This method has been published in BMC Microbiology, "Dynamic metabolic modelling of overproduced protein secretion in Streptomyces lividans using adaptive DFBA" 08-Feb-2019 DOI:https://doi.org/10.5281/zenodo.2560170
The paper gives an introductory view of the method, with examples of how to use it. We have been working on an R program to make using this method (as well as all other traditional analyses, like FBA, MTF, FVA, DFBA, etc...) trivial and will be publishing it as soon as possible. Sadly, the CoV crisis caught us with a long experience in CoV research and our interest had to shift to that line of work. If you are interested in using our automated program, please contact jrvalverde@cnb.csic.es.
ADFBA is a DFBA extension that allows you to control and steer a metabolic simulation with total freedom. In a traditional DFBA simulation you define a metabolic model, set up initial conditions and run the simulation.
In ADFBA you also define an initial metabolic model and conditions (metabolite concentrations and possibly exchange rates), but at any step during the simulation you can inspect the status of the simulation, querying concentration of any metabolite, values of any flux (not just exchange rates), and model configuration.
Just as you can query information on the fly, you can, at any and every step during the simulation introduce any arbitrary change in metabolite concentrations, flux rates or limits, or even the model itself.
Being able to change metabolite concentrations allows us to model fed-batch systems where metabolites are/may be added or removed at arbitrary points in time. E.g. giving pulses of a carbon source like glucose or removing/harvesting interesting or toxic products. Coupled with knowledge of the status of the system, we can attach these changes to current conditions, like, e.g. detect whenever glucose or pH falls below a given level (which we cannot predict in advance) and apply the changes desired to the medium (e.g. as having sensors in a production tank and adding more nutrients or removing producs/toxins when a suitable concentration is reached).
Being able to change the model allows us to simulate almost any physiological situation: say you are modeling a plant, knowing that at some times light will be switched off. Its metabolism should also switch off photosynthesis, but there is no way a metabolic model in DFBA knows this. With ADFBA we can detect when the night-time is reached and modify the limits of specific reactions in the model to activate/inactivate specific routes (and vice-versa to return to normal when light is restored). Or say that you are modeling response to fever or climate: environmental temperature will change and with it, metabolic rates should be increased or reduced correspondingly.
Coupled with sensors of time, concentration, etc, this allows us to model situations dependent on environment (like oxidative stress) or internal fluxes: we simply detect when a given metabolite of flux has surpassed a threshold and modify flux limits or any other aspect of the simulation as required.
We can even modify the model itself: let's say we want to know what would be the effect of interrupting a gene or modifying gene expression (e.g. because we have transcriptomic data) at a given point or in response to specific conditions: we just need to knock out or activate the corresponding genes/reactions. Or that we want to know what would happen if we added new capabilities to a growing or stable culture (e.g. we add a plasmid or vector carrying new genes): we just modify the model to add/remove reactions. Or the effect of progressively substituting a bacterial species by another. We can even define this progressively by changing limits for the new reactions slowly, increasing or reducing them through sucessive steps to simulate the spread of a vector or change in the population.
This has proven most useful (as shown in the paper) to simulate heterologous protein expression: TAT protein secretion is activated as a stress response, meaning that it cannot remain active all the time, it has to be activated only after the oxidative stress response is triggered at the end of the exponential phase. Similarly, SEC protein secretion is active during exponential growth, but becomes minor during stress conditions / static growth phases. You cannot activate SEC at the start of a simulation and leave it activated: it must be canceled at the end of exponential growth, when TAT (which was inactive) must in turn be activated. And this is not an all or nothing switch: it must be done progressively over several time steps.
To be able to do this, we need to be able to deal with two situations. One in which we know in advance the modifications to be made and when will they occur (for instance, day/night timetables or fever cycles, or replicating available experimental data), and one in which we do not know in advance and will need to act in response to specific environmental/model conditions whenever they occur.
We have provided two mechanisms to steer the simulation:
The first, easier and simpler one is to use tables of changes indicating the time at which the change should be applied and the new values, indicating concentrations or flux limits. This will be useful if you know in advance at which times changes happen and which changes are these (e.g. because you have experimental data that you want to model).
The second is more powerful but requires more work: it consists in providing an R callback function. Your functions will be called with all the information it needs to know the system status and will return new values for either metabolites, flux limits or even a new, modified model to continue the simulation. This may be used for fixed-time changes (just wait for the correct time and apply the changes) but also allows us to react in response to any change in the system.
The complexity of the situations to be modeled can be as large as you want. The trick is that, by using any of these methods, steering the simulation becomes trivial. Even answering to trends is easy: just save the last n values and compare at each step to detect a tendency.
As an example, we have (unpublished results) collected changes in metabolite concentrations over time in various steered simulations based on experimental data. One would expect the evolution of a given flux to be a function of the relative concentrations of environmental metabolites. For instance, glucose consumption would adapt to glucose concentration changes, which is something you can readily model in most current DFBA schemes, but it may also depend on the relative concentration of other metabolites: Streptomyces will prefer to use some amino acids over glucose if they are present in sufficient concentration, even if there is an excess of glucose.
For key fluxes (exchange or internal fluxes), we have collected their calculated value as environmental metabolite concentrations changed, as a function of all other metabolites, then we have tried to fit them statistically, eliminate the less significant variables and obtained a simplified formula that matched flux evolution in response to an ensemble of (indirectly related) environmental metabolite concentrations. We did also try several AI/ML methods to predict the evolution of given fluxes of interest in response to environmental conditions.
And then, we defined an R function that would, at each step, obtain the system conditions and substitute the flux values calculated by DFBA by the ones obtained with our curve fits or AI/ML models to see how well would the simulation using our predictions emulate the real system behaviour.
This means that at each step, our function would collect the chosen relevant concentrations (or conditions), make a prediction (using an statistical or an AI/ML model) on what the proper value should be, and substitute the FBA/MTF computed value by our predicted one.
Besides its academic interest (verifying the quality of simplified model predictions), this entangles for us a major advantage: we do not want to "know-in-advance" the magnitude and dependence of all changes in a system. That's too much work. This allows us to have the computer learn what changes are needed and when, and apply them for us.
As an example: we could try to hand-tune our predictions for day/light or fever cycle simulations until our runs match experimental data. Or we could use the experimental data to have the computer figure out how to tune the response to these situations and force them into the model automatically. Once you have a non-DFBA-predictable model of a dependence (say, of a flux on external metabolite concentrations) you would no longer need to measure experimentally the response to a new situation, you could theoretically use the model to force the appropriate response in the model).
For instance: in the above paper we found an individual instantaneous-time optimal solution using DFBA for the consumption of some metabolites (like Alanine, i.e. eat it all while you can), which contradicted evidence (the model would die after exhausting nutrients). Experimental evidence, instead showed that cells behave "suboptimally": they relase Alanine early in time (instead of the optimal consumption) which accumulates in the medium. When sugars are scarce, the cell enters the stationary phase and starts using the secreted Alanine, but now at a lower rate because it is not growing exponentially. A similar pattern applied to other metabolites. This allows it to survive longer at the expense of subotimal growth in the exponential phase.
This conduct is not mathematically, time-instantaneous optimal. It makes sense because a population of suboptimal cells would outlive an optimal population in times of scarcity and get selected by evolution. It also implies that there is no way a system searching for an optimal solution will ever reach that conclusion. But we could detect the dependence of alanine flux on the environment and our statistical/AI models knew that on exponential-phase medium, a suboptimal solution should be forced, and on an exhausted medium, alanine consumption should be activated to feed on the reserve built during the times of wealth.
This is not so uncommon: many organisms take a similar subotimal strategy. In times of abundance they store energy as fat (which is suboptimal since it consumes energy and resources that do not have any immediate benefit, may actually be counterproductive and reduce their chances of survival -think cardiopathies-, and may indeed never be needed), so that when the times of need come, they have a reserve to feed upon and enlarge their survival expectation. This means they won't multiply so fast in times of abundance, exponential growth, but will be able to last longer and their populations may outlast fast growers. This of course will only work if times of hardship happen, for otherwise, the fast growers will outgrow them and occupy the echological niche, displacing suboptimal energy savers. But, as we all know, times of hardship are not so uncommon, and a well-stricken balance may actually be a great plus. And it likely must be, because so many organisms follow this strategy.
There is, I suspect, a sociological/political/economical lesson to learn from all this (or so I am told),and indeed, I seem to vaguely remember there were lots of popular sayings related, but this is not the place to discuss it.
For now, suffice it to say that the R program we have been developing makes using these strategies even easier yet (and more intuitive). We hope to publish it as soon as our work on CoV allows us to round off all our development and prepare a publication.
You will also find here the banneR package (to print UNIX(TM)-like banners in R scripts, example data and an example driver script that can be used as a command line program to simplify adpative dynamic FBA calculations in most cases.
Please, read the Supplementary Materials to the paper to learn more about installing this software.
Basically: you need to install R, sybil, sybilDynFBA, one ODE solver (to choose among GLPK, CPLEX, CLP or LP-SOLVE) and its R binding (the corresponding glpkAPI, cplexAPI, clpAPI or lpSolveAPI).
Then, download ADFBA, unzip it, and install it using the R 'devtools' package (which you will need to install it until we have time to get it on CRAN).
A sample session follows (assuming that you have R installed and an ODE solver installed (which should be trivial on Linux using a package manager).
In Ubuntu, for instance, you could install the ODE solvers with
sudo apt install lp-solve liblpsolve-dev coinor-clp coinor-libclp-dev glpk-utils libglpk-dev
$ wget https://github.com/jrvalverde/AdaptiveDFBA/archive/master.zip
$ unzip master
$ cd AdaptiveDFBA-master
$ R
install.packages(c('devtools', 'sybil', 'sybilDynFBA', ‘glpkAPI’, ‘clpAPI’, ‘lpSolveAPI’), dep=T)
library(devtools)
install('adfba', dep=T)
library(adfba)
help(adaptiveDFBA)