Prepared by: Adib Samin and Fatih Olmez

TITLE??? Leukocyte OverviewLeukocyte Chemotaxis(How they find bact? A:They move in the direction of increasing

chemoattractan...)Derivation of a simple model for directed motion

in 1DThe inflammatory Response(Story of leukocyte

moving in the tissue and ingesting bact.)Equations, BC, dimensionless forms and steady-

stateAssumptions and Approximations

Phase-plane Analysis

Simple Model for Directed Motion [TF,1987]

J c=v+ n+−v-n -

n+ x , t: Right moving cellsn-x , t: Left moving cells

v+ x , t:Velocity of right moving cellsv-x , t: Velocity of left moving cells

J c : Flux

Simple Model for Directed Motion [TF,1987]

n+

t=−

vn+ x

p -n -−p+ n+

n-

t=

vn- x

p+n+− p- n-

p+ : probability per unit time that a right-moving-cell changes directionp- : probability per unit time that a left-moving-cell changes direction

(aka turning rates)

Cell velocity should be a function of local conditions, so assume that v+ = v- = v.

Simple Model for Directed Motion [TF,1987]

J c t

−J cv

v t

=−J c p+ p-−v vc

x−vc p+− p - .

Differentiating the flux,

we find

J c= v+ n +− v - n -

Simple Model for Directed Motion [TF,1987]

J c t

−J cv

v t

=−J c p+ p-−v vc

x−vc p+− p -

Differentiating the flux,

we find

Simple Model for Directed Motion [TF,1987]

n+

t=−

vn+ x

p -n -−p+ n+

n-

t=

vn- x

p+n+− p- n-

p+ : probability per unit time that a right-moving-cell changes directionp- : probability per unit time that a left-moving-cell changes direction

(aka turning rates)

Cell velocity should be a function of local conditions, so assume that v+ = v- = v.

Why model leukocytes and inflammation?? (Motivation)1. The advances in immunology have lead to the

development of a variety of vaccines, diagnostic tests (ELISA)and numerous cancer medications.

2. To gain a better understanding of hypersensitivity and autoimmune diseases.

3. To also have a deeper insight into the transplant rejection process.

4. To develop a profound understanding of diseases arising from immune deficiencies.

5. To improve our comprehension of the process of inflammation (which is normally protective against injurious stimuli), and diseases caused by chronic inflammation such as rheumatoid arthritis, asthma, and hey fever.

Immune System overview

1.The innate immune system includes all mechanisms that protect the body in a NON-specific manner. The cells involved may include Natural Killers, Macrophages, Neutrophils and the complement..2. The adaptive immune system comprises Specialized cells. It is adaptive because the immune system, through exposure to specific antigens, prepares itself for similar future attacks.The cells involved in adaptive immunity include B- and T- lymphocytes.The active memory displayed by B- and T-cells allows for immunization to be effective against future attacks from a specific antigen.

Leukocyte overviewLeukocytes are derived from the

hematopoietic stem cells in the bone marrow.They can be divided into two main

categories: Granulocytes and Agranulocytes.Granulocytes (also clinically known as

polymorphonuclear leukocytes or PMNs): are leukocytes characterized by the presence of distinctly staining granules in their cytoplasm when viewed under light microscopy.

Leukocyte overview (continued)The granulocytes include three types of

leukocytes, namelythe neutrophils, basophils, and eosinophils.

The granulocytes and the Monocytes and the Macrophages act primarily through the process of phagocytosis.

The process of phagocytosis mainly describes the engulfment of particulates, followed by the formation of a phagosome and its degradation by combining with a lysosome.

Leukocyte overview (continued)Endocytosis can further be utilized by the

aforementioned cells.Similarly, endocytosis involves the absorption

of extracellular molecules utilizing a clarithin mediated pathway.

The granules in granulocytes contain enzymes which are effective in degrading endocytosed particles trapped in the endosomes.

Leukocyte overview (continued)Agranulocytes, on the other hand, lack the

granules in their cytoplasm. However, they do contain other granules which are mainly lysosomes.

Monocytes, Macrophages, and Lymphocytes fall under this category.

Granulocytes and monocytes and macrophages protect via phagocytosis while utilizing the mechanism of opsonization.

OpsonizationIn this process the antigens (molecules

recognized by the immune system) are coated with antibodies or other complement molecules.

Phagocytic cells (such as macrophages) express receptors that bind opsonin molecules.

With the antigen coated in these molecules, binding of the antigen to the phagocyte is greatly enhanced.

Most phagocytic binding cannot occur without opsonization of the antigen.

Granulocytes vs. Agranulocytes

A = Basophil B = Eosinophil C = Neutrophil D = Band neutrophil or Stab cell 630X

Leukocyte types and functions1. Neutrophils : They form about 62% of all

leukocytes. Their main targets are bacteria and fungi. They are further characterized by a multi-lobed nucleus.

2. Eosinophils: They form about (1-6%) of all leukocytes. They target parasites and contribute to the inflammatory response.

3. Basophils: <1% of all WBCs. They release histamine and contribute to the symptoms of allergy.

Leukocyte types and functions4. Lymphocytes: form about 25-30% of all

leukocytes. They include B-lymphocytes which release antibodies, and activate T-cells. They further include NK cells which mainly kill infected cells. T-cells also fall under this category and include the:

A. CD4+ T cells which activate and regulate T and B cells.

B. CD8+ T cells which kill virus infected and tumor cells.

C. Regulatory T-cells which basically prevent autoimmunity.

D. γδ T cells which have a distinct type of TCR on their surfaces.

Leukocyte types and functions5. Monocytes: They constitute about (2-10%)

of all leukocytes and migrate from the bloodstream into other tissues and differentiate into macrophages.

6. Macrophages: Their main role is phagocytosis of cellular debris and pathogens. Moreover, they contribute to the stimulation of lymphocytes in response to pathogens.

Some macrophages migrate into the tissues of the body to become permanently localized in those tissue. These leukocytes consequently are given specific names. Examples of this include the Kupffer cells in the liver or the microglia in the central nervous system

7.Dendritic cells: They are the messengers between adaptive and innate immunity and they activate T cells.

InflammationLocal reaction of living tissues to injury or

illness, including burns. Its major signs are heat, redness, swelling,

and pain.The process is triggered by the dilation of

nearby arterioles (small arteries), followed by the flushing the capillaries with blood from which fluid, plasma proteins, and leukocytes pass into the injured tissues, causing swelling as they attack the cause of injury.

The process of inflammation, both vascular and cellular

Inflammation –The good and the bad1. Allergies: (type 1 hypersenstivity). Asthma is

a good example, where the bronchi of patients are hypersensitive to certain triggers which cause inflammation and excessive mucus production.

2.Hypersensitivity (types 2,3,4,5): Type 5 corresponds to receptor-mediated autoimmune disease such as Myasthenia Gravis and Grave’s disease which have Immunoglobulins IgM and IgG and the complement as mediators.

3. Cancer: Inflammation produces the microenvironment conducive to the proliferation of cancerous cells.

4. Anaphylactic shock: a severe whole body allergic reaction triggered by antigen binding to the IgE receptor on mast cells…it leads to circulatory collapse and suffocation.

AND THE LIST GOES ON…….

Artery and Vein

1

23

4

5

6

7

8

1) Medium Artery (muscular artery)2) Medium Vein—reduced tunica media, inc adventitia thickness3) Internal Elastic Lamina4) Tunica Media (7)5) External Elastic Lamina—separates t media from adventitia6) Tunica Adventitia (8)

Artery

prominent internal elastic lamina (IEL) separating the tunica intima from the tunica media (TM) that is composed of smooth muscle cells and fine elastic fibers. There is usually a well-defined external elastic lamina (EEL) separating the tunica media from the collagen and thick elastic fibers of the tunica adventitia (TA).

Lymphocyte

Monocyte

Platelets

12-15m

6-15m

1.5-3.5m

Granules uniform and smooth, easily see nucleusSometimes bright red granules

Neutrophil

Eosinophil

Basophil

12-17m

9-12m

8-10m

Eosinophil

BasophilBasophil

Neutrophil

Extravasationis the movement of leukocytes out of the

circulatory system, towards the site of tissue damage or infection.

The steps involved in this process include:1. Chemo-attraction: resident macrophages

in the infected tissue release cytokines such as IL-1, TNF-α. IL-1 and TNF-α cause the endothelial cells of blood vessels near the site of infection to express cellular adhesion molecules(such as Selectins).

Circulating leukocytes are directed towards the site of infection bythe presence of chemokines.

Extravasation2. Rolling adhesion: ligands on the leukocytes

(such as Integrins) bind to Selectin molecules on the blood vessel, with small affinity. This causes the leukocytes to slow down and begin rolling along the inner surface of the vessel wall. During this rolling motion, bonds are continually formed and broken between Selectins and their ligands.

3. Tight adhesion: chemokines released by macrophages activate the rolling leukocytes and cause surface integrins to switch from the low-affinity state to a high-affinity state. This causes the leukocytes to come to a complete stop.

Extravasation4.Transmigration: Leukocytes change their

form and spread out over the endothelial cells. Then, they extend pseudopodia (temporary projections) and pass through gaps between endothelial cells. The leukocytes secrete proteases that degrade the basement membrane, allowing them to escape the blood vessel.

Following this and once in the infected tissue, the leukocytes are in the intercellular matrix and migrate according to chemotactic gradients.

Cytokines and ChemokinesCytokines: Any of a group of soluble proteins that

are released by a cell to send messages which are delivered to the same cell, an adjacent cell, or a distant cell. The cytokine binds to a specific receptor and causes a change in function or in development of the target cell. Cytokines are released by a cell population on contact with a specific antigen. Cytokines act as mediators in the formation of immune response.

Chemokines : are chemo-attractant cytokines. They are produced by macrophages stimulated by bacterial endotoxins, and control the nature and magnitude of cell infiltration in inflammation.

Interleukinsclass of proteins that are secreted mostly by

macrophages and T lymphocytes and induce growth and differentiation of lymphocytes and hematopoietic stem cells. Antigens promote the production of interleukins, which induce the generation of various types of lymphocytes.

Leukocyte motilityLeukocytes move by utilizing their

pseudopodal extensions through which they adhere to the tissue matrix.

In uniform chemical concentrations of chemical stimulus, their motion is a “persistent random walk” since leukocytes randomly switch their direction of motion.

The “persistence time” is defined as the average time between changes in direction. This is usually on the order of minutes and the speed of migration is on the order of 2-20µm/min

Leukocyte motilityLeukocytes determine the presence of an

attractants when they bind to the receptors on their surface.

When there exists a spatial gradient of attractants then there is also a spatial gradient in the concentration of bound receptors.

The side of the cell that experiences a higher concentration of attractants will have a higher concentration of occupied receptors.

Leukocyte motilityResearch has shown that leukocyte velocity is

a linearly increasing function of the logarithm of concentration over the range of concentrations 10-9M to 10-6M.

Moreover, it has been experimentally determined that the fraction of leukocytes that move toward higher attractant concentrations is dependent on the gradient in receptor occupancy via the expression:

Leukocyte motility

Wheref: is the fraction of cells moving towards

higher concentrations.Χ0: chemotactic sensitivity

Nb: is the number of bound cell receptors ( a function of a –the concentration of the chemo-attractant-) and a: is a function of (x).

Leukocyte motility

We can see from the previous equation that for very large, then f≈ 1.

For small gradients we can see that:

It was estimated that χ0 =2*10-5 cm/receptor

Mathematical Model Assumptions1. Bacteria diffuse and reproduce and are

destroyed upon contact with the leukocytes.2. The chemo-attractant is produced by

bacterial metabolism and diffuses.3. The leukocytes are chemo-tactically

attracted to the attractant and they die as they digest the bacteria.

Approximations made on the model1. Ignore bacterial diffusion and assume

bacterial invasion occurs at the skin surface.2. Assume the chemo-attractant diffusion is

significantly large.3.Leukocyte diffusion is considered large. Biologically speaking these are sound

approximations because airborne bacteria attach to the surface of the skin but they do not move much on the time scale of leukocyte and chemo-attractant motion.

References1. “the Immune system” Peter Parham,

Garland science, 2009.2. “Fundamental Immunology” William Paul

Lippincott, Williams and Wilkins, 2008.3. Leukocytes. James Keener, James Sneyd.

Mathematical physiology. Vol II: Systems Physiology, Chapter 16, 495-507.