The Immunology Problem Book - 300 Solved Problems in Immunology

In a nutshell:-

Master immunology with this comprehensive digital book featuring 300 solved problems covering innate, adaptive, and clinical immunity. Designed for undergraduate, premedical, and medical students, it offers both quantitative and conceptual practice to strengthen your understanding and exam performance.

Overview

The Immunology Problem Book is a quantitative and conceptual problem course built on one conviction: immunology cannot be memorized, only solved. Its 300 problems are distributed evenly across 15 chapters of 20 problems each, organized into four parts following the logic of an actual immune response rather than the history of the discipline. Every problem shares an identical five-part skeleton — a question-form heading, a Given block listing exactly what may be used, a numbered Solution showing every intermediate quantity, an Answer box, and an Interpretation paragraph explaining why the result matters.

The book targets upper-division undergraduate immunology, first-year graduate and professional coursework, premedical entrance examination preparation, and foundational science review for licensing examinations. No calculus is required. The mathematical toolkit is limited to logarithms, exponents, simple exponential decay, elementary probability, and proportional reasoning.

 Chapter 1: Cells, Tissues, and Organs

Opens with a patient whose lymphocyte percentage of 28% sits inside the reference range, masking an absolute count of 588 cells per µL — roughly a third of normal. Central lesson: percentages hide people; absolute numbers find them.

Core Concepts: Hematopoiesis and the two great lineages; stem cell self-renewal and multipotency; lineage marker table (CD34, CD33, CD14, CD19, CD3, CD4, CD8, CD56, glycophorin A); primary versus secondary lymphoid organs; the three-step trafficking handshake (L-selectin/PNAd rolling, CCR7/CCL21 activation, LFA-1/ICAM-1 arrest).

Case Study: An infant with cardiac anomaly, hypocalcemic seizures, absent thymic shadow, and CD3 count of 210/µL — all tracing to a single pharyngeal pouch defect.

Representative Problems: Absolute neutrophil count (5,460/µL); lymphopenia behind a normal percentage (588/µL); febrile neutropenia grading (180/µL); CD4 count from three measurements (296/µL); inverted CD4:CD8 ratio from CD8 expansion; lymph node residence time (14.3 hours); circulating lymphocyte pool (1 × 10¹⁰ cells, only 2% of total); daily marrow neutrophil output (5.94 × 10¹⁰ cells); thymic output at age 50 (22%); thoracic duct flux (2 × 10¹⁰ cells/day); marrow cellularity (1.3 × 10¹² cells); limiting-dilution stem cell frequency using the 37% Poisson landmark.

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 Chapter 2: Innate Recognition, Barriers, and Phagocyte Function

Opens with a child drowning in neutrophils who could not deliver a single one to the site of infection.

Core Concepts: Pattern recognition receptors as germline-encoded and identical in every cell of a type; receptor table (TLR2, TLR3, TLR4, TLR5, TLR7/8, TLR9, Dectin-1, NOD2, NLRP3, RIG-I, cGAS-STING); why nucleic acid receptors sit in endosomes; five stages of phagocytosis; the critical distinction between oxidase and myeloperoxidase defects; natural killer decision as the sum of activating and inhibitory inputs.

Representative Problems: Phagocytic index (3.2 bacteria/neutrophil); superoxide output (7.23 × 10⁹ molecules/cell); flat dihydrorhodamine response to phorbol indicating chronic granulomatous disease; percent specific lysis (33.6%) with subtraction of spontaneous release; lytic units (320 LU); local defensin concentration (36 µg/mL); opsonization enhancement (23-fold); CD18 deficiency localizing to firm arrest; interleukin-1 beta release (2.48 × 10⁴ molecules/macrophage); phagocyte clearance versus bacterial division threshold (break-even at 1.44 × 10⁶ organisms); chemotaxis index (8.0); identifying MyD88 as missing adaptor.

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 Chapter 3: Complement, Regulation, and Acute Phase Response

Opens with recurrent facial swelling unresponsive to antihistamines because the mediator was bradykinin, not histamine.

Core Concepts: Three pathways converging on one terminal sequence; the key asymmetry that only classical and lectin pathways consume C4; four functions of complement; REGULATION IS THE WHOLE STORY — three regulator failures producing three unrelated diseases (C1 inhibitor → hereditary angioedema; CD55/CD59 → paroxysmal nocturnal hemoglobinuria; factor H → atypical hemolytic uremic syndrome).

Representative Problems: CH50 endpoint by interpolation (51.4 units/mL); convertase output (541 C3b molecules); membrane attack complex C9 stoichiometry (16 molecules); anaphylatoxin potency ranking (C5a 100× C3a); 1,000-fold relative risk for neisserial disease in terminal deficiency; C3b saturation (78,540 molecules/bacterium); C-reactive protein kinetics (205 mg/L at 48 hours); von Krogh transformation (67.3 units/mL) showing linear interpolation overshoots by 59%; C4 gene copy number and lupus risk (odds ratio 2.85); amplification loop exhausting plasma C3 in 72 minutes.

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 Part II — Antigen Recognition and the Molecules of Immunity

 Chapter 4: Antigens, Epitopes, and Measurement of Binding

Opens with two laboratories reporting the same antibody in apparently different terms — reciprocals of each other.

Core Concepts: Affinity is not avidity; occupancy depends on concentration; the dissociation constant equals the free ligand concentration at half occupancy.

Representative Problems: Kd from equilibrium concentrations (4.0 nM); residence time (33.3 minutes); Scatchard plot reading (Kd 4.0 nM, Bmax 32 nM); fractional occupancy (75%); IgM avidity gain (10⁴-fold over single site); hapten-carrier principle; cross-reactivity energy penalty (170-fold weaker, 13.2 kJ/mol).

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 Part III — Lymphocyte Development and Adaptive Responses

 Chapter 5: Immunoglobulin Structure, Isotypes, and Effector Function

Opens with two curves — maternal IgG falling, infant production rising — crossing at five months, the valley when most children first get seriously ill.

Representative Problems: Isotype effector assignments; total IgG pool (80 g); surviving fraction after 28 days (39.7%); replacement dose (36 g every four weeks); papain versus pepsin fragments; maternal antibody blocking vaccination until 138 days; secretory IgA daily output (2.8 g); hinge length and complement activation; Fc receptor assignments; ADCC versus complement lysis controls; pentamer valence (10 structural, 5 functional); neutralizing titer (160); daily IgG synthesis (2.6 g/day, 38 mg/kg/day).

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 Chapter 6: Generating Receptor Diversity

Opens with an accounting problem: 20,000 genes cannot encode receptors for molecules that did not exist when the genes evolved.

Representative Problems: Heavy chain combinatorial diversity (6,000); both chains (1.92 × 10⁶); junctional diversity factor (3 × 10⁵, total 5.76 × 10¹¹); spacer rule; reading frame determination (out of frame); productive rearrangement probability (one third); allelic exclusion evidence; recombinase deficiency (T−B−NK+); radiosensitivity indicating Artemis defect; somatic hypermutation rate (10⁶× background); mutations per variable region (7); activation-induced cytidine deaminase deficiency; receptor editing; kappa:lambda ratio (12.0); spectratype interpretation; realized versus theoretical repertoire (4 × 10⁶ versus 5.76 × 10¹¹).

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 Chapter 7: Major Histocompatibility Complex and Antigen Presentation

Opens with the 1974 experiment showing killer cells recognize infected cells only on the same genetic background.

Representative Problems: Sibling match probability (25%); registry size for 95% confidence (74,892 donors); homozygote frequency (1.44%); 12 distinct presenting molecules; peptide length assignments; cytosolic protein to class I; phagocytosed protein to class II; cross-presentation; TAP defect; invariant chain and HLA-DM; peptide binding motif; restriction experiment; 10⁴ distinct peptides per cell; polygeny versus polymorphism; relative risk (12, absolute difference 0.55%); gluten sensitivity and DQ2/DQ8; bare lymphocyte syndrome type 2; superantigen recruitment (2 × 10⁴× more T cells); linkage disequilibrium (31× expected); class I stripping exposing natural killer targets.

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 Chapter 8: T Cell Development and Selection

Opens with the observation that the thymus kills almost everything it makes — 97% die because they were examined and found unsuitable.

Representative Problems: Developmental staging; beta selection; death by neglect; clonal deletion; survival fraction (3%); daily thymic export (1 × 10⁷, 0.003% of pool); AIRE deficiency; class II absence eliminating CD4 cells; ZAP-70 deficiency; CD4 versus CD8 lineage decision; gamma delta T cells; absent excision circles; thymic involution half-life (23 years); pre-receptor signaling; Notch instruction; thymic epithelial graft; cortical versus medullary selection; single affinity threshold; regulatory diversion; 80-fold expansion after beta selection.

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 Chapter 9: T Cell Activation and Effector Function

Opens with a naive T cell — perhaps 100 in a body of 300 billion — expanding to one in ten circulating CD8 cells within a week.

Representative Problems: Signal one without signal two producing anergy; CTLA-4 summation (net −29,700 units); precursor frequency (9.94 × 10⁻⁶); 37% shortcut limitations; helper subset assignments; opposite leprosy courses; Th17 deficiency; serial killing (5 targets/hour); granule versus death receptor; memory subset homing; tetramer frequency (1.05 × 10⁴ cells); dye dilution; EC50 (2.2 units/mL); calcineurin inhibition; anergy reversal; superantigen activation (21%, 2.08 × 10¹⁰ cells); checkpoint blockade selectivity; CD40 ligand bidirectional failure; synapse zones; expansion-contraction arithmetic (500-fold residual memory).

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 Chapter 10: B Cell Responses and Immunological Memory

Opens with 1918 influenza survivors still carrying neutralizing antibodies ninety years later.

Representative Problems: Helper-dependent versus independent antigens; linked recognition; primary versus secondary response curves (3.5× shorter lag, 300× higher peak); endpoint titer (1024); affinity rise (2,500-fold across three immunizations); germinal center selection stringency (0.1% survive); plasma cell secretion (1,998 molecules/second); serology limitations; avidity index (0.35); memory B cell frequency (9 × 10⁻⁵); conjugate vaccine rescue; prime-boost interval; maternal antibody blocking until 144 days; centroblast cycle time (4 divisions/day); follicular helper deficiency; cytokine-directed isotype selection; antibody persistence over decades; clonal burst arithmetic (4,096 progeny); spot assay (340 per million); original antigenic sin.

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 Chapter 11: Cytokines, Chemokines, and Tolerance

Opens with tumor necrosis factor killing tumors locally and patients systemically — dose and location decide.

Representative Problems: Cytokine family assignments; STAT pairings; common gamma chain deficiency; interleukin-6 pleiotropy consequences; EC50 (1.48 ng/mL) with 71% error from arithmetic interpolation; receptor occupancy (50%); chemokine gradient steepness (20% difference); interleukin-12/interferon gamma axis defects; FOXP3 deficiency; central versus peripheral tolerance; silencing mechanism discrimination; interleukin-10 versus transforming growth factor beta; cytokine surge (2.4 × 10³-fold); pleiotropy/redundancy/synergy/antagonism; decoy receptors; shared p40 subunit; molecular mimicry; oral tolerance; short-range cytokine action; regulatory T cell suppression (77%).

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 Part IV — Clinical Immunology and Applied Practice

 Chapter 12: Hypersensitivity and Autoimmunity

Opens with a milligram of peanut protein killing a sensitized person — lethality supplied entirely by the victim's own immune system.

Representative Problems: Hypersensitivity type classification; receptor cross-linking threshold (0.8% of receptors); skin test interpretation (6 mm net wheal); epinephrine dosing (0.22 mL of 1:1000); transfusion reaction timing; hemolytic disease of the newborn; serum sickness timing (day 10); Arthus reaction; tuberculin cutoffs by risk group; nickel as hapten; relative risk (50) with 95% of carriers unaffected; odds ratio (6.0); streptococcal molecular mimicry; epitope spreading; blocking versus stimulating receptor antibodies; complement consumption in lupus; immunotherapy mechanism; penicillin as hapten; celiac disease mechanism; predictive value (9% screening versus 86% referred).

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 Chapter 13: Immunodeficiency and Immune Evasion

Opens with the diagnostic trick: list the organisms before choosing tests.

 Chapter 14: Vaccines, Transplantation, and Tumor Immunology

Opens with three apparently unrelated problems that are the same problem: controlling the threshold between response and tolerance.

 Chapter 15: Immunological Methods and Assay Interpretation

Opens with the observation that most disagreements in immunology's history were arguments about assays rather than about biology.