# Sarah Carratt: Week 3

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## Instructions

1. Look up the terms and provide definitions. For each definition, three elements are required: you must quote a source, reference the source, and interpret the definition in your own words.
2. Construct differential equations that model the reactions. Be sure to define your state variables and rate constants. Please note that the symbolis used to denote arrows (reactions) in both directions.
3. Use the matlab code provided at my lionshare folder to study the simple reaction that we have studied in class. Plot the output, and save the plot as an image. Post the image on the wiki as the answer to the question. Set the parameters as follows:
1. [S0] = 1.0
2. [E0] = 0.2
3. [ES0] = 0.0
4. [P0] = 0.0
5. k1 = 2.0
6. k-1 = 0.0
7. k2 = 10

## Student Response

Sarah Carratt 01:54, 31 January 2011 (EST)

### Terminology

1. dynamical system: "a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space," meaning that a dynamical system is an equation that illustrates how a variable changes over time. [1]
2. law of mass action: "the law that states the following principle: the rate of a chemical reaction is directly proportional to the molecular concentrations of the reacting substances. A law stating that the intensity of a reaction is dependent on the degree of presence of the reactants responsible for the reaction." This means that this law describes the way the production of a product is dependent on how much substrate is available to react and generate the product. [2]
3. homeostasis: "the tendency of an organism or a cell to regulate its internal conditions, usually by a system of feedback controls, so as to stabilize health and functioning, regardless of the outside changing conditions," meaning that homeostasis is the term for the ability to maintain a good balance in an internal environment even as the external environment changes. [3]
4. equilibrium: "the condition in which all acting influences are balanced or canceled by equal opposing forces, resulting in a stable system," meaning that this is the point in time when a reaction stops or is completely balanced in the creation and use of a substance. [4]
5. oscillation: "fluctuation, variation, change back and forth;" meaning that during a reaction, oscillation would be seen in inconsistencies of production and the changing rates or outputs. [5]
6. autocatalysis: "a reaction in which one or more of the products formed acts to catalyze the reaction; beginning slowly, the rate of such a reaction rapidly increases." This describes a reaction that helps propel itself, being its own instigator. [6]

### Applying the Law of Mass Action

• A + BC
• A and B produce C.
• No backward reaction.
• Proportions accounted for by a constant (k1).
• d[A]/dt = (-k1)[A][B]
• d[B]/dt = (-k1)[A][B]
• d[C]/dt = (k1)[A][B]
• A + BC
• A and B produce C.
• C also produces A and B.
• Proportions accounted for by constants (k1, k-1) .
• d[A]/dt = (-k1)[A][B]+(k-1)[C]
• d[B]/dt = (-k1)[A][B]+ (k-1)[C]
• d[C]/dt = (k1)[A][B]
• A + B ↔ 2C
• A and B produce twice concentration of C as problem one.
• C produces half the concentration of A and B as problem one.
• Proportions accounted for by both constants (k1, k-1) and exponents.
• d[A]/dt = (k1)[B]+(k-1)[C]2
• d[B]/dt =(-k1)[A]+(k-1)[C]2
• d[C]/dt = ((k1)[A][B]+(-k-1)[C]2)1/2
• 2A + 3BC+D
• Twice the concentration of A and three times the concentration of B produce the same concentration of C as problem one.
• Twice the concentration of A and three times the concentration of B produce the new product D (in equal proportion with C) which is not seen in problem one.
• Proportions accounted for by both constants (k1, k-1) and exponents.
• d[A]/dt = ((k-1)[C][D])1/2+(-k1)[B]3/2[A]
• d[B]/dt =((k-1)[C][D])1/3+(-k1)[A]2/3[B]
• d[C]/dt = (k1)[A]2[B]3+(-k-1)[C][D]
• d[D]/dt =(k1)[A]2[B]3+(-k-1)[C][D]

### Simulating Reaction Kinetics

 Concentration/Time MM Comparison Programing 1: Catalysis Programing 2: Catalysis Driver Programing 3: Michaelis Menten Programing 3: Michaelis Menten Product