater reservoirs, or aquifers , are the source of drinking or irrigation water drawn up through wells. In many cases these aquifers are being depleted faster than they are being replenished by water percolating down from above.
Rain and surface runoff are major ways in which minerals, including phosphorus and sulfur, are cycled from land to water. The environmental effects of runoff will be discussed later as these cycles are described.
The Carbon Cycle
Carbon is the second most abundant element in organisms, by mass. Carbon is present in all organic molecules (and some molecules that are not organic such as CO 2 ), and its role in the structure of biomolecules is of primary importance. Carbon compounds contain energy, and many of these compounds from dead plants and algae have fossilized over millions of years and are known as fossil fuels . Since the 1800s, the use of fossil fuels has accelerated. Since the beginning of the Industrial Revolution the demand for Earth’s limited fossil fuel supplies has risen, causing the amount of carbon dioxide in our atmosphere to drastically increase. This increase in carbon dioxide is associated with climate change and is a major environmental concern worldwide.
The carbon cycle is most easily studied as two interconnected subcycles: one dealing with rapid carbon exchange among living organisms and the other dealing with the long-term cycling of carbon through geologic processes. The entire carbon cycle is shown in Figure \(\PageIndex{3}\) below.
The Biological Carbon Cycle
Organisms are connected in many ways, even among different ecosystems. A good example of this connection is the exchange of carbon between heterotrophs and autotrophs by way of atmospheric carbon dioxide. Carbon dioxide (CO 2 ) is the basic building block that autotrophs use to build high-energy compounds such as glucose. The energy harnessed from the Sun is used by these organisms to form the covalent bonds that link carbon atoms together. These chemical bonds store this energy for later use in the process of respiration. Most terrestrial autotrophs obtain their carbon dioxide directly from the atmosphere, while marine autotrophs acquire it in the dissolved form (bicarbonate, HCO 3 – ).
Carbon is passed from producers to higher trophic levels through consumption. For example, when a cow (primary consumer) eats grass (producer), it obtains some of the organic molecules originally made by the plant’s photosynthesis. Those organic compounds can then be passed to higher trophic levels, such as humans, when we eat the cow. At each level, however, organisms are performing respiration , a process in which organic molecules are broken down to release energy. As these organic molecules are broken down, carbon is removed from food molecules to form CO 2 , a gas that enters the atmosphere. Thus, CO 2 is a byproduct of respiration. Recall that CO 2 is consumed by producers during photosynthesis to make organic molecules. As these molecules are broken down during respiration, the carbon once again enters the atmosphere as CO 2 . Carbon exchange like this potentially connects all organisms on Earth. Think about this: the carbon in your DNA was once part of plant; millions of years ago perhaps it was part of dinosaur.
The Biogeochemical Carbon Cycle
The movement of carbon through land, water, and air is complex, and, in many cases, it occurs much more slowly than the movement between organisms. Carbon is stored for long periods in what are known as carbon reservoirs, which include the atmosphere, bodies of liquid water (mostly oceans), ocean sediment, soil, rocks (including fossil fuels), and Earth’s interior.
As stated, the atmosphere is a major reservoir of carbon in the form of carbon dioxide that is essential to the process of photosynthesis. The level of carbon dioxide in the atmosphere is greatly influenced by the reservoir of carbon in the oceans. The exchange of carbon between the atmosphere and water reservoirs influences how much carbon is found in each. Carbon dioxide (CO 2 ) from the atmosphere dissolves in water and reacts with water molecules to form ionic compounds. Some of these ions combine with calcium ions in the seawater to form calcium carbonate (CaCO 3 ), a major component of the shells of marine organisms. These organisms eventually die and their shells form sediments on the ocean floor. Over geologic time, the calcium carbonate forms limestone, which comprises the largest carbon reservoir on Earth.
On land, carbon is stored in soil as organic carbon as a result of the decomposition of organisms or from weathering of terrestrial rock and minerals (the world’s soils hold significantly more carbon than the atmosphere, for comparison). Deeper underground are fossil fuels, the anaerobically decomposed remains of plants and algae that lived millions of years ago. Fossil fuels are considered a non-renewable resource because their use far exceeds their rate of formation. A non-renewable resource is either regenerated very slowly or not at all. Another way for carbon to enter the atmosphere is from land (including land beneath the surface of the ocean) by the eruption of volcanoes and other geothermal systems. Carbon sediments from the ocean floor are taken deep within Earth by the process of subduction : the movement of one tectonic plate beneath another. Carbon is released as carbon dioxide when a volcano erupts or from volcanic hydrothermal vents.
The Nitrogen Cycle
Getting nitrogen into living organisms is difficult. Plants and phytoplankton are not equipped to incorporate nitrogen from the atmosphere (where it exists as tightly bonded, triple covalent N 2 ) even though this molecule comprises approximately 78 percent of the atmosphere. Nitrogen enters the living world through free-living and symbiotic bacteria, which incorporate nitrogen into their organic molecules through specialized biochemical processes. Certain species of bacteria are able to perform nitrogen fixation , the process of converting nitrogen gas into ammonia (NH 3 ), which spontaneously becomes ammonium (NH 4 + ). Ammonium is converted by bacteria into nitrites (NO 2 − ) and then nitrates (NO 3 − ). At this point, the nitrogen-containing molecules are used by plants and other producers to make organic molecules such as DNA and proteins. This nitrogen is now available to consumers.
Organic nitrogen is especially important to the study of ecosystem dynamics because many ecosystem processes, such as primary production, are limited by the available supply of nitrogen. As shown in Figure \(\PageIndex{4}\) below, the nitrogen that enters living systems is eventually converted from organic nitrogen back into nitrogen gas by bacteria (Figure \(\PageIndex{4}\)). The process of denitrification is when bacteria convert the nitrates into nitrogen gas, thus allowing it to re-enter the atmosphere.
Human activity can alter the nitrogen cycle by two primary means: the combustion of fossil fuels, which releases different nitrogen oxides, and by the use of artificial fertilizers (which contain nitrogen and phosphorus compounds) in agriculture, which are then washed into lakes, streams, and rivers by surface runoff. Atmospheric nitrogen (other than N 2 ) is associated with several effects on Earth’s ecosystems including the production of acid rain (as nitric acid, HNO 3 ) and greenhouse gas effects (as nitrous oxide, N 2 O), potentially causing climate change. A major effect from fertilizer runoff is saltwater and freshwater eutrophication , a process whereby nutrient runoff causes the overgrowth of algae, the depletion of oxygen, and death of aquatic fauna.
In marine ecosystems, nitrogen compounds created by bacteria, or through decomposition, collects in ocean floor sediments. It can then be moved to land in geologic time by uplift of Earth’s crust and thereby incorporated into terrestrial rock. Although the movement of nitrogen from rock directly into living systems has been traditionally seen as insignificant compared with nitrogen fixed from the atmosphere, a recent study showed that this process may indeed be significant and should be included in any study of the global nitrogen cycle.
The Phosphorus Cycle
Phosphorus is an essential nutrient for living processes. It is a major component of nucleic acids and phospholipids, and, as calcium phosphate, it makes up the supportive components of our bones. Phosphorus is often the limiting nutrient (necessary for growth) in aquatic, particularly freshwater, ecosystems.
Phosphorus occurs in nature as the phosphate ion (PO 4 3- ). In addition to phosphate runoff as a result of human activity, natural surface runoff occurs when it is leached from phosphate-containing rock by weathering, thus sending phosphates into rivers, lakes, and the ocean. This rock has its origins in the ocean. Phosphate-containing ocean sediments form primarily from the bodies of ocean organisms and from their excretions. However, volcanic ash, aerosols, and mineral dust may also be significant phosphate sources. This sediment then is moved to land over geologic time by the uplifting of Earth’s surface. (Figure below)
Phosphorus is also reciprocally exchanged between phosphate dissolved in the ocean and marine organisms. The movement of phosphate from the ocean to the land and through the soil is extremely slow, with the average phosphate ion having an oceanic residence time between 20,000 and 100,000 years.
Excess phosphorus and nitrogen that enter these ecosystems from fertilizer runoff and from sewage cause excessive growth of algae. The subsequent death and decay of these organisms depletes dissolved oxygen, which leads to the death of aquatic organisms such as shellfish and fish. This process is responsible for dead zones in lakes and at the mouths of many major rivers and for massive fish kills, which often occur during the summer months (see Figure \(\PageIndex{6}\) below).
A dead zone is an area in lakes and oceans near the mouths of rivers where large areas are periodically depleted of their normal flora and fauna. These zones are caused by eutrophication coupled with other factors including oil spills, dumping toxic chemicals, and other human activities. The number of dead zones has increased for several years, and more than 400 of these zones were present as of 2008. One of the worst dead zones is off the coast of the United States in the Gulf of Mexico: fertilizer runoff from the Mississippi River basin created a dead zone of over 8,463 square miles. Phosphate and nitrate runoff from fertilizers also negatively affect several lake and bay ecosystems including the Chesapeake Bay in the eastern United States.
The Sulfur Cycle
Sulfur is an essential element for the molecules of living things. As part of the amino acid cysteine, it is involved in the formation of proteins. As shown in Figure \(\PageIndex{7}\) below, sulfur cycles between the oceans, land, and atmosphere. Atmospheric sulfur is found in the form of sulfur dioxide (SO 2 ), which enters the atmosphere in three ways: first, from the decomposition of organic molecules; second, from volcanic activity and geothermal vents; and, third, from the burning of fossil fuels by humans.
On land, sulfur is deposited in four major ways: precipitation, direct fallout from the atmosphere, rock weathering, and geothermal vents. Atmospheric sulfur is found in the form of sulfur dioxide (SO 2 ), and as rain falls through the atmosphere, sulfur is dissolved in the form of weak sulfuric acid (H 2 SO 4 ). Sulfur can also fall directly from the atmosphere in a process called fallout. Also, as sulfur-containing rocks weather, sulfur is released into the soil. These rocks originate from ocean sediments that are moved to land by the geologic uplifting of ocean sediments. Terrestrial ecosystems can then make use of these soil sulfates (SO 4 2- ), which enter the food web by being taken up by plant roots. When these plants decompose and die, sulfur is released back into the atmosphere as hydrogen sulfide (H 2 S) gas.
Sulfur enters the ocean in runoff from land, from atmospheric fallout, and from underwater geothermal vents. Some ecosystems rely on chemoautotrophs using sulfur as a biological energy source. This sulfur then supports marine ecosystems in the form of sulfates.
Human activities have played a major role in altering the balance of the global sulfur cycle. The burning of large quantities of fossil fuels, especially from coal, releases larger amounts of hydrogen sulfide gas into the atmosphere. As rain falls through this gas, it creates the phenomenon known as acid rain, which damages the natural environment by lowering the pH of lakes, thus killing many of the resident plants and animals. Acid rain is corrosive rain caused by rainwater falling to the ground through sulfur dioxide gas, turning it into weak sulfuric acid, which causes damage to aquatic ecosystems. Acid rain also affects the man-made environment through the chemical degradation of buildings. For example, many marble monuments, such as the Lincoln Memorial in Washington, DC, have suffered significant damage from acid rain over the years. These examples show the wide-ranging effects of human activities on our environment and the challenges that remain for our future.
Suggested Supplementary Reading
Bruckner, M. 2018. The Gulf of Mexico Dead Zone. [Website] < https://serc.carleton.edu/microbelif...one/index.html >
Contributors and Attributions
- Biogeochemical Cycles by OpenStax is licensed under CC BY 4.0. Modified from the original by Matthew R. Fisher.


6: Elliptic Geometry
Elliptic geometry is the second type of non-Euclidean geometry that might describe the geometry of the universe. In this chapter, we focus our attention on two-dimensional elliptic geometry, and the sphere will be our guide. The chapter begins with a review of stereographic projection, and how this map is used to transfer information about the sphere onto the extended plane. We develop elliptic geometry in Sections 6.2 and 6.3, and then pause our story in Section 6.4 to reflect on what we have established, geometry-wise, before moving on to geometry on surfaces in Chapter 7.
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- 6.3: Measurement in Elliptic Geometry
- Rather than derive the arc-length formula here as we did for hyperbolic geometry, we state the following definition and note the single sign difference from the hyperbolic case. This sign difference is consistent with the sign difference in the algebraic descriptions of the transformations in the respective geometries.
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- 6.4: Revisiting Euclid's Postulates
- Without much fanfare, we have shown that the geometry (P^2,S) satisfies the first four of Euclid's postulates, but fails to satisfy the fifth. This is also the case with hyperbolic geometry (D,H). Moreover, the elliptic version of the fifth postulate differs from the hyperbolic version. It is the purpose of this section to provide the proper fanfare for these facts.


5.6A: Mitochondria
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- Ying Liu
- City College of San Francisco
Briefly describe mitochondria and state their function.
State where in the mitochondria the electron transport chain is located.
State where in the mitochondria the enzymes for the citric acid cycle (Krebs cycle) are located.
Mitochondria function during aerobic respiration to produce ATP through oxidative phosphorylation. The respiratory enzymes and electron carriers for the electron transport system are located within the inner mitochondria membrane. The enzymes for the citric acid cycle (Krebs cycle) are located in the matrix.
- Electron micrograph of mitochondria courtesy of Dennis Kunkel's Microscopy .
- Electron micrograph of a mitochondrion from the Biology Department at the University of New Mexico.
| Concept map for Eukaryotic Cell Structure |
Summary
- Mitochondria are rod-shaped structures ranging from 2 to 8 micrometers in length surrounded by two membranes.
- Mitochondria are located throughout the cytoplasm.
- Mitochondria function during aerobic respiration to produce ATP through oxidative phosphorylation.
- The respiratory enzymes and electron carriers for the electron transport system are located within the inner mitochondria membrane. The enzymes for the citric acid cycle (Krebs cycle) are located in the matrix.
- Mitochondria replicate giving rise to new mitochondria as they grow and divide. They also have their own DNA and ribosomes.
Questions
Study the material in this section and then write out the answers to these questions. Do not just click on the answers and write them out. This will not test your understanding of this tutorial.
- Briefly describe mitochondria and state their function.
- State where in the mitochondria the electron transport chain is located.
- State where in the mitochondria the enzymes for the citric acid cycle (Krebs cycle) are located.