A Simple Protein Synthesis Model - Clemson CECAS

Starting Calculus for Biologists

A Simple Protein Synthesis Model

James K. Peterson

Department of Biological Sciences and Department of Mathematical Sciences Clemson University

September 30, 2013

Starting Calculus for Biologists

Outline

1 A Simple Protein Synthesis Model 2 Sample Protein Models

Example One Example Two 3 The General Picture

Starting Calculus for Biologists

Abstract

This lecture is going to talk a lot a simple protein synthesis model.

Starting Calculus for Biologists A Simple Protein Synthesis Model

We can model protein synthesis very simply as follows: A signal S binds to the promoter of the gene that controls the construction of a protein. After binding, the nucleotides in the gene are transcribed into a messenger RNA fragment which is the complement of the original nucleotide chain. The messenger RNA fragment is sent to the ribosome where it is used to assemble the protein which is a string of amino acids. The signal S can thus be used to start and stop the transcription process.

Starting Calculus for Biologists A Simple Protein Synthesis Model

A mathematical model: Let P(t) denote the concentration of the protein in the cell's cytoplasm.

Growth

Decay

After a short period of time, usually milliseconds or less, protein transcription reaches full production at a constant rate of (millimoles/ cc). So we assume Pgrowth = .

There are enzymes that break apart proteins for reuse and as living cells grow their volume increases causing the protein's concentration to drop. Combine these two effects and assume an exponential decay model: Pdecay = -P where is a positive number.

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