Quantitative biology I

This is an introductory course in the mathematical and computational methods useful to students of the life sciences. The course is not intended to recapitulate a full degree program in physics, mathematics or computer science. Rather, the goal is to provide hands-on training, so that the student can use already available techniques and canned software, even if they are not ready to develop new tools. The course is intended to be useful to students in a wide variety of disciplines, e.g., biochemistry, genetics, cellular biology, microbiology, physiology, systems biology and metabolomics.

This course falls within the Department of Biochemistry within the School of Biology.

Rough syllabus

The plan is to present the topics in the following order; the rationale is that each topic builds on those preceding it.

• Basic math
• Basic statistics
• Statistical correlations
• Curve fitting
• Noise and noise reduction
• Diffusion, estimates of hydrodynamic size and molecular weight
• Matrix methods, computational efficiency
• Kinetics, linear and nonlinear
• Equilibrium; thermodynamics and statistical mechanics
• Electronic structure, spectroscopy and covalent bonds
• Non-covalent molecular forces
• Nuclear isotopes and NMR
• Resolution in various guises
• Fourier transforms
• Normal modes, molecular dynamics, Monte Carlo methods
• Computational predictions in molecular biology

Alternatively, these topics can be sorted into four major groups

• Group 1: Statistical topics
  • Basic statistics, statistical correlations, curve fitting
  • Noise and noise reduction
  • Diffusion and hydrodynamic methods

• Group 2: Matrix methods and kinetics
  • Matrix methods, computational efficiency
  • Kinetics, linear and nonlinear
  • Equilibrium; thermodynamics and statistical mechanics

• Group 3: Chemical/physical topics
  • Electronic structure, spectroscopy, and covalent bonds
  • Non-covalent molecular forces
  • Nuclear isotopes and NMR

• Group 4: Mathematical and computational methods
  • Fourier transforms and linear differential equations
  • The concept of resolution
  • X-ray crystallography
  • Molecular dynamics, Monte Carlo methods, normal modes

It is anticipated that the full curriculum would correspond to two semester-long courses.

Detailed syllabus

This is an initial draft; the timings should not be taken seriously.

Week 1: Basic mathematics

• Daily lesson 1.1: Units; basic measurements: gel-box volume
• Daily lesson 1.2: Solution math:serial dilutions, colony-forming units
• Daily lesson 1.3: Calibration of a pipette
• Daily lesson 1.4: pH, pI; maleic/fumaric acids
• Daily lesson 1.5: linear, semilog and log-log plots; polar plots
• Daily lesson 1.6: asymptotic behavior; perturbations
• Daily lesson 1.7: powers of 10; Fermi problems

Week 2: Basic statistics

• Daily lesson 2.1: discrete vs. continuous stochastic variables
• Daily lesson 2.2: 1-dimensional statistical distributions; error bars vs. confidence limits
• Daily lesson 2.3:
• Daily lesson 2.4:
• Daily lesson 2.5:
• Daily lesson 2.6:
• Daily lesson 2.7:

Week 3:

• Daily lesson 3.1:
• Daily lesson 3.2:
• Daily lesson 3.3:
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• Daily lesson 3.5:
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• Daily lesson 3.7:

Week 4:

• Daily lesson 4.1:
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Week 5:

• Daily lesson 5.1:
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Week 6:

• Daily lesson 6.1:
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Week 7:

• Daily lesson 7.1:
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Week 8:

• Daily lesson 8.1:
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Week 9:

• Daily lesson 9.1:
• Daily lesson 9.2:
• Daily lesson 9.3:
• Daily lesson 9.4:
• Daily lesson 9.5:
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Week 10:

• Daily lesson 10.1:
• Daily lesson 10.2:
• Daily lesson 10.3:
• Daily lesson 10.4:
• Daily lesson 10.5:
• Daily lesson 10.6:
• Daily lesson 10.7:

Instructors

• Prof. Bill Wedemeyer, from Michigan State University