Appendices
Appendix A: Plasmid Definitions
Supplementary Table A.1: Plasmid Definitions
Plasmid
pRH195
pRH196
pRS414
pRS424
Plasmid Definitions
Description
pRS414 PHXT7:XKS1:THXT7
pRS424 PHXT7:XKS1:THXT7
pBluescript II SK+, TRP1, CEN6, ARSH4 (low-copy vector)
pBluescript II SK+, TRP1, 2µ origin (high-copy vector)
Appendix B: Particle Swarm Fitting
In particle swarm analysis a set of random solutions is created and their
fitness objective functions are calculated. Each solution (or particle) is “aware” of
its personal best solution and of the best solution ever found by any particle.
Competing forces (one pulling towards the global best solution, one pulling
towards a particle’s personal best solution, and one pulling in a random direction)
pull on the particle and give it a “velocity.” Identifying appropriate weighting
factors for the competing forces is important to ensure that the heuristic fully
searches the solution space in a timely manner. The parameters utilized in this
particle swarm are summarized in the table below.
Supplementary Table B.1: Particle Swarm Parameters
Parameter Name
Inertia
Global Best Weighting
Personal Best Weighting
Entropy
Abbreviation Parameter Value
I
0.75
GBW
0.1 ∗ 1.03𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
PBW
0.2 ∗ 0.98𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
E
±10% 𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑉𝑉𝑉𝑉𝑉 ∗ 0.97𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
Velocity was calculated as in the equation below. New velocity (NV) is equal to
the sum of current velocity (CV) times a random amount (R 1-3 here represent
random values between 0 and 1) of inertia (I) plus a random fraction of the
distance between the current value of the parameter and the global and personal
best (GB and PB) positions seen for the parameter plus a random amount of
random velocity.
Supplementary Equation B.1: Particle Swarm Velocity Calculation
𝑁𝑁 = 𝑅1 ∗ 𝐶𝐶 ∗ 𝐼 + 𝑅 ∗ (𝐺𝐺 − 𝐶𝐶) ∗ 𝐺𝐺𝐺 + 𝑅2 ∗ (𝑃𝑃 − 𝐶𝐶) ∗ 𝑃𝑃𝑃 + 𝑅3 𝐸
Each particle’s unique velocity transports it (and its associated
parameters) to a new solution (unique set of variables) and the process is
repeated. Over several iterations the particles in the swarm should converge to
the global best solution. This process is diagramed in the flow chart below.
Supplementary Figure B.1: Particle Swarm Heuristic Flow Chart
Our particle swarm heuristic was run 8 total times with 7 of the 8 runs converging
on a similar minimal objective function (within 0.5% of the global best solution
identified). The convergence of best the best identified solution over the course of
each run is shown below. Here a lower optimization score represents a better fit.
Supplementary Figure B.2: Convergence of Eight Particle Swarm Runs
Particle Swarm Running Bests
145
144
Optimization Score
143
142
141
140
139
138
137
136
135
0
10
20
30
Heuristic Iteration
40
50
60