Document describes the second version of the morbidostat device from Osterman Lab. Software was implemented by DIVO Systems.

The original morbidostat algorithm was proven to drive evolution of antibiotic resistance in bacteria in effective and robust way. However, we decided to add flexibility in the control software to address two main issues of the “original” morbidostat approach that was implemented in the previous version of the morbidostat device:

1. The “original” approach is comparing growth rate with dilution rate. However, if a drug has a delay in action this method to control culture density can lead towards excessive addition of the drug and results in the crash of the culture.

2. Drug addition to the reactor is defined by stock concentration as displacement volume and cycle time cannot be changed during the experiment without disruption in the work of algorithm. Often drug resistance evolve fast with large increase in MIC. To address changes in MIC an operator needs to change drug stock every time when culture stops responding to the drug.

3. Using concentration of the drug stock as the main factor defining scale of the drug administration brings an additional challenge. When using multiple reactors with various pace of evolution towards resistance some reactors could receive not enough drug and others – too much.

4. In the “original” approach culture is only limited by drug. If it will be resistant to the current maximum achievable drug concentration, then it will grow until it’s growth rate will match dilution rate. This can result in very high density of the culture.

To address the issue with control of the drug concentration in the dilutions we mix of two media (no-drug and drug-containing) each time when software decides to add a drug into reactor. Technically it was achieved by the following:

1. Tubing for each type of media for each reactor is controlled by a separate pinch valve. In our case 6 reactors have 2 inputs each resulting in 12 pinch valves.

2. If software decides to add drug it:

   1. based on the stock concentration and displacement volume calculates volume of drug and drug-free media that should be mixed;

   2. open pinch valve of the drug media tubing;

   3. engage pump for drug media (Pump 2)

   4. close pinch valve;

   5. open pinch valve of the drug-free media tubing;

   6. engage pump for drug-free media (Pump 1);

   7. close pinch valve.

Example:

We usually using 20% displacement volume from 20mL reactor volume which is 4mL. We trust our pumps to administer 400uL volume (10% from displacement volume). If we want to make 1xMIC in the reactor with one dilution we can setup the software to add 400uL of drug media and 3600uL of drug-free media. Then in the stock we can keep 0.4 * C_pump2 / 20 = 1xMIC => C_pump2=50xMIC. Therefore, we can achieve up to 50xMIC in the reactor without changing media bottles. In the “original” setup 50xMIC bottle will cause 10xMIC with one dilution. The concentration could be decreased with subsequent dilutions, but typical time between dilution in 15min will likely cause culture to crash.

The basis of the algorithm is similar to the “original” morbidostat approach:

• once in fixed time interval (usually 15min) do a dilution with fixed volume (usually 4mL).

• Choose mode of action based on the culture optical density (OD) (Figure 1). For this change we propose three thresholds:

  • Lower threshold (LT)

  • Drug threshold (DT)

  • Upper threshold (UT)

Figure 1. Comparison of modes of action allocation in three implementations of morbidostat approach: 1. “original” morbidostat approach described by Toprak et. al. uses one threshold: below this threshold software uses only drug-free media, above – choses between drug (id growth rate is greater than dilution rate) and no-drug media (if growth rate is lower than dilution rate); 2. first implementation of morbidostat in the Osterman Lab added additional threshold where low-density culture diluted with an extended time between dilutions (usually 60min); 3. the novel algorithm (see in text below).

These thresholds provide 4 modes of action for morbidostat (Figure 1):

1. Culture OD < LT: Culture is diluted with fresh no-drug media using prolonged cycle time (TBL – time between dilutions below lower threshold). The aims of this mode:

   1. prevent culture washout if will crash after antibiotic exposure;

   2. support culture growth in the lag phase in the beginning of the experiment.

2. LT≤ Culture OD < DT: Culture is diluted with fresh no-drug media using standard cycle time (TAL – time between dilutions above lower threshold). The aim of this mode is:

   1. wash culture from the drug;

   2. restore culture growth rate.

3. DT≤ Culture OD < UT: Culture is diluted with drug or with no-drug media based on the culture behavior (see below). The mode:

   1. keeps selection pressure for evolution of resistance.

4. UT≤ Culture OD: Culture is forbidden to grow above UT.

   1. If culture reaches UT it will be diluted with short dilutions until Culture OD ≤ DT.

   2. After culture reaches UT algorithm considers that the current level of drug is insufficient to control growth. It increases drug concentration in dilutions until it become equivalent to concentration in the stock.

In the drug mode software decides if it should increase of reduce drug concentration in the culture. The general idea is to keep culture OD by drug concentration. For this purpose the “original” algorithm compares OD before it makes a dilutions (Figure 2). If ∆OD > 0 than growth rate is greater than dilution rate and “original” algorithm added drug, otherwise it added fresh media to support growth and decrease drug concentration. From our experience we see that this approach misses much of signal from the culture behavior as for a lot of drugs the culture response is delayed and gradual. Therefore, the main idea to utilize changes in growth rate as a primary signal for drug administration.

Figure 2. Comparison of the drug administration algorithms. At the end of the current time interval (TAL) algorithm decides what media it should add to the culture. The “original” looks on the difference between last OD measurements of the current and last intervals (∆OD); The novel algorithm works with the logic explained below.

The following logic was implemented:

if (rate₂ > rate₁ + (AvgOD₂ > AvgOD₁ ? Eur : Euf])):

  dilute with drug (mixture of Pump1 and Pump2)

if (AvgOD₂ > AvgOD₁ + Eod):

  dilute alternating drug (mixture) and no-drug media

else:

  dilute with no-drug media

where:

AvgOD₂ – average OD on the current interval between dilutions;

AvgOD₁ – average OD on the previous interval;

AvgOD₀ – average OD on the two intervals before;

rate₂ = AvgOD₂ - AvgOD₁ – proxy for growth rate determination in the current interval;

rate₁ = AvgOD₁ – AvgOD₀ – proxy for growth rate determination for previous interval;

E_ur – bias coefficient if culture increase OD;

E_uf – bias coefficient if culture decrease OD;

E_od – bias coefficient for comparison AvgOD₁ and AvgOD₂.

Examples:

For next three examples we suppose that bias coefficients are equal to zero.

1. Culture is growing with acceleration (Figure 3)

Figure 3. Culture growth with acceleration.

rate₂ > rate₁ => the first condition in the algorithm logic is true.

Software signals to add mixture of drug and no-drug media.

2. Culture grows, but decelerates (Figure 4)

Figure 4. The culture still growing, but drug started to work, and growth rate decreased.

rate₂ < rate₁ => the first condition is false, go to the second conditions.

AvgOD₂ > AvgOD₁ => the second condition is true.

Software starts alternating drug and no-drug mode. In setup user can define the length of the sequence X. Sequence is built by one drug dilution and X-1 no-drug dilutions. If the previous dilution was a drug dilution, then the software will do X-1 no-drug dilutions and then add drug. If the last dilution was no-drug dilution, then otherwise one drug dilution will be added following by X-1 no-drug dilutions. For example, if X=3 and previous dilution was drug dilution, then the following sequence of operations will happen: 1^st – no-drug dilution; 2^nd – no-drug dilution; 3^rd – drug dilution.

Note that each time algorithm still looks on the full condition logic and can break the alternating sequence.

3. Culture growth rate is lower than dilution rate (Figure 5)

Figure 5. Culture growth rate became low and culture OD is falling.

rate₂ < rate₁ => the first condition is false, go to the second conditions. Although rate₂ is greater by absolute value it will have a negative sign and therefore be lower than rate₁.

AvgOD₂ < AvgOD₁ => the second condition is false.

Software will administer no-drug media.

Figure 6. Borderline situations. Situations when decision logic is highly unstable. Three bias coefficients (E_ur, E_uf, E_od) were introduced to push morbidostat towards desired behavior. The general rule: coefficient greater than 0 leads towards more aggressive drug administration. Subplots numbered according text below.

Three bias coefficients were proposed to guide algorithm in borderline situations (Figure 6). Each borderline situation has high variance as even small errors in OD measurements can switch morbidostat behavior. Bias coefficients push morbidostat towards desired behavior.

1. What to do if rate₁ = rate₂?

The answer depends on the culture behavior:

1. If culture is growing faster than it is diluted (AvgOD₂ > AvgOD₁) – likely we want to add more drug.

We setup E_ur < 0 => = rate₂ > rate₁ + E_ur is true=> drug will be administered.

2. If culture is growing faster than it is diluted (AvgOD₂ > AvgOD₁), but we want to make drug administration less aggressive.

We setup E_ur > 0 => rate₂ > rate₁

• E_ur is false => AvgOD₂ > AvgOD₁ is true => drug will be administered in the alternating regime.

3. If culture is growing slower than it is diluted (AvgOD₂ < AvgOD₁) likely we will want to add no-drug media.

We setup E_uf > 0 => rate₂ > rate₁

• E_uf is false => AvgOD₂ > AvgOD₁ is false => no-drug media will be added.

2. What to do if AvgOD₂ = AvgOD₁?

1. If we want to support a culture and think that this situation is likely due to the errors in OD reading, but in reality OD is falling (the true AvgOD₂ = AvgOD₁ situation should handled by E_uf) => setup E_od > 0 => AvgOD₂ > AvgOD₁ + E_od is false => no-drug media will be added

2. If we want to be more aggressive and think that this situation is more likely due to plato situation => setup E_od < 0 => AvgOD₂ > AvgOD₁ + E_od is true => alternating regime is engaged. Additionally aggressiveness could be increased by shortening the sequence X (X=1 is equal to drug administration).

The software interface was built using MegunoLink Pro interface builder (https://www.megunolink.com/). The interface contains several panels that can be arranged as tabs, panes or separate windows:

1. OD plot panel (Figure 7)

2. Connection Manager (Figure 8)

3. Main Control (Figure 9)

4. Experiment Settings (Figure 10)

5. Message Monitor (Figure 11)

6. Debug (Figure 12)

7. Pumps Monitor (Figure 13)

8. Calibration (Figure 14)

9. Logs (Figure 15)

OD plot panel displays OD values received from reactors.

Figure 7. Optical Density plot panel. Contains: (1) OD plots; (2) the instrument menu that allow to move plots, zoom in/out, save plot data and clean plot space; (3) table of plot stats that allows to turn on/off display of the plot for particular reactor.

Figure 8. Connection Manager. Required for connection to Arduino.

Figure 9. Main Control. The panel contains main indicators and settings to start, pause or stop an experiment. The sub-panes description:

1. Manual interventions settings.

   1. Active – set active reactors (“green” checkbox) where experiment will be running.

   2. Set Concentrations – change current dilution concentrations for drug administration.

   3. Volume/Manual Dilution Concentration – setup volume that was sampled from the reactor and concentration of drug in the replacement media.

2. “OD Readings Only” button turns on OD readings without dilutions.

3. Morbidostat experiment control. “Start” button – start experiment. After start of the experiment switches with the “Stop” button. It stops OD readings and dilutions. “Pause” button – pause experiment (no dilutions of OD readings). The “Pause” button has the same action as the “Stop” button. “Init Params” checkbox overrides current dilution concentrations with concentrations “C” from the “Experimental Settings” panel and set current reactor concentrations as 0.

4. Cleaning mode. Dilutions are made for all selected reactors using dilution volume from the “Experiment settings” panel. There is no wait time between dilutions. “# of Cycles” set number of dilutions that each reactor will receive.

5. Interval between subsequent OD readings from a reactor.

6. Checkbox to turn on/off the Air pump.

7. During dilution Air pump is turned off. Air delay sets additional time of turned off air to avoid media displacement and allow better mixture.

8. Thermostat settings

   1. On/Off - checkbox to turn on/off thermostat.

   2. Current - current temperature in °C.

   3. Min/Max - minimum/maximum observed temperature.

9. Concentrations and Valves

   1. Dilution Concentration. Concentration of the drug in the dilution volume (e.g. 4mL).

   2. Valves. Green indicator - valve is open.

   3. Tube Concentration. Computed drug concentration in a reactor.

10. Heartbeat – indicate status of Arduino connection.

    1. Blinking indicator - Arduino is connected.

    2. Red indicator - Arduino is disconnected.

    3. Green stable indicator - The connection was broken.

11. Status of main morbidostat control equipment. If indicator is green – the equipment is engaged:

    1. P1 – Pump 1

    2. P2 – Pump 2

    3. Air – Air pump

    4. Heat – Heating element

Figure 10. Experiment Settings.

1. Main settings:

   1. LT – Lower OD threshold.

   2. DT – Drug OD threshold.

   3. UT – Upper OD threshold.

   4. TBL – Time between dilutions below lower threshold in minutes.

   5. TAL – Time above dilutions below lower threshold in minutes.

   6. dV – Dilution volume in mL.

   7. Initial C – Initial concentration in dilution volume. Abstract units. Should match C1 and C2 parameters,

2. Concentrations in bottles and reactor volume.

   1. C1 – Drug concentration in Pump 1 bottle. For case when it will contain drug.

   2. C2 – Drug concentration in Pump 2 bottle.

   3. V – reactor volume, mL.

3. Interval between dilutions for the case when culture reaches UT. The culture diluted with this interval (typical 2 minutes) until it reaches DT.

4. Advanced parameters:

   1. M – Current concentration multiplier. When culture reaches UT and dilution that should bring culture OD to the DT level started the current dilution concentration is multiplied by this number.

   2. X – Sequence length for alternating mode.

   3. Zone4 C – If we want to dilute culture with some fixed drug concentration after it will reach UT we can set this concentration here.

   4. Zone4 C Fixed – Checkbox that turns on dilution with Zone4 C concentration.

   5. E_od, E_ur, E_uf – Bias coefficients.

Figure 11. Message monitor. Log of all actions that were performed with morbidostat software. Also contains output that could be produced from the “Debug” panel.

Figure 12. Debug Panel. Contains checkboxes that turn on/off valves, pumps and heating element. These controls override morbidostat program. If a valve of other equipment was engaged by morbidostat program the checkbox is checked automatically. “Print Experiment Params” button prints table of the current experiment settings in the Message Monitor (Figure 11). “Print Run Status” prints table of current dilution concentration, current reactor concentration, last average OD, Zone (position of average OD relative to the OD thresholds) and mode (mode of morbidostat action in the current interval).

“Print OS Statistics” is used for software debug. “Factory Reset” resets Arduino to default parameters.

Figure 13. Pumps Monitor. Running log of pumps engagements. Each time when software initiate dilution the following information is written in this log:

• Tube – Name of reactor where dilution is initiated.

• TimeL – Time of Pump 1 work in milliseconds.

• TimeH – Time of Pump 2 work in milliseconds.

• State – what mode of action should be used for dilution decision:

  • 1 - No-drug growth support

  • 2 - No-drug

  • 3 - Drug

  • 4 - Forced dilution after culture reaches UT

• Mode – Mode of drug administration:

  • 0 – No drug

  • 1 – Drug

  • 2 – Alternation drug and no-drug

  • 3 – Forced dilution (typically the same as no-drug)

• OD – Average OD on the interval.

• TubeC – Drug concentration that will be achieved after dilution.

• C1 – Concentration in the Pump 1 bottle.

• C2 – Concentration in the Pump 2 bottle.

• LT – Current lower threshold.

• DT – Current drug threshold.

• UT – Current upper threshold.

Figure 14. Calibration Panel. To read OD from reactors we use photodiodes. Photodiodes produce output in voltage. To convert voltage (V) to OD we use the following equation OD = C * log(V) + V₀. The “C” and “V₀” coefficients are calculated from the linear regression OD ~ log(V) based on the measurements of calibration solutions.

Figure 15. Logs. Three tabs that specify output files for “OD measurements” log, “Pump Monitor” log and “Message Monitor” log.

Let’s imagine experiment with drug X that has MIC=1mg/L and we will use 6 reactors.

We made Pump 1 media as no-drug media and Pump 2 media containing 500xMIC=500mg/L.

We can specify thresholds LT = 0.1, DT = 0.2, UT = 0.6.

1. Check all checkboxes to activate all reactors on the Main Control panel.

2. After morbidostat reactors will be filled with media turn on Heat checkbox to warm optics.

3. Turn on “OD READING ONLY” and in about 20 minutes read zero OD readings.

4. On Experimental settings panel setup for each reactor:

   1. LT = zero + 0.1

   2. DT = zero + 0.2

   3. UT = zero + 0.6

   4. TBL = 60

   5. TAL = 15

   6. dV = 4

   7. Initial C = 50. In the current implementation of algorithm C is integer number and we need to use numbers proportional to the real concentrations). We want 5xMIC in dilution volume as we displace 20% which will result in 1xMIC after the first dilution.

5. Set:

   1. C1 = 0 (as we have no drug in the Pump 1 media)

   2. C2 = 500 (equivalent to 50mg/L)

   3. V = 20 (20mL of reactor volume)

6. For each reactor set advanced parameters:

   1. M = 2. When culture will reach UT the current dilution concentration “C” will be increased to 2*C (first time it will be 2 * 50 = 100).

   2. X = 3. Alternating mode sequence will contain one drug dilution and two no-drug dilutions.

   3. Zone4 C = 0 and “Zone4 C Fixed” unchecked. Forced dilutions after culture reach UT will be made with no drug.

   4. Eod = -0.01. The bias between alternating regime and no-drug regime will be towards alternating regime.

   5. Eur = -0.01. When culture will rise (average OD on the current interval will be greater than average OD on the previous interval) the bias between alternating regime and drug regime will be towards drug regime.

   6. Eur = 0.01. When culture will fall the bias between drug regime and no-drug regime will be towards no-drug regime.

7. Set log files paths. Enable “Insert time stamp” for each log (clock icon).

8. Turn on logging (icon with pencil and paper).

9. Before inoculation turn off “OD READINGS ONLY”.

10. After inoculation check “Init Params” box and click on the “Start” button on Main Control/Morbidostat panel.