7.3: Putting It Together- Cell Membranes - Biology

7.3: Putting It Together- Cell Membranes - Biology

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Let’s return to our discussion of cystic fibrosis. This in turn leads directly to many of the symptoms of CF: thick, sticky mucus, frequent chest infections, and coughing or shortness of breath.


Cystic fibrosis is a difficult disease to treat. As we mentioned at the beginning of the module, patients with CF often suffer lung infections and sometimes require lung transplants. In addition to this, many CF patients are on one or more antibiotics at all times—even when healthy—to suppress infection. Several mechanical techniques are used to dislodge sputum and encourage its expectoration. In the hospital setting, chest physiotherapy is utilized. As lung disease worsens, mechanical breathing support may become necessary. Bi-lateral lung transplantation often becomes necessary for individuals with cystic fibrosis as lung function and exercise tolerance declines.

Gene therapy has been explored as a potential cure for cystic fibrosis. Ideally, gene therapy attempts to place a normal copy of the CFTR gene into affected cells. Transferring the normal CFTR gene into the affected epithelium cells would result in the production of functional CFTR in all target cells, without adverse reactions or an inflammation response. Studies have shown that to prevent the lung manifestations of cystic fibrosis, only 5–10 percent the normal amount of CFTR gene expression is needed.

Finally, a number of small molecules that aim at compensating various mutations of the CFTR gene are under development. About 10 percent of CF cases result from a premature stop codon in the DNA, leading to early termination of protein synthesis and truncated proteins. One approach to combating a faulty receptor is to develop drugs that get the ribosome to overcome this premature stop codon and synthesize a full-length CFTR protein.

7.3: Putting It Together- Cell Membranes - Biology

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COURSE DESCRIPTION This course provides an introduction to the most powerful engineering principles you will ever learn - Thermodynamics: the science of transferring energy from one place or form to another place or form. We will introduce the tools you need to analyze energy systems from solar panels, to engines, to insulated coffee mugs. More specifically, we will cover the topics of mass and energy conservation principles first law analysis of control mass and control volume systems properties and behavior of pure substances and applications to thermodynamic systems operating at steady state conditions. COURSE FORMAT The class consists of lecture videos, which average 8 to 12 minutes in length. The videos include integrated In-Video Quiz questions. There are also quizzes at the end of each section, which include problems to practice your analytical skills that are not part of video lectures. There are no exams. GRADING POLICY Each question is worth 1 point. A correct answer is worth +1 point. An incorrect answer is worth 0 points. There is no partial credit. You can attempt each quiz up to three times every 8 hours, with an unlimited number of total attempts. The number of questions that need to be answered correctly to pass are displayed at the beginning of each quiz. Following the Mastery Learning model, students must pass all 8 practice quizzes with a score of 80% or higher in order to complete the course. ESTIMATED WORKLOAD If you follow the suggested deadlines, lectures and quizzes will each take approximately

3 hours per week each, for a total of

6 hours per week. TARGET AUDIENCE Basic undergraduate engineering or science student. FREQUENTLY ASKED QUESTIONS - What are the prerequisites for taking this course? An introductory background (high school or first year college level) in chemistry, physics, and calculus will help you be successful in this class. -What will this class prepare me for in the academic world? Thermodynamics is a prerequisite for many follow-on courses, like heat transfer, internal combustion engines, propulsion, and gas dynamics, to name a few. -What will this class prepare me for in the real world? Energy is one of the top challenges we face as a global society. Energy demands are deeply tied to the other major challenges of clean water, health, food resources, and poverty. Understanding how energy systems work is key to understanding how to meet all these needs around the world. Because energy demands are only increasing, this course also provides the foundation for many rewarding professional careers.

Получаемые навыки

Energy, Energy Systems, Mechanical Engineering, Energy Analysis


Margaret mam has done excellent job. Nicely designed the contents and videos were really helpful to solve the questions in the assignments.Thanks to mam. and Please Add course on Heat Transfer.

Great practical information to thermodynamical processes and machines with many calculated examples. A bit light on the fundamental definitions, like entropy, but very good for hands-on work.

In this module we focus on in-depth analysis of a Rankine power plant. The Rankine power plant is the fundamental design for stationary power generation when the working fluid is water (or steam) and the energy carrier is nuclear, coal, gas, or thermal solar power. We also learn that conventional power plants generate a lot of waste heat! Co-generation is a great way to use that waste heat. Can you think of a few ways you might capture waste heat and use it productively? Then you might have your next environmentally sustainable business venture!


Margaret Wooldridge, Ph.D.

Arthur F. Thurnau Professor

Текст видео

Okay. Whenever we're trying to define a state, we need to take information about the process, both before and after that state, when we're considering a cycle. So, for this case, remember we were looking for the enthalpy at the exit stage of the first turbines. So, if this is state one, we wanted the information at state two. Now, from one to two, we know that that's an isentropic process, and then from two to three, we know that that's an isoberic process. So to define state two, we need to realize that P2 is given. We know the pressure is 25 bar and that, that's equal to P3. In this case I told you the reheater has an inlet pressure of 25 bar and that is exactly P2. Conversely, I could have told you. The reheater has an exit pressure of 25 bar and you should have mapped that successfully to the fact that that's P3. so that gives us the information from 2 to 3. We then need to look upstream to determine the rest of the information to fully define the state and that's the isentropic nature of the process. And so, we use the entropy that we found from our online steam calculator. And between those two pieces of information, pressure and entropy are always independent. As we see in our figure, and as we show here, state two is in the super heat region. And again, our hint here is that we don't like steam turbines to experience phase change. And so we're going to consider those generally to always be super heat region. So, we would go look up in our steam tables. So if we had more extensive online calculators, steam tables online, we would find that for a pressure of 25 bar and an entropy that was given at state one of 6.9, so S1 equals 6.904 kilojoules per kilogram kelvin. Which equals S2, we come up with an enthalpy of 3149 kilojoules per kilogram. Okay, at this point we now have enthalpy values for essentially all stated information at every single state condition in this process. So we can determine whatever information we want. Now, our original question that we were asked is to calculate the cycle efficiency of the power plant. And we're going to do that, and we're going to pick up some different addition information along the way that's going to be very informative about telling us scale, magnitude, and how we can interpret the information from this type of a cycle. Okay, so the next step is let's find the heat transfer into the cycle. Now, remember from our process diagram let's go ahead and draw that again. We have our steam generator. And here's where we add heat. And remember because there's a re-heater, there's two points in this cycle where we add heat. So this is QN1. We had our first stage of the turbine, and then we had our re-heater. And that's where we added heat a second time. So, this is state one. This is state two. Here's state three, and again to complete the diagram, here's my second stage of the turbine, my condenser, and then here is my pump. And we would finish our labeling, it looks like that. Okay, so we want to find the heat transfer into the cycle. We're going to invoke all the assumptions we typically do for these types of turbo machinery. So, we're going to assume that we have steady state. Steady flow. So all those time derivatives are going to go to zero. We're going to consider that the kinetic, the changes in kinetic and potential energy are negligible. And so, we don't have to worry about those and that leaves us for each of these component. Recall, all we're going to have to consider is the heat transfer, the work transfer and the enthalpy. Okay. For the turbines, we're going to consider those adiabatic. So, they'll have work out of the turbine but all turbines are considered adiabatic. And for our steam generators, of course, they, the heat exchangers, so any heat exchanger, there's no work transfer. Okay, so I'm going to simplify this conservation of energy analysis to be the very simplified form that we had determined before. And I'm just going to cut straight to the chase just so we can get to some numbers faster here. So if we consider the heat transfer in, into the steam generator, that's going to be given by a balance between the enthalpy at the exit and an enthalpy at the entrance. So, H1, minus H6. That's heat transfer into the system, so we expect this number to be greater than 0, because that's our sign convention. And if we go ahead and plug in the numbers that you've been collecting in the past units, we're going to have an enthalpy at state one of 3625.8 minus the enthalpy at state 6 which is 426.5. And again, these are normalized by the mass flow rates so this is a kilo joules per kilogram number and if we wanted to be precise here we could label this as a q, lower case q. Qn1 and I like to keep the, I want to keep it normalized by mass flow rate just for a little while. Because we're going to actually determine this mass flow rate in just a couple of moments, well a few more than a couple of moments. And if you go ahead math we get a number of 3199.3 kilojoules per kilogram. Are added in the steam generator. So, this the amount of energy on a per mass basis, added to the water in the steam generator. We go through that exact same process for the reheater to determine the second portion of heat added to our system. So, for the reheater, we have heat addition in 2. That's this one here. Again, we're going to normalize everything by the mass flow rate. And we're going to have when we plug in the values here, this is going to be for H3 minus H2, enthalpy at state 3 minus the enthalpy at state 2. And that's going to give us values of 3686.8 minus 3149.0 on the kilojoule per kilogram basis which gives us a total of 537.8 kilojoules per kilogram. So, to be very precise in our language, this is the net heat that we're interested in here. The net heat into the cycle, which is the sum of these two contributions. The contribution from the steam generator and the contribution from the reheater. So Q in total. Again, all normalized on a mass flow rate, is equal to Q in 1 plus, which is a sum of the 3,199 and the 538 kilojoules per kilogram. Giving us a net value of 3,737.1 kilojoules per kilogram are added to the cycle, between those two heat exchangers. Okay, we're going to take that information. And remember, for us to determine the cycle efficiency, we need to have, remember cycle efficiency. We'll just do a reminder of that. Is the work transfer for the cycle, divided by the heat transfer in. And we remember the work transfer for the cycle, the net work transfer is identically equal to the heat transfer for the cycle, divided by the heat transfer in. Okay. So, we've just found the denominator that we need for this calculation. We still need the numerator. We can determine either net work transfer or net heat transfer, one of the two, but we don't need to do both. Since we've already started with our heat transfer calculations, I think we should continue to work with the heat transfers. So, that's what we'll do. So, we're going to find the net heat transfer for the cycle. Remember, we need to know all the heat transfer in, and all the heat transfer out. Now again, we've already found all the heat transfer in. And again, we can make these on a rate basis. Now we need to find the heat transfer out. There's only one heat exchanger where we reject heat, that's the condenser, and so if we want to find the heat transfer out. Again, normalized on mass basis, that's simply the enthalpy difference across the condenser. So, that's going to be h5 minus h4. And if we go ahead and substitute in the values that we determined for those two enthalpies, we get 417.46 minus 2756.4 kilojoules per kilogram. And we get a number when we punch that into our calculator, which is minus 2,338.9. It's a negative number, which is, as we would expect, because remember, this is heat transfer out of the system. So, to find that cycle efficiency, just like we had on the previous slide, we need to know the net heat transfer for the cycle divided by the net heat transfer in. Go ahead and put these on a rate basis. Everything normalized by the one mass flow rate that's consistent for all the components in this example. In this cycle, because there's only one loop. So, we have one mass transfer in this system. Again, the net heat transfer for the cycle is simply the sum of the heat transfer in and out. So if we go ahead and do that calculation, we get 537.8 plus 3,199.3 minus 2,338.9 all divided by net heat transfer in, which was 3737.1. Which is a value in the numerator here and that heat transfer is 1398.2 kilojoules per kilogram. And then the denominator, we have 3737.1 kilojoules per kilogram, so our cycle efficiency is dimensional, as we would expect it to be. And we get a cycle efficiency of 37.4%. Okay, next. I want to give you some food for thought. We're still going to keep working on this problem. We're still going to keep looking at the numbers. But before we do this, I want you to think about some of the power issues that we face in the United States and abroad. What you're looking at here is a diagram of where the electricity production is by coal within the United States. And we're looking at terawatt hours here in this figure. But more importantly, what you see is that power production is typically by coal where there are coal reserves. So if you're not aware of it, Illinois has significant coal reserves, so does the Midwest, in general, and Texas. And so, what you see is power production by coal is, of course, where generally located where the coal reserves are. The turbo US annual power capacity is about 340 gigawatts of power generated typical capacity within the United States. That's about 50% of the power generation in the United States is by coal. 90% of these power plants are over 25 years old. At least 25% or 50 gigawatts of the coal fired capacity is expected to be retired within the next ten years. They're beyond any terms of re-licensing of those facilities. Nuclear energy within the United States is expected to retire another 40 gigawatts or more of power in the same time period. So that's about 90 gigawatts of power is coming offline in the next ten years. What's going to be the most likely energy carrier for the new, or next generation, of stationary power plants? And this really is a, just sit back and think about it question. We really don't have the tools, yet, for us to identify which one of the energy carriers is most likely to be replacing or coming online in the next ten years. But we'll discuss that when we get started next time, and we'll continue to look at that example of a steam power plant. Thank you.

7.3: Putting It Together- Cell Membranes - Biology

C2006/F2402 '04 -- Outline on Immunology -- revised 4/25/03

(c) 200 4 Dr. Deborah Mowshowitz Columbia University, New York, NY. Last Update: 04/27/04 07:43 PM . The order of topics in the lecture and the order of topics in the problems do not match, so you may find it easier to do all the problems after reviewing the lecture. By the end, you should be able to do problems 13-4 to 13-12.

Major Players in the Immune System:

Cells Secreted Proteins Cell Surface Proteins
B cells Antibodies (Ab or immunoglobulins 5 classes) MHC
TC cells Perforin BCR
TH cells Cytokines (Interleukins & interferons) TCR
phagocytic cells CD4

The chart above summarizes the major players in immunology. By the end of the next lecture, you should be able to describe what each item is, its significance, and how it is related to all the others.

Handout: 224A (Antigen Presenting Cells & Activation of T cells) -- Posted version is from a previous year there are some minor differences.
Handout 24B is not on web it includes clonal selection (Purves 19.7), T & APC cell interactions (like Purves 19.17) & activation of B cells (like Purves 19.18 (a) -- to be discussed next time).

I. Specific (or Acquired) Immune Response -- Major Features

A. Intro. What are major components of the specific immune system?

1. Proteins -- antibodies, TCR's & MHC's. See lecture 23.

2. What Cells are involved? (See bottom of 23B.) White blood cells (leukocytes) -- contain no hemoglobin. WBC divided into two main types

a. Phagocytes -- macrophages, dendritic cells, etc. ( See Purves 19.2). Involved in processing antigens as will be explained.

b. Lymphocytes. Found in lymph nodes and elsewhere. Lymphocytes (WBC) do actual production of antibodies and/or execution of cellular immune response. Divided into B and T cells.

(1). Both B & T cells come from same line of stem cells in bone marrow.

(2). B cells mature in bone marrow T cells in thymus

B. Specific Immune system has 2 branches

1. Humoral response -- binding and destruction of antigen done by proteins in "humors" = antibodies in blood and secretions (for ex. milk, tears). Antibodies made by B cells.

2. Cellular or cell-mediated response -- binding and destruction of antigen done by whole cells. Destruction carried out by cytotoxic T cells.

C. Major features of 2 branches of specific immune system -- see table on handout 23B and last lecture & below:

1. Action of B cells to combat infection:

B cells --> release antibody --> Ab (antibody) binds Ag (antigen -- usually on surface of microbe) --> trigger destruction of microbes (microbes are engulfed by phagocytes or lysed) often with the help of complement. (See Purves 19.12 & 19.3) Allergies are a side effect of this system.

2. Action of (cytotoxic) T cells

T cells --> bind to Ag on surface of virus infected eukaryotic cell --> destroy cell either by lysis or triggering of apoptosis. For lysis, T cells use proteins called perforins to make holes in and kill targets (with the assistance of other proteins). Note complement is similar but works on prokaryotic invaders perforins work on rogue eukaryotic cells. (See Purves 19.15) This is why grafts fail foreign cells of graft look like infected (defective?) cells and are destroyed. (*See section on MHC below -- foreign MHC looks like host MHC plus antigen.)

3. Role of helper T cells -- needed for function of both B and cytotoxic T cells details below.

II. Immune System -- Important Features to explain

A. Specificity & Diversity -- each Ab or TCR is directed against one epitope or antigenic determinant (= piece of antigen -- see Purves 19.6), and there are many, many different antigens. How can you make so many different Ab's or TCR's, each specific for a particular antigen or piece of it?

B. Memory -- secondary response is faster, larger, better than primary response. In secondary response, make more Ab, Ab is more effective (binds better to Ag because of slight changes in amino acid sequence of Ab), and Ab response lasts longer. (Purves 19.8 [18.9]) How is this done?

C. Tolerance -- can distinguish self/nonself or normal/abnormal -- make Ab only to foreign/abnormal stuff (except in disease states). How does this work?

D. Response is adaptable -- response depends on amount and type of antigen. How do you "know" which antibody to make in response to a particular antigen?

E. You need helper T's for both cytotoxic T's and B's to work. How are helper T's involved in both humoral and cellular immune responses?

III. Clonal Selection -- How do you account for the "important features" listed above?

A. B cells (See Purves fig. 19.7)

1. Each cell differentiates --> produces a single type of Ab on surface ("virgin" or "naive" B). Each cell rearranges its DNA during differentiation, so each cell has a unique set of Ab coding genes and makes a unique antibody -- that is, with a unique set of "grabbers."

Note: As B cells mature and specialize, changes in the antibody they make may occur because of alternative splicing and/or additional rearrangements of the DNA. Structure & rearrangement of Ab coding genes and antibodies will be discussed in detail next time.

2. Ab on surface of cell acts as a "trap". Surface antibody (also called BCR or B cell antigen receptor) acts as trap/receptor for Ag.

3. Activation or destruction of B cell is triggered by binding of Ag to surface Ab (BCR)

a. Destruction. If Ag is perceived as "self" --> cell destroyed or suppressed (--> tolerance).

b. Activation. If Ag is perceived as foreign --> cell divides --> clonal expansion, further differentiation into

(1). Effector cells -- short lived but secrete lots of Ab --> destroy or inactivate targets class of Ab determines fine points. (In earlier lecture we explained how alternative splicing can allow cell to switch from making surface bound Ab to secreted Ab.)

(2). Memory cells -- long lived and more specialized to make Ab wait for next time (responsible for memory).

c. Whether antigen is perceived as "self" or "foreign" depends on time of exposure (embryonic vs adult) and additional factors. (This turns out to be very complicated, so we are ignoring the "additional factors.")

4. What's the point?

a. Clonal Selection: Each cell makes a little Ab before any Ag present. Each cell makes a different Ab. This antibody stays on the cell surface and acts as BCR = trap for antigen. Ag acts as a trigger -- binding of Ag to "trap" stimulates only those cells that happen to make Ab that binds to that particular trigger. (This is the selection part that accounts for specificity, diversity, and adaptability.)

b. Clonal expansion: The cells triggered by binding of Ag grow and divide --> (more) effector cells & memory cells. Both types of cells make only the antibody that binds to the trigger Ag. (This is the clonal expansion part that accounts for memory & tolerance -- memory when Ag triggers multiplication, and tolerance when Ag triggers destruction or suppression).

5. Why do you need helper T cells? For most antigens, helper T must bind to B cell-Ag complex in order to activate B (step 3b above see below for details).

Try Problem 13-4.

B. T cells -- similar process as with B cells -- DNA rearrangement occurs so one type of protein with unique binding site made per cell -- but there are differences/complications as follows:

  • Cytokines are secreted proteins that are required for the development of the immune system.

  • Cytokines are generally paracrines or autocrines

  • Cytokines secreted by WBC are sometimes called lymphokines

  • Most cytokines are made by helper T cells. However, many different cells of the immune system, and some non-immune cells, secrete cytokines.

  • Many of the cytokines are called IL-1, IL-2, etc. for interleukin 1, 2 etc. Interleukins are generally cytokines made by WBC that regulate the functions of WBC.

  • Which cytokine is made depends on the cell type (B, TH, TC, etc.), the antigen it meets, and other factors. Which cytokine is made influences the next step in the immune response, and so on. See texts for details.

  • Cytokines are involved in other (nonimmune) functions, for example production of RBCs & wound healing.

5. T cell activation requires "Antigen Presentation." Antigen must be on surface of another cell (a so called "antigen presenting cell" or APC). Ag must be bound to a particular protein (MHC -- found only in eukaryotes) on the surface of the "presenting cell." See Purves 19.17. In other words, signals to activate T cells are all juxtacrines -- require cell-cell surface interactions.

a. Cytotoxic T's are activated by antigens on the surface of infected cells -- these infected target cells "present" viral antigens on their surface + MHC I see below. Activated cytotoxic T cells then kill the infected target cell.

b. Helper T's are activated by antigens on the surface of macrophages, B cells (& other immune cells) -- these cells "present" antigens on their surfaces + MHC II. Activated Helper T cells assist effector immune cells in producing

C. Two major types of T cells (See handout 24B, top, for comparison of B, TH and TC cells, surface proteins, etc.)

1. There are two types of T cells -- helper T (TH) or cytotoxic T (CTL or TC). Discussion above deals only helper T's. How do cytotoxic T's & helper T's compare?

2. Functions

a. Helper T's required for other two cell types (B and TC) to mature and respond to antigen. (Therefore defects in helper T's are very serious.)

b. Cytotoxic T's kill infected cells (& maybe cancer cells) as described above.

Try problem 13-7.

3. H ow do you tell the two types apart? Surface proteins/markers on T cells and their significance

a. TH have the protein named CD4 on their surface (therefore are said to be CD4 + )

(1). CD4 helps normal action of TH -- helps TH bind to normal target cell of immune system & helps activation of immune cell.

(2). CD4 serves as identifying marker for helper T's.

(3). HIV binds to CD4. Therefore CD4 (accidentally) acts as an HIV receptor (there are other co-receptors) -- allows HIV to enter helper T cells. HIV infection --> loss of helper T's --> complete loss of immune function

(1). CD8 helps normal function of TC -- helps TC bind to usual target cell = infected or rogue cell.

(2). CD8 serves as identifying marker for cytotoxic T's.

4. (FYI only): More than one type of helper T's exist. Currently thought to be two major kinds -- TH1 (mostly helps macrophages and cytotoxic T's) and TH2 (helps B's to function). Details are beyond scope of this course, but this is currently a hot research area.

5. How do two types of T's match up with proper targets?

a. CD8 or CD4 binds to respective protein on surface of target cell.

b. CD8 on cytotoxic T binds to a protein -- MHC I -- found on surface of infected cells.

c. CD4 on helper T binds to a different protein -- MHC II -- on surface of cells of immune system. So what is MHC??

d. How do cytoxic T's tell normal from infected cells? That's what's next!

Try problem 13-6.

IV. Antigen Presentation & Major Histocompatibility Complex (MHC) . See handout 24A. (For better pictures see Purves 19.18).

A. What is MHC?

1. MHC = very variable surface protein. There are 2 main types, and many versions of each type. Each individual has several different genes for each of the two main types of MHC. Each of these genes has 20-40 or even more variants (alleles). Since there are several genes per person and many different alleles of each gene in the population, there is a lot of variation in the actual MHC proteins (and DNA) from person to person. These genes, unlike genes for antibodies and TCR's, do not rearrange during development. So there is variation from person to person, but all cells in a single person have the same MHC genes.

2. Two types of MHC

a. All nucleated cells have MHC I on their surface.

b. Cells of immune system (all APC's) have MHC II on their surface. (Not all T cells have MHC II at all times, & we will assume T cells do not have MHC II.)

B. What are Antigen Presenting Cells (APC's)? APC's = Cells that have antigens bound to MHC on their plasma membranes. How they get their antigens/epitopes and attach them to MHC is shown on the top of 24A. T cells bind to the MHC-Antigen complex, as shown in the middle of the handout. (See Purves 19.17)

1. APC's do not present whole antigens -- APC's present fragments of antigens called epitopes or antigenic determinants. See top 1/2 of 24A & See Purves 19.16

(1). Ordinary cells (not from immune system) present fragments of whatever proteins they are making (+ MHC I). These epitopes come from proteins made inside the APC itself and then partially digested in proteosomes.

(2). Immune system cells (B cells, dendritic cells & macrophages = "classic" APC's) present fragments of whatever they have engulfed or endocytosed (+ MHC II) -- Purves 19.16. These epitopes come from proteins that were originally outside the APC and were partially digested in lysosomes/endosomes.

2. Each APC presents many different epitopes at once (even if they are all derived from a single antigen).

3. How do the epitopes reach the cell surface?

a. The endogenous fragments digested in proteosomes enter the ER (by a special transporter), and combine with newly made MHC molecules (in the ER membrane). The complex is transported to the cell surface through the ER, Golgi, etc. in the same way as any cell surface protein.

b. The exogenous fragments digested in lysosomes/endosomes combine with newly made MHC in the lysosomes/endosomes and the complex reaches the cell surface the same way that used receptors recycle to the surface.

C. Why do you need MHC & APC's?

1. T cells are "MHC restricted" B cells are not

a. B cells recognize plain Ag = Antibodies bind to Ag in plasma or on bacterial/viral surfaces.

b. T cells recognize only Ag that is bound to MHC on (euk.) cell surface ( Purves 19.17 and handout 24B.)

(1). T cell receptors bind to variable part of MHC-Ag complex = bind to Ag itself

(2). CD4 or CD8 binds to constant part of corresponding MHC.

2. Two types of T's recognize (bind to) Ag associated with different MHC's -- this is how T cells tell immune cells and infected (ordinary) cells apart. See handout 24B.

a. Cytotoxic T's (CD8 + ) recognize Ag + MHC I (said to be "MHC I restricted") -- note target must have MHC I and Ag.

b. Helper T's (CD4 + ) recognize Ag + MHC II (said to be "MHC II restricted") -- note target must have MHC II and Ag.

The point: T cells recognize their targets (in part) by the type of MHC they have -- infected cells have MHC I and immune cells have MHC II.

V. Putting it all together -- Purves 19.18 or handout 24A

A. T cell is activated (Middle of 24A)

1. Need binding to APC -- either

a. Binding to classic APC (B cell or phagocytic cell -- macrophage or dendritic cell) to activate TH

(1). In primary response, APC probably a phagocytic cell (not specific for any particular antigen)

(2). In secondary Response, APC likely to be a B cell (with antibody specific for that antigen)

b. Binding to infected cell to activate TC.

2. T cell - APC cell binding requires match

a. APC must have Ag (epitope) + MHC

b. T cell must have TCR that matches Ag, and CD4 or CD8 to match proper MHC.

Note: Picture on handout shows epitope in middle, in between both MHC of APC and TCR of T cell. The epitope is firmly bound to the MHC and stays with the APC when the T cell finishes activation and detaches. The activated T cell now has an empty TCR and will bind to another (B) cell with the same epitope.

3. Cytokines must be provided for activation -- to bind to receptors on T cell.

a. Cytokine (IL-1) from APC needed to activate TH .

b. Different cytokine (IL-2) from TH needed to activate TC. ( This is why you need TH's for cytotoxic T response.)

4. Activation --> clonal expansion (more TH cells) AND more specialization of T cells. These activated T cells can disassociate from the APC and find another cell to "help."

B. What activated TH cell does (see bottom of handout 24A)

1. Humoral Response: Activated TH cell then divides and/or activates a B cell -- activates the same APC that just activated it or finds a new B cell.

2. Cell Mediated Response: Activated TH cell divides and/or helps activate a TC cell (by providing cytokines) -- details of this not discussed.

C. What Activated TC cell does (see bottom of handout): Divides and/or kills an infected cell.

Try problems 13-9 & 13-10. To review all the terminology so far, try 13-11.

VI. How do T and B cells get activated? Wrap Up. See handout 24A. and topic V above. -- This will be discussed next time.

7.3 Normalization by deconvolution

As previously mentioned, composition biases will be present when any unbalanced differential expression exists between samples. Consider the simple example of two cells where a single gene (X) is upregulated in one cell (A) compared to the other cell (B) . This upregulation means that either (i) more sequencing resources are devoted to (X) in (A) , thus decreasing coverage of all other non-DE genes when the total library size of each cell is experimentally fixed (e.g., due to library quantification) or (ii) the library size of (A) increases when (X) is assigned more reads or UMIs, increasing the library size factor and yielding smaller normalized expression values for all non-DE genes. In both cases, the net effect is that non-DE genes in (A) will incorrectly appear to be downregulated compared to (B) .

The removal of composition biases is a well-studied problem for bulk RNA sequencing data analysis. Normalization can be performed with the estimateSizeFactorsFromMatrix() function in the DESeq2 package (Anders and Huber 2010 Love, Huber, and Anders 2014) or with the calcNormFactors() function (Robinson and Oshlack 2010) in the edgeR package. These assume that most genes are not DE between cells. Any systematic difference in count size across the non-DE majority of genes between two cells is assumed to represent bias that is used to compute an appropriate size factor for its removal.

However, single-cell data can be problematic for these bulk normalization methods due to the dominance of low and zero counts. To overcome this, we pool counts from many cells to increase the size of the counts for accurate size factor estimation (Lun, Bach, and Marioni 2016) . Pool-based size factors are then “deconvolved” into cell-based factors for normalization of each cell’s expression profile. This is performed using the calculateSumFactors() function from scran, as shown below.

We use a pre-clustering step with quickCluster() where cells in each cluster are normalized separately and the size factors are rescaled to be comparable across clusters. This avoids the assumption that most genes are non-DE across the entire population - only a non-DE majority is required between pairs of clusters, which is a weaker assumption for highly heterogeneous populations. By default, quickCluster() will use an approximate algorithm for PCA based on methods from the irlba package. The approximation relies on stochastic initialization so we need to set the random seed (via set.seed() ) for reproducibility.

We see that the deconvolution size factors exhibit cell type-specific deviations from the library size factors in Figure 7.2. This is consistent with the presence of composition biases that are introduced by strong differential expression between cell types. Use of the deconvolution size factors adjusts for these biases to improve normalization accuracy for downstream applications.

Figure 7.2: Deconvolution size factor for each cell in the Zeisel brain dataset, compared to the equivalent size factor derived from the library size. The red line corresponds to identity between the two size factors.

Accurate normalization is most important for procedures that involve estimation and interpretation of per-gene statistics. For example, composition biases can compromise DE analyses by systematically shifting the log-fold changes in one direction or another. However, it tends to provide less benefit over simple library size normalization for cell-based analyses such as clustering. The presence of composition biases already implies strong differences in expression profiles, so changing the normalization strategy is unlikely to affect the outcome of a clustering procedure.

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1 It&rsquos a Small, Small World: A Brief History of Biological Correlative Microscopy 1
Christopher J. Guérin, Nalan Liv, and Judith Klumperman

1.1 It All Began with Photons 1

1.2 The Electron Takes Its Place 2

1.3 Putting It Together, 1960s to 1980s 3

1.4 CLEM Matures as a Scientific Tool 1990 to 2017 4

2 Challenges for CLEM from a Light Microscopy Perspective 23
Kurt Anderson, Tommy Nilsson, and Julia Fernandez‐Rodriguez

2.1.1 Electron and Light Microscopy 23

2.1.2 Correlative Microscopy: Two Cultures Collide 25

2.2 Microscopy Multiculturalism 26

2.2.1 When Fluorescence Light Microscopy Resolution is Not Enough 26

2.2.2 The Fluorescence Microscopy (FM), Needle/Haystack Localization 27

2.2.3 Electron Microscopy, Visualizing the Ultrastructure 27

2.2.4 Finding Coordinates 28

2.3 Bridging the Gap between Light and Electron Microscopy 29

2.3.1 Finding the Same Cell Structure in Light and Electron Microscopes 29

2.3.2 Making the Fluorescence Labels Visible in the Electron Microscope 29

2.3.3 Visualizing Membrane Trafficking Using CLEM 30

2.4 Future CLEM Applications and Modifications 31

2.4.1 Correlative Reflection Contrast Microscopy and Electron Microscopy in Tissue Sections 31

2.4.2 Dynamic and Functional Probes for CLEM 32

3 The Importance of Sample Processing for Correlative Imaging (or, Rubbish In, Rubbish Out) 37
Christopher J. Peddie and Nicole L. Schieber

3.2 Searching for Correlative Electron Microscopy Utopia 40

3.3 Sample Processing for Correlative Imaging: A Primer for the First Steps 40

3.4 Making It Go Faster (We Want More Speed, More Speed&hellip) 42

3.6 Keeping the Region of Interest in Sight 45

3.7 Correlation and Relocation with Dual Modality Probes 48

3.8 Integration of Imaging Modalities, and In‐Resin Fluorescence 49

3.9 Streamlining the Correlative Approaches of the Future: SmartCLEM 51

3.10 How Deep Does the Rabbit Hole Go? 52

3.11 Hold That Thought, Though &minus Is This All Completely Necessary? 53

3.12 Improving Accessibility to Correlative Workflows 54

4 3D CLEM: Correlating Volume Light and Electron Microscopy 67
Saskia Lippens and Eija Jokitalo

4.3 Comparative and Correlative LM and EM Imaging 69

4.4 CLEM is More than LM + EM 69

4.6 Two Workflows for 3D CLEM 71

4.7 Where is CLEM Going in the Future? 74

5 Can Correlative Microscopy Ever Be Easy? An Array Tomography Viewpoint 81
Irina Kolotuev and Kristina D. Micheva

5.2 Why Array Tomography? 81

5.3 Array Tomography of Abundant Subcellular Structures: Synapses 82

5.4 Array Tomography of Sparsely Distributed Structures: Cisternal Organelle 84

5.5 Array Tomography of Small Model Organisms: C. elegans 87

5.6 To Summarize: Finding the Right AT Approach 90

5.7 Areas of Improvement 91

5.7.2 Serial Ultrathin Sectioning 91

5.7.4 EM Compatible Fluorophores 92

5.7.5 Detectors and EM Resolution 92

5.7.6 Image Registration and Alignment Tools 93

6 Correlative Microscopy Using Scanning Probe Microscopes 99
Georg Fantner and Frank Lafont

6.3 AFM and Optical Microscopy Correlative Approaches 103

6.4 Correlation with CLSM 104

6.5 Correlation with Cell Mechanics 104

6.5.1 Correlation with Super‐Resolution Light Microscopy (SRLM) 105

6.5.2 Future Developments 107

6.6 AFM and Correlation with Electron Microscopy 109

6.6.1 Correlation Involving AFM, EM, and Chemical Surface Characterization 110

6.6.2 Future Developments 113

6.7 Future Developments Involving Correlation Microscopy Using HS‐AFM 113

6.8 Concluding Remarks 114

7 Integrated Light and Electron Microscopy 119
R. I. Koning, A. Srinivasa Raja, R. I. Lane, A. J. Koster, and J. P. Hoogenboom

7.2 Large‐Scale and High‐Throughput (Volume) Microscopy 120

7.2.1 Advantages and Challenges for Large‐Scale EM 120

7.2.2 Advantages of CLEM for Large‐Scale EM 121

7.2.3 Prospects for Integrated Microscopy 121

7.3 Super‐Resolution Fluorescence Microscopy 123

7.3.1 Advantages and Challenges for CLEM with Super‐Resolution Fluorescence 123

7.3.2 Implementation of SR‐FM with CLEM 124

7.3.3 Prospects for Integrated SR‐CLEM 124

7.4 Cryo‐Electron Microscopy 125

7.4.1 Advantages of CryoEM 125

7.4.2 Possibilities and Challenges for Correlative Cryo‐Microscopy 126 Super‐Resolution Fluorescence Cryo‐Microscopy: Probes and Instruments 126 Transfer of Cryo‐Samples between Microscopes 127 Sample Thickness 127 Data Collection Speed 128

7.4.3 Integrated Systems for CryoCLEM 129

7.4.4 Prospects for Integrated Cryo‐Microscopy 129

8 Cryo‐Correlative Light and Electron Microscopy: Toward in situ Structural Biology 137
Tanmay A.M. Bharat and Wanda Kukulski

8.2 Cryo‐CLEM to Support Single Particle Analysis of Purified Macromolecules 138

8.3 Capturing Structural Dynamics of in vitro Reconstituted Systems 141

8.4 Identifying Macromolecules in Plunge‐Frozen Whole Cells 142

8.5 Macromolecular Structures in Thinned Samples from Thick Cell Areas 144

8.6 Enabling Structural Biology in Multicellular Organisms and Tissues by Cryo‐CLEM 145

9 Correlative Cryo Soft X‐ray Imaging 155
Eva Pereiro, Francisco Javier Chichón, and Jose L. Carrascosa

9.1 Introduction to Cryo Soft X‐ray Microscopy 155

9.2 Cryo‐SXT Correlation with Visible Light Microscopy 159

9.3 Cryo‐SXT Correlation with Cryo X‐ray Fluorescence 160

9.4 Cryo‐SXT Correlation with TEM 163

9.5 Multiple Correlation and Integration of Methods 165

10 Correlative Light‐ and Liquid‐Phase Scanning Transmission Electron Microscopy for Studies of Protein Function in Whole Cells 171
Niels de Jonge

10.2 Limitations of State‐of‐the‐Art Methods 172

10.3 Principle of Liquid STEM 173

10.3.1 Example 1: Determination of ORAI Channel Subunit Stoichiometry by Visualizing Single Molecules Using STEM 175

10.3.2 Example 2: New Insights into the Role of HER2 179

10.4 Advantages of Liquid STEM 182

11 Correlating Data from Imaging Modalities 191
Perrine Paul‐Gilloteaux and Martin Schorb

11.2 Registration during CLEM Stages 194

11.2.1 Registration to Guide Sample Preparation 194

11.2.2 Registration to Guide the Acquisition 195 Software Packages 195 Typical Features and Fields of View 195

11.2.3 Post‐Acquisition Registration (Accurate Relocation) 196 Software and Approaches for Post‐Acquisition Registration 196

11.2.4 Trust in Alignment: Accuracy in Practice 198

11.3 Registration Paradigm 198

11.3.1 Image Features to Guide the Registration 198

11.3.2 Distance Function 199

11.3.3 Transformation Basis 199

11.3.4 Optimization Strategy 200

11.4 Envisioned Future Developments 201

11.4.1 Integrative Microscopy versus Correlative Microscopy 201

11.4.2 Incorporate a Priori Knowledge of the Specimen 202

11.4.3 Toward the Use of Machine Learning 202

11.5 Visualization of Correlation 204

12 Big Data in Correlative Imaging 211
Ardan Patwardhan and Jason R. Swedlow

12.2 The Protein Data Bank 212

12.3 Resources for Cryo‐EM 212

12.4 Light Microscopy Data Resources 214

12.6 IDR: A Prototype Image Data Resource 216

12.7 Public Resources for Correlative Imaging 217

12.7.1 CLEM Data Formats 217

12.8 Future Directions 218

12.8.1 A BioImage Archive 218

12.8.2 CLEM Data Submission Pipelines 219

12.8.3 Scaling Data Volumes and Usage 219

12.8.4 Community Adoption and International Engagement 220

13 The Future of CLEM: Summary 223
Lucy Collinson and Paul Verkade

Students and researchers in biomedical engineering, computational biology, mathematics, computer science and life sciences who are interested in understanding and applying mathematical modelling

Unit 1 Introduction to Modeling using Difference Equations
1.1 Discrete-Time Models
1.1.1 Solutions to First-Order Difference Equations
1.1.2 Using Linear Regression to Estimate Parameters
1.2 Putting it all together: The Whooping Crane
1.3 CaseStudy1: Island Biogeography
1.3.1 Background
1.3.2 Model Formulation
1.3.3 Rakata Story
1.3.4 Modern Approach: Lineage Data
1.3.5 Back to MacArthur and Wilson: Effects of Distance and Area
1.4 CaseStudy2: Pharmacokinetics Model
1.4.1 Background
1.4.2 Formulating the model
1.4.3 Understanding the Model
1.4.4 Parameter Estimation
1.4.5 Model Evaluation/Analysis
1.4.6 Further Exploration
1.5 CaseStudy3: Invasive Plant Species
1.5.1 Background
1.5.2 Model Formulation
1.5.3 Parameter Estimation
1.5.4 Model Predictions
1.5.5 Management Strategies
1.6 Wet Lab: Logistic Growth Model of Bacterial Population Dynamics
1.6.1 Introduction
1.6.2 Modeling populations
1.6.3 The Experiment
1.6.4 Model Calibration and Analysis
1.6.5 Experiment Part2: Effect of changing Media

Unit 2 Differential Equations: Model Formulation, Nonlinear Regression, and Model Selection
2.1 Biological Background
2.2 Mathematical and R Background
2.2.1 Differential Equation Based Model Formulation
2.2.2 Solutions to Ordinary Differential Equations
2.2.3 Investigating Parameter Space
2.2.4 Nonlinear Fitting
2.3 Model Selection
2.4 Case Study 1: How Leaf Decomposition Rates Vary with Anthropogenic Nitrogen Deposition
2.4.1 Background
2.4.2 The Data
2.4.3 Model Formulation
2.4.4 Parameter Estimation
2.4.5 Model Evaluation
2.5 Case Study 2: Exploring Models to Describe Tumor Growth Rates
2.5.1 Background
2.5.2 The Data
2.5.3 Model Formulation
2.5.4 Parameter Estimation
2.5.5 Model Evaluation: Descriptive Power
2.5.6 Model Evaluation: Predictive Power
2.6 Case Study 3: Predator Responses to Prey Density Vary with Temperature
2.6.1 Background
2.6.2 Analysis of functional response data: determining the parameters
2.6.3 Exploring functional responses as a function of temperature
2.7 Wet Lab: Enzyme Kinetics of Catechol Oxidase
2.7.1 Overview of Activities
2.7.2 Introduction to Enzyme Catalyzed Reaction Kinetics
2.7.3 Deriving the model
2.7.4 Estimating KM and Vmax
2.7.5 Our Enzyme: Catechol Oxidase
2.7.6 Experiment: Collecting Initial Rates for the Michaelis-Menten Model
2.7.7 Effects of Inhibitors on Enzyme Kinetics
2.7.8 Experiment: Measuring the Effects of Two Catechol Oxidase Inhibitors, Phenylthiourea and Benzoic Acid

Unit 3 Differential Equations: Numerical Solutions, Model Calibration, and Sensitivity Analysis
3.1 Biological Background
3.2 Mathematical and R Background
3.2.1 Numerical Solutions to Differential Equations
3.2.2 Calibration: Fitting Models to Data
3.2.3 Sensitivity Analysis
3.2.4 Putting it all together: The Dynamics of Ebola Virus Infecting Cells
3.3 Case Study: Influenza: Adapting the Classic SIR Model to the 2009 Influenza Pandemic
3.3.1 Background
3.3.2 The SIR Model
3.3.3 Cumulative Number of Cases
3.3.4 Epidemic Threshold
3.3.5 Public Health Interventions
3.3.6 2009 H1N1 Influenza Pandemic

3.4 Case Study 2: Prostate Cancer: optimizing immuno-therapy
3.4.1 Background
3.4.2 Model Formulation
3.4.3 Model Implementation
3.4.4 Parameter Estimation
3.4.5 Vaccination Protocols and Model Predictions
3.4.6 Sensitivity Analysis
3.4.7 Simulating Other Treatment Strategies
3.5 Case Study 3: Quorum Sensing
3.5.1 Introduction
3.5.2 Model Formulation
3.5.3 Parameter Estimation
3.5.4 Model Simulations
3.5.5 Sensitivity Analysis
3.6 Wet Lab: Hormones and Homeostasis—Keeping Blood Glucose Concentrations Stable
3.6.1 Overview of Activities
3.6.2 Introduction to blood glucose regulation and its importance
3.6.3 Developing a model
3.6.4 Experiment: Measuring Blood Glucose Concentrations Following Glucose Ingestion
3.6.5 Analysis
3.6.6 Thoughts to Consider for Potential Follow-up Experiments

Unit 4 Technical Notes for Laboratory Activities
4.1 Introduction
4.2 Population Growth
4.3 Enzyme Kinetics
4.3.1 Notes on other enzymes or similar experiments
4.4 Instructor Notes for the Blood Glucose Monitoring Lab
4.4.1 Tips for glucose monitoring
4.4.2 Other Lab Activities

AC Circuit Complex Impedance, Part 3: Putting It All Together

In Part 1 of this series, It’s Just a Passing Phase, we defined the sine waveform of the most common AC signals, illustrated how AC voltage and current each vary as a sine waveform in AC circuits, and we examined the concept of phase angles in describing the alignment (or lack of it) between a voltage sine wave and a current sine wave.

In Part 2, Reacting Nicely, we examined a bit of the dynamics of voltage and current within capacitors and inductors to get a sense for just how these components impose phase angles between voltage and current sine waves. We described the concept of reactance and illustrated the calculations of capacitive and inductive reactances.

Returning to the big picture points laid out in Part 1 and Part 2:

  1. Voltage and current applied to AC circuits are each represented by smoothly changing sine waveforms of equal frequency, depicting the regular reversals of direction and smoothly changing magnitudes of each.
  2. The applied voltage and current sine waves often get out of step with one another so the two representations no longer oscillate together, as if one sine wave is shifted ahead or behind the other in time, or phase.
  3. The amount of deviation between the voltage and current sine wave signals in a circuit is described by a phase angle between the two signals, in units of degrees.
  4. Phase angle shifts between voltage and current are imposed by a type of opposition to current flow called reactance in AC circuit components, specifically inductive reactance and capacitive reactance, measured in units of ohms.
  5. Inductive and capacitive reactances combine in a complex way with resistance in a circuit to determine the overall impedance of the circuit.
  6. Complex impedance is described with both a magnitude in ohms and a phase angle in degrees, and there are two primary shorthand methods of representing complex impedance in writing (rectangular and polar forms).
  7. Impedance magnitude and phase angle impact the behavior of AC circuits, particularly with respect to power transfer and resonance, as in RF antenna circuits, oscillator circuits, matching networks, power supply circuits, and many others.

We covered points 1 through 3 in Part 1. In Part 2 we focused on point 4. We will now complete this series with elaboration of points 5, 6, and 7. These really put it all together!

Complex Impedance: You may recall that impedance (Z) is defined as the opposition to the flow of current in an AC circuit. Impedance combines the effects of simple resistance with reactance due to capacitive and inductive components in the circuit. However, the relationship among resistance, capacitive reactance, and inductive reactance is more complex than simple addition of each factor. Let’s consider the interactions among resistance and reactances in more detail on the way to understanding and computing the impedance of a circuit.

First, resistance in a circuit with capacitors and/or inductors will affect the phase angle between voltage and current. The “pure” cases of only capacitance or only inductance that we considered in Part 2 are only ideal models that provide a perfect 90-degree phase angle between voltage and current sine waves. All real circuits will have some resistance due to wires and components, and often will also have component resistors, all of which shift the phase angle when combined with capacitors and/or inductors. So, the phase difference between voltage and current can be angles less than 90 degrees, and the precise phase angle depends on the relative values of resistance and reactance in the AC circuit.

Resistance affects the phase angle between voltage and current in AC circuits containing capacitive and inductive components.

Second, resistance and reactance combine as vectors and not via simple addition. We will examine “vector addition” in a moment using the graphs below.

Third, inductive reactance and capacitive reactance have opposite effects on phase angle. Remember, an inductive reactance makes the voltage lead the current, while a capacitive reactance makes the current lead the voltage. When inductive and capacitive components are combined in a series circuit these opposing reactances negate one another, in part or in whole, thereby determining the resultant reactance of the series circuit and impacting the overall impedance of the circuit.

Inductive reactance and capacitive reactance in a series AC circuit offset one another.

Series Circuit Impedance: Currently, we will consider only series circuit cases. Parallel circuits require a bit of a twist on the series case and we will consider them later in this article. Let’s take an example series circuit problem derived from the Extra Class question pool and solve it using a vector graph of the circuit, with explanation along the way.

Q. What is the impedance of a circuit consisting of a 400-Ω resistor in series with an inductor that has 300-Ω of reactance?

As we noted above, resistance and reactance add as vectors. We can depict this graphically using a common rectangular coordinate plane and plotting a vector for resistance and reactance. By standard convention, we will plot the resistance value along the X axis (horizontal axis), and we will plot reactance along the Y (vertical axis).

In this first example we have 400-Ω resistance, so we will draw a vector from the origin (0, 0) along the horizontal resistance axis to 400, or the coordinate plane position (400, 0).

Resistance value plotted as vector.

Next, we must plot a 300-Ω inductive reactance. In order to add these two vectors we must start this inductive reactance vector at the head of the already-plotted resistance vector, or at the point (400, 0). By standard convention, all inductive reactance is plotted in the positive vertical axis, or “upward” in the coordinate plane.

Since the inductive reactance is 300-Ω, we draw a vector straight up from the (400, 0) position to a position 300 units above. The point we have reached is the coordinate (400, 300).

Inductive reactance vector added to resistance vector.

Now, we complete the vector diagram by connecting the origin with the vector resultant position, or a vector extending from (0, 0) to (400, 300).

Resultant impedance vector depicts magnitude and phase angle.

In the parlance of rectangular coordinates like this, we use the following shorthand to represent this impedance picture:

Z = 400 + j300 Ω

To express complex impedance (Z) in rectangular form first state the value of the resistance (400) and tack on value of the reactance (+300) with the lowercase letter ‘j’ preceding it, as shown above. Consider the j as a special designator to indicate that the value following it is reactance.

The resultant vector in the rectangular coordinate system picture represents the series circuit’s complex impedance. We can express it in the rectangular shorthand above or we may convert to polar form notation. Notice that the resultant vector has a length that represents the magnitude of the impedance in ohms and it has an angle as measured counterclockwise from the horizontal resistance axis that represents the phase angle between voltage and current. In order to properly state the complex impedance of the circuit in polar form we must compute both the magnitude (length) and the angle.

Call upon some middle school math with the Pythagorean Theorem that works for all right triangles like the one resulting from our vector plots. The side opposite the right angle (90-degree angle) is always the hypotenuse, and it is always the longest side of the right triangle. This is the side depicting the magnitude of impedance. We will call that side ‘C’. The other two sides we will dub ‘A’ and ‘B’. The theorem states, as I’m sure you’ll now remember…

A 2 + B 2 = C 2

You know the values of sides A and B from the resistance and reactance that you plotted, so you can solve this problem for side C by a little algebraic rearranging of the equation to get

Impedance vector magnitude calculation and phase angle calculation.

Plug in the values of A and B to solve as

This means the magnitude of the impedance for the circuit is 500-Ω.

Computing the phase angle is a little headier, requiring some very basic trigonometry. But it’s really quite simple. We’ll use the trigonometry concept of the tangent that relates the angle in question to the two sides of the triangle we plotted as vectors for resistance and reactance. Specifically, we use the inverse of the tangent, or “arctangent.” (This is sometimes depicted on calculators as tan -1 .)

First, we compute the value of the tangent of the phase angle as the “opposite side over the adjacent side.” The side opposite the desired angle is the side we plotted as inductive reactance, equal to 300-Ω. The side adjacent to the desired angle (and that is not the hypotenuse side) is the vector we plotted for resistance, equal to 400-Ω. Thus,

Tangent of Phase Angle = 300 / 400 (the fraction: reactance / resistance).
Tangent of Phase Angle = 0.75

Now we may determine the angle in degrees by taking the inverse tangent, or arctangent, of 0.75. On most calculators with trigonometric functions this is a “shift” key followed by the “tan” key. (Be sure “degrees” mode is selected, and not “radians.”)

Phase Angle = 37 degrees

We may now state the complex impedance (Z) of the circuit in polar form as 500-Ω at 37 degrees. Since this phase angle is due to inductive reactance we know that the voltage leads the current by 37 degrees. We can also recognize this inductive case because the angle is a positive value. Reflecting back to the voltage-current waveform relationship diagrams we used in Part 1, the 37 degree phase angle appears as follows:

Voltage leads the current by 37 degrees, indicated by the phase angle calculation for
Z = 400 + j300 Ω

The polar form of impedance states the magnitude in ohms and the phase angle in degrees.

Now let’s consider a capacitive reactance and resistance series circuit case. It is very similar to the inductive reactance case.

Q. What is the impedance of the circuit consisting of a 300-Ω resistor in series with a capacitor that has 400-Ω of reactance?

Again, we construct a vector diagram to help us keep straight the scenario. A 300-Ω resistance is plotted as a vector from the origin along the resistance axis. Then we plot the 400-Ω capacitive reactance beginning at the head of the resistance vector.

But this time we plot the reactance vector downward instead of upward. By standard convention all capacitive reactances are indicated in the –Y direction and with negative phase angles. In rectangular form this scenario is:

Z = 300 – j400 Ω

Once we connect the resultant vector from the origin to the head of the reactance vector we again have a magnitude and phase angle to compute to convert to polar form.

Vector plot of resistance and capacitive reactance, and resultant impedance vector.

The magnitude is calculated with the same method as before, only this time there is a negative value (-400) to include.

Again we have an impedance of magnitude 500-Ω. However, the phase angle will differ…

Tangent of Phase Angle = -400 / 300
Tangent of Phase Angle = -1.333

Again using the arctangent function we find:

Phase Angle = -53 degrees

Thus, Z = 500-Ω at -53 degrees is the polar form definition of this complex impedance. This means that the current leads the voltage by 53 degrees (ICE), and the reactance must be capacitive.

In a rectangular coordinate plane inductive reactance is plotted in the positive Y direction and capacitive reactance is plotted in the negative Y direction, and this is indicated by the sign of the reactance part (j) of the rectangular form notation or the sign of the phase angle in polar form notation.

How about the scenario in which the series circuit contains resistance (R) and both inductive (L) and capacitive (C) reactance, the so-called RLC series circuit? One more example to illustrate the RLC case:

Q. What is the impedance of the circuit consisting of a 4Ω resistor in series with an inductor with 4Ω of reactance and a capacitor with 1Ω of reactance?

We can again start with the rectangular coordinates by plotting the resistance vector of 4Ω.

However, we must compute a single reactance value to plot in the vertical direction. This is where the negation of inductive and capacitive reactances comes into play. You may simply subtract the capacitive reactance from the inductive reactance and plot the result, either positive (up, inductive) or negative (down, capacitive). You may also think graphically of plotting the inductive reactance value up from the head of the resistance vector and then plotting the capacitive reactance value down from the head of the inductive reactance vector.

Inductive and capacitive reactances offset one another on the vertical axis.

In this example the result of the offsetting reactances is: X = 4Ω – 1Ω, or X = 3Ω. This is a net inductive reactance (a positive value) and we should complete the vector diagram with a vector to the resultant point of (4, 3). The rectangular form notation here is:

Considering the resultant impedance vector, we may calculate its magnitude and phase angle just as before for the polar form.


Arctan (3/4) = 37 degrees (phase angle)

Z = 5Ω at 37 degrees.

With the series circuit impedance under your belt, you’re ready to consider the twists that come with parallel circuits.

Parallel Circuit Impedance: We will tackle a couple of parallel circuit examples, but first we must introduce the concept of admittance. Admittance is the inverse of impedance, and you may think of it as a measure of how easily a circuit will allow current to flow.

Consider a capacitive circuit in which AC of high frequency is readily passed (low impedance) and where AC of low frequency experiences high impedance. The admittance measure for the circuit would be exactly the opposite – the admittance of high frequencies is great in value, and the admittance of low frequencies is small in value.

Admittance is designated with ‘Y’, and it may be computed as Y = 1/Z. The unit of admittance is siemens (S).

Similarly, there are component inverse measures for resistance and reactance, each in units of siemens. The inverse of resistance is called conductivity (G), computed as G = 1/R. The inverse of reactance (X) is called susceptance (B), and B = 1/X.

Admittance (Y) is the inverse of impedance. Y=1/Z
Conductivity (G) is the inverse of resistance. G=1/R
Susceptance (B) is the inverse of reactance. B=1/X

These inverse measures, called admittances generally, come in handy with parallel circuits. Why? Admittances in parallel add together simply. So, to determine the impedance of a parallel circuit we may perform these steps:

  1. Invert the values of resistance and reactance to conductivity and susceptance
  2. Add these admittances together
  3. Revert the summed values back to impedance

Voila! Simple! Well, there is one nuance regarding the phase angle or the rectangular form ‘j’ part. Any time you invert a reactance value the sign of the angle (the sign of the j) flips to the opposite sign. That is, + becomes –, or – becomes + in the course of any inverting or reverting calculations between reactance and susceptance.

Let’s try an example to keep this clear.

Q. What is the impedance of the circuit consisting of a 300-Ω resistor in parallel with an inductor that has 400-Ω of reactance?

First: Convert impedances to admittances.

G = 1/R [Conductivity is the inverse of resistance]
G = 1/300-Ω
G = 0.0033 S

BL = 1/XL [Susceptance is the inverse of reactance]
BL = 1/j400 [Reactance should include the j, positive or negative]
BL = –j0.0025 [When inverting reactance, reverse the j sign]

Second: Add together the computed admittances above.

Y = 0.0033 – j0.0025 S

Third: Compute the admittance(Y) in polar form using the same method as for impedance.

Angle Y = Arctan (-0.0025 / 0.0033)
Angle Y = -37 deg.

Y = 0.00414 at -37 deg S

Fourth: Revert the admittance (Y) back to impedance.

Z = 1/Y
Z = 1/0.00414 at – (-37 deg) [Flip the sign of the angle]

Z = 240 at 37 deg Ω

And there you have it! You can see how the same technique will work for a resistor and capacitor in parallel, only the sign of j or the angle will be the opposite of the parallel inductor example above.

Further, in more elaborate cases where multiple series components are arranged in parallel with other series components, use the series computation method to get a total impedance for each of the series component sets, and then combine series results by the parallel method.

Summary Rules for Computations

  1. Series impedances add together.
  2. Inductive reactance and capacitive reactance cancel or offset one another with simple subtraction.
  3. Admittance is the inverse, or reciprocal, of impedance. Y=1/Z
  4. Parallel admittances add together.
  5. The sign of j or the sign of the phase angle reverses with each conversion between impedance and admittance.

Impedance Matching Wrap-Up

While we won’t go into great detail on the nuances of impedance matching, you are probably aware that impedance matching is very important for getting the most out of your transmitter-antenna system. Impedance mismatches in a transmission line cause reflections of power that reduce the effective power transfer. You want your transmitter, feed line, and antenna feed point to be closely matched in impedance to avoid high SWR values that indicate the presence of such reflections.

You may recognize now that impedance matching must involve more than just ensuring that the magnitude of impedance is closely matched. Yes, in most transmitters and coaxial cable-based antenna systems we use 50-Ω impedance, and we seek an antenna feed point impedance near that magnitude. But impedance matching also involves the phase angle, or the reactance j part of the impedance. Ideally, we would like the feed point impedance at the antenna to be mostly resistive and have little reactive component to it. That is, impedance with a small or zero value of j is easiest to match. Matching is simpler if there is little or no phase angle difference to wrangle with.

We’ll finish up the discussion with one power transfer principle that may be grasped with the nature of complex impedance now firmly in mind. When the output impedance of a power source (the transmitter) has a significant reactive component (a large j part indicating a phase angle difference), the maximum possible power is delivered to the load (the antenna) if the impedance of the load is equal to the complex conjugate of the power source impedance. What is a complex conjugate, you ask?

Maximum possible power is transferred to a load if the impedances of the source and load are complex conjugates.

A complex conjugate is a pair of numbers, each like the form of the complex impedance rectangular notation, with identical values but opposite signs for the j part. For example:

Z = 53 + j12 Ω

The complex conjugate of this impedance would be

Z = 53 – j12 Ω

Impedance matching devices, such as so-called antenna tuners, may use matching networks of capacitors and inductors to perform complex conjugate impedance matching to aid power transfer. You may have intuited that the complex conjugates provide a matching compensation for phase angle differences, optimizing power transfer for the particular impedance conditions.

Complex impedance is one of the most difficult concepts of radio science to wrap you mind around. I hope our discussion in Parts 1, 2, and 3 have helped you get a better grasp of how complex impedance works and why it is important to electrical and RF systems. Good luck with your studies! 73.

Biology Midterm exam questions

The Archaea: Prokaryotic, unicellular organisms, Lack a membrane-bounded nucleus, Reproduce asexually many are autotrophic by chemosynthesis some are heterotrophic by absorption, unique rRNA base sequence, Distinctive plasma membrane and cell wall chemistry

A compound is a substance consisting of two or more different elements combined in a fixed ratio.

Fluoride is added to the human diet to reduce tooth decay it is added to drinking water and dental products.

An electron is a subatomic particle with a single negative charge.

neutron is electrically neutral. If an atom were the size of a baseball stadium, the nucleus would be the size of a fly in the center field, and the electrons would be like two tiny gnats buzzing around the stadium.

Electrons move around the nucleus only at certain energy levels, called electron shells.

It is the number of electrons in the outermost shell, called the valence shell, that determines the chemical properties of an atom.

In polar covalent bonding, the pulling of shared, negatively charged electrons closer to the more electronegative atom makes that atom partially negative and the other atom partially positive.

When the attraction of two ions with opposite charges holds ions together, it is called an ionic bond.

Starting materials are the reactants and products are the materials resulting from the chemical reaction.

Adhesion- The attraction between different kinds of molecules.

Temperature--A measure of the intensity of heat in degrees, reflecting the average kinetic energy of molecules

Solvent--The dissolving agent of a solution. Water is the most versatile solvent known.

Hydrocarbons: compounds composed of only carbon and hydrogen

Carbon skeleton: A carbon skeleton is a chain of carbon atoms that can differ in length and be straight, branched, or arranged in rings.

These five groups are polar, so compounds containing them are typically hydrophilic (water-loving) and soluble in water.

•We will consider three types of lipids:
1. fats,
2. phospholipids, and

•A fat is a large lipid made from two kinds of smaller molecules:
•glycerol and
•fatty acids.

•A fatty acid can link to glycerol by a dehydration reaction.
•A fat contains one glycerol linked to three fatty acids.
•Fats are often called triglycerides because of their structure.
-saturated and unsaturated (shown by hydrogen bond that bends the fatty acid)

•very diverse, with tens of thousands of different proteins, each with a specific structure and function, in the human body.

•Proteins are composed of different arrangements of a common set of just 20 amino acid monomers.
•serve as catalysts and

•regulate virtually all chemical reactions within cells.

•Other types of proteins include
•transport proteins embedded in cell membranes, which move sugar molecules and other nutrients into your cells,
•defensive proteins, such as antibodies of the immune system,
•signal proteins such as many hormones and other chemical messengers that help coordinate body activities,
•Other types of proteins include (continued)

receptor proteins, built into cell membranes, which receive and transmit signals into your cells,

•contractile proteins found within muscle cells,

•structural proteins such as collagen, which form the long, strong fibers of connective tissues, and

•A polypeptide chain contains hundreds, or thousands of amino acids linked by peptide bonds.

Scanning Electron Microscope (SEM) - Study detailed surface of cells. 100x better than LM. Coat surface of organism with gold, which kills organism

Transmission Electron Microscope (TEM) - Can study details of internal cell structure. Stains with atoms of heavy metals, which kills organism

Magnification - How much larger an organism is being projected

Cell's compartmentalization different localized environments so that multiple incompatible functions can go on inside the cell at the same time

Shape Round <Rectangular>
(irregular shape) <(fixed shape)>

Vacuole 1+ (small) <One, large central>
vacuoles <vacuole - takes up 90% of cell>

Centrioles Present in all <Only present in lower>
animal cells <plant forms>

Chloroplasts None <Present>
Cytoplasm Present <Present>

Reticulum> and Rough
Ribosomes Present <Present>
Mitochondria Present <Present>
Plastids Absent <Present>
Golgi Apparatus Present <Present>
Plasma Membrane Present <Yes +cell wall>

Nucleolus - Prominent structure of the nucleus where ribosomal RNA (rRNA) is synthesized according to instruction from the DNA.

Nuclear Envelope - A double bi-layer membrane that encloses the nucleus, controls the flow of materials in and out of nucleus

rRNA - forms the sub units of ribosomes.

-Free floating ribosomes are structurally identical but make proteins for use in the cytosol

Vesicles - Connects the endomembrane system sacs made of membrane that transfer membrane segments between them

Endoplasmic Reticulum - Largest component of the endomembrane system, it is an extensive network of flattened sacs and tubules. It divides the cell into functional departments

Smooth ER - synthesizes lipids and processes toxins

Rough ER - Takes instructions from mRNA to produces membrane, ribosomes on it's surface make membrane and secretory proteins

Golgi Apparatus - Stacks of flatten stacks act as a sorting department for products of the ER. Also serves as a shipping center to other organelles and cell's surface

Lysosomes - Membrane enclosed sac of digestive enzymes, also breaks down damaged organelles. Provides an acidic environment for enzymes and safely houses them from rest of cell

Vacuoles - large vesicles w/ a variety of functions like contracting. Plant cells contain a large central vacuole that stores molecules, wastes, and facilitates growth

Watch the video: Chapter 7 Section (February 2023).