Exploring Peptides and Processes through State-of-the-Art Modeling

Through computer modeling, we want to further explore the special Rare-Earth binding peptides we researched in our wetlab as well as the innovative MycoFlux process from our hardware project. With our molecular modeling we contribute to the field of metal-binding peptides by introducing the first molecular structures and dynamic simulations for the binding domains we worked with. Through explorative process modeling, we created a digital companion that helps communities to adapt and extend our bio-based recycling processes.

Peptide Molecular Dynamics


Molecular dynamic simulations enable us to develop a better understanding of peptide-ion interactions. They can help us to determine optimal working conditions of our candidate peptides used in the laboratory. On top of that, they can establish educated guesses for new peptide designs with enhanced binding properties. As binding affinity of peptides can be tested in the lab, modelling and lab results can be set side by side and therefore checked for consistency.

Goals and Methods

We envision to comprehend which exact sections of our peptide candidates are relevant to binding metal-ions. This can be accomplished with so-called contact-maps, which are obtainable by performing a molecular dynamic simulation with GROMACS.

These kinds of binding maps literally map which sections of the amino acid sequence contribute to binding, e.g., ions. This will establish a steppingstone towards new peptide designs.

Fig 1. | Peptide-folding (‘most standard tag’) over time.

To make our simulations accessible to future iGEM-Teams we were exclusively using open-source software. We made use of Google’s Alpha 2 to generate 3D-structure files from the amino acid sequences of our candidate peptides used in the lab. GROMACS was used to perform dynamic simulations of our peptides.

AlphaFold 2

There were no existent 3D-structure files of our candidate peptides through X-ray crystallography. However, for molecular dynamic simulation a 3D-structure file (pdb-files) is needed. To overcome this problem, we utilized Alpha Fold 2, an artificial intelligence-based tool. Although the entire software is open source, the full version of Alpha Fold 2 is hard to run on local computer systems due to the need of high computing capacities. Even running it on university computer clusters can be challenging, as the required libraries are of significant storage size.

Fig 2. | Visualized model of ‘most standard tag’ peptide, created with AlphaFold2.

For our purpose, Google’s Collab Fold is just as good. Collab Fold is an online Jupyter Notebook providing a trimmed-down version of Alpha Fold 2 where no local computing power is needed. For the peptide ‘most standard tag’ 1 in water, we achieved 78% accuracy which corresponds to a well model with good backbone prediction 2, 3. This accuracy is sufficient as we do an additional equilibration phase for our dynamic simulation anyway. The predicted peptide structure is visualized in Figure 1.


As GROMACS simulations are based on particle-particle Coulomb-interactions the most important choice for the simulation is the used force field. We chose the AMBER-ff99SB force field as it is working well with the chosen water model TIP3P. Both force field and water model are commonly used and established for short peptides. 4

Fig 3. | 100ns Equilibration for the ‘most standard tag’ peptide – root-mean-square deviation over time.

Before considering simulating the peptide-ion interaction the peptide must be equilibrated in the given environment. Equilibrating the peptide means finding, in best case, the global energy minimum. In that case we expect no excessive folding of the peptide anymore. We rather expect minor vibration and movement through the defined space. To quantify peptide movement regarding the entire peptide we look at the root-mean-square deviation of the individual distance between every amino acid in the given sequence. The results of our first equilibration are shown in figure 2. More detailed information on how the production run in GROMACS was done is presented in our tutorial that is part of our iGEM Contributions.

At around roughly 40ns we can clearly see the RMSD reaching a constant value except for some noise, indicating that our system is equilibrated. To verify that we found a global energy minimum, we repeated the equilibration phase multiple times so it can be assured that the found energy minimum is truly a global one and not a local one. With the VMD visualizer we can visualize our equilibration phase:


We were able to model a full dynamic system of our candidate peptides. This goes along with developing a deep understanding of the tools and setting up the infrastructure. Although we didn’t quite manage to model the system with rare earth element ions, we gained significant knowledge about GROMACS and its limitations. One of them being the fact, that GROMACS can’t truly model electrons with their respective orbitals but only the respective charges. We tried multiple approaches of trouble shooting, such as extensions like AlphaFill. Unfortunately, we didn’t quite get there, nonetheless we are confident that a solution can be found.

One possible approach for future projects could be to model the system with ions featuring large ion radiuses and thus resembling lanthanide ions. Lastly you could make use of contact maps literally mapping the parts of our amino acid sequence relevant to binding the lanthanide ions. These could be used to establish educated guesses for new peptide designs tested in the lab. By testing their binding affinity, one could put a feedback loop in place between the lab and model to further refine the simulation. However, there always will be the limitation of GROMACS not modelling the quantum mechanics of orbital physics which are important to the binding process. If not solved with other plugins, extensions or tools one might even consider a different software solution.

Process Simulation


Our MycoFlux bioremediation apparatus is an innovative system that combines many functions to study and deploy fungi-based synthetic biology. Specifically, two unit operations are combined in one device, making it a compact and adaptable system to scale-up fungal processes beyond the lab-scale.

These operations are: 1. the cultivation of (genetically modified) fungi in a tray-based system like in solid-state fermentation, and 2. the use of the generated biomass as a biosorption material to extract valuable resources (or other contaminants) from liquid sources. The extraction process itself can be further subdivided into a loading stage (binding ions from solution to the metal-binding peptides of the fungi) and into a concentration stage (redissolving the ions into a concentrated solution).

On our Hardware Page, we focused on the physical realization of our system and performing field-tests with a wild-type fungus.

Fig 4. | Our hardware solution MycoFlux that we want to model.

In this part, we explore the process operation and conditions through modeling. We want to set up systems of equations that can help us predict and optimize the performance of the MycoFlux. Thereby we also prepare a proof-of-concept of deploying a genetically modified fungus in the MycoFlux. Through modeling, we can “put the puzzle pieces” of our project together and work towards a digital twin of our process that helps communities to build, deploy and adapt sustainable synthetic biology to help in their daily lives. See how we worked towards a metal-binding GMO fungus on our Wetlab Page!

In short, this modeling does not serve do conclude specific process settings, but serves as an explorative system in which properties of the MycoFlux can be varied and further examined to assist future product and process development.

Model Structure

Fig 5. | Graphical model representation based on a device-connection-structure.

Rooted in systems theory, process models are built up from devices and connections. In a physical setting, devices may represent single phases, equilibrium stages, or aggregated subsystems. Connections describe the interrelations of devices such as mass and heat transfer. Additionally, relationships not directly rooted in physical relationships can be described by signal transformers (as devices) and signal connections.

We have developed a device-connection model for the MycoFlux as a reference point for our modeling and further adaptations of the system. The main devices of the model are the mycelium biomass that serves as a filter, the fluid to be filtered, and the dissolution fluid that redissolves the product into a concentrated solution.

All liquid flows are transported from the environment via a pump. Between the interacting mediums are heat and mass transfer flows. An overview of all connections can be found in the following table.

Enumeration and Description of the Connections
TABLE 1  Connections
1Dissolution Fluid from Pump to Environment
2Dissolution Fluid from Environment to Pump
3Filtered Fluid from Environment to Pump
4Filtered Fluid from Pump to Environment
5Dissolution Fluid from Inside to Pump
6Dissolution Fluid from Pump to Inside
7Filtered Fluid from Pump to Inside
8Filtered Fluid from Inside to Pump
9Mass Transfer of Target Components from Filter to Dissolution Fluid
10Mass Transfer of Target Components from Filtered Fluid to Filter
11Biomass Contamination to Box Chassis
12Evaporation Losses and Heat Transfer from Filtered Fluid to Environment
13Evaporation Losses and Heat Transfer from Dissolution Fluid to Environment
14Power Input to Pump

Model Assumptions

Several assumptions have already been made in the graphical description of the system. For example, we do not explicitly consider the air inside the apparatus, but consider it part of the environment. We also disregard heat transfer between fluid and mycelium and in the following restrict ourselves to the mass transfer phenomena. For now, we also disregard evaporation and energy balances. It could be interesting to extend the model to the influence of heat distribution on the biomass, but as we describe on the Hardware Page we assume that the tray-based system allows for sufficient cooling and also oxygen supply. Further, we also assume that the biomass stays within its confines of the trays and does not spread to the box chassis, as we have made several precautions against it on the hardware side. In theory, it could be interesting to assess this via real life data to assess the life time and sustainability of the employed building materials.

Now, for a principle proof of concept, we model the fluid to be filtered as a two-component system of carrier and target component. This, of course, does not correspond to the reality of a heterogeneous e-waste solution as other components could also be held back by the filter. However, the specificity of the Rare-Earth binding peptides on the fungal surface is very high, so in this model we only consider the adsorption of these components. We assume the convective flow to be in a steady-state and only consider the time-dependence of the mass transfer phenomena. In conclusion, we restrict ourselves to the main functionalities that we want to realize overall: mycelium growth and Rare-Earth extraction.

These functionalities, in real-life, are executed sequentially. The mycelium is grown as a biosorption material in the MycoFlux, assisted by a suite of sensors that measure and allow the user to control various parameters such as humidity or temperature. Then, the e-waste solution that will be filtered is introduced to bind the target components to the metal-binding peptides expressed in the fungi. After that, a dissolution agent redissolves the Rare-Earth ions into a concentrated solution, effectively filtering them off from the heterogeneous e-waste. To mimic that in our model, we execute the model equivalents of these phases also sequentially while saving the important data between the phases, e.g. how much the biomass is affected through the extraction process.

Fig 6. | The phases of the MycoFlux process: growth - adsorption - desorption - growth.

Model Equations

Our model undergoes three phases: Adsorption, biomass growth and desorption. These phases are separately modeled and then combined in series by the program (see Software and Simulation).

1. Adsorption Phase

The adsorption process is modelled by two mole balances. First, the amount of target components (index REE) in the filtered liquid is balances. Into this state flows the incoming dissolved target component from the pump and it leaves with a residual loading. Through the interactive with the metal-binding biomass, a adsorption modeled as a reaction takes place that removes the target component from the filtered liquid.

\begin{align*} \frac{dn_{REE}}{dt} &= \dot{N}_{in} \: X_{REE,in} - \dot{N}_{out} \: X_{REE} - R_{ad} \\ \\ REE &+ BS \overset{k_{ad}}{\rightarrow} B \\ R_{ad} &= k_{ad} \: c_{REE} \: n_{BS} \end{align*}

Secondly, the amount of bound binding places at the mycelium is balanced. The bound binding places are described by a reaction of target components with free binding sites, which is the adsorption kinetic. Therefore, the amount of bound sites increases with that kinetic applied over the surface of the mycelium. The number of binding sites is limited: the number of bound and free binding sites sum up to a finite value, i.e., the maximum adsorption capacity of the biomass which correlates to the surface expression of the metal-binding peptides.

\begin{align*} \frac{dn_{B}}{dt} &= R_{ad} \\ n_{BS} &= B_{\infty} - n_{B} \end{align*}

2. Desorption / Concentration Phase

Desorption function in reverse to the adsorption model. The dissolution agent does not contain any target components, so their number decreases with the outflow of the concentrated solution. The desorption kinetic functions in reverse to the adsorption by changing the kinetic parameters, e.g., through a shift in pH. Again, the number of overall binding sites is limited. \begin{align*} \frac{dn_{REE}}{dt} &= - \dot{N}_{out} \: X_{REE} + R_{de} \\ \\ B &\overset{k_{de}}{\rightarrow} REE + BS \\ R_{de} &= k_{de} \: c_{B} \\ \\ \frac{dn_{B}}{dt} &= - R_{de} \\ n_{BS} &= B_{\infty} - n_{B} \end{align*}

3. Mycelial Growth Phase

There are extensive methods to calculate the growth of filamentous fungi on solid substrates in three dimensions with respect to the mycelial geometry and growth strategy. Right now, we are only interested in the overall biomass of the fungus and its disturbance by the extraction phases.

\begin{align*} \frac{dX_{bio}}{dt} &= \mu \: X_{bio} \\ \frac{dS}{dt} &= - \frac{1}{Y_{XS}} \: \mu \: X_{bio} \\ \mu &= \mu_{max} \: \frac{S}{S+K} \end{align*}

For now, we describe the biomass growth through a simple Monod kinetic limited by the solid substrate available in the MycoFlux apparatus. What we want to explore through the model is the effect of biomass destruction by the extraction phases. We assume for the adsorption and desorption phase respectively a linear factor of biomass destruction caused by acidity, flushing out, or other unexpected effects with respect to time. For the growth period between different extraction phases, only the summed up biomass destruction is relevant as the initial condition of the growth simulation. It resolves to the biomass at the end of the previous growth phase minus the destruction that took place during the preceding extraction phases.

\begin{align*} X_{bio}(t=0) &= X_{bio}^{pre} - d_{ad} \: t_{end}^{ad} - d_{de} \: t_{end}^{de} \\ \end{align*}

Connecting the growth and extraction phases is the maximum capacity of the engineered fungi to bind the target component based on the cultivated biomass. We describe its relationship with the following formula and estimate the conversion factor by the binding efficiency from the wetlab experiments.

\begin{align*} B_{\infty} &= \theta_{\infty} \: X_{bio}^{pre} \end{align*}

Lab Data Integration

From the wetlab, we have an idea of how effective the binding peptides are at binding the Rare-Earth elements. We can use the ranges and uncertainties determined by the wetlab to perform sensitivity analysis with our model and feed back these information to the product development of the MycoFlux. In parallel, we use the geometric properties and design choices from the hardware construction as parameters in the model to match the real life process as closely as possible. Of course, the domain of these parameters can also be explored through simulation to inform and influence the development of the next hardware prototypes.

One of the most important values is the amount of Rare-Earth ions bound by a gram of biomass. Our lab experiments assessed a value of \( \theta_{\infty} = 0.064 \) µg(Nd)/µg(Yeast) which is in the range of comparable literature values and according to our experiment evaluation at the lower end of what could be potentially achieved with our technology.

The follow tables explain the variables and parameters that appear in the models. Variables are calculated by the model based on the DAE system. Especially interesting are the parameters: in the min/max columns we give numerical values that we estimated based on laboratory or hardware assessments.

Model Variables, Parameters and their Ranges
TABLE 2  Variables
NameDefinition Unit
\begin{equation} n_{REE} \end{equation}Amount of REE in Liquid in Tray mol
\begin{equation} n_{BS} \end{equation}Number of Unoccupied Binding Sites on Mycelium mol
\begin{equation} n_{B} \end{equation}Number of Occupied Binding Sites on Mycelium mol
\begin{equation} X_{REE} \end{equation}Load of REE on Filtered Solution mol/mol
\begin{equation} R_{ad} \end{equation}Adsorption Kinetic m^2
\begin{equation} R_{de} \end{equation}Desorption Kinetic m^2
\begin{equation} \dot{N}_{out} \end{equation}Flow Rate of Solution out of Tray mol/s
\begin{equation} \dot{N}_{in} \end{equation}Flow Rate of Solution into Tray mol/s
\begin{equation} n_{S} \end{equation}Amount of Filtered Solution in Tray mol
\begin{equation} V_{S} \end{equation}Volume of Filtered Solution in Tray m^3
\begin{equation} n_{D} \end{equation}Amount of Dissolution Fluid in Tray mol
\begin{equation} V_{D} \end{equation}Volume of Dissolution Fluid in Tray m^3
\begin{equation} c_{REE} \end{equation}Concentration of Target Component in Liquid Volume mol/m^3
\begin{equation} n_{prod} \end{equation}Amount of Target Component in Recovered Fluid after Extractionmol
\begin{equation} V_{prod} \end{equation}Volume of Recovered Fluid after Extractionm^3
\begin{equation} B_{\infty} \end{equation}Maximum Binding Capacity of Mycelium mol
\begin{equation} S \end{equation}Solid Substrate kg
\begin{equation} X_{bio} \end{equation}Biomass kg
\begin{equation} t_{end}^{ad} \end{equation}Total Duration of Last Adsorption Phase h
\begin{equation} t_{end}^{de} \end{equation}Total Duration of Last Desorption Phase h
\begin{equation} X_{bio}^{pre} \end{equation}Biomass at the End of Last Growth Phase kg
TABLE 3  Parameters
NameDefinition Min MaxUnitComment
\begin{equation} X_{REE,in} \end{equation}Incoming Load of REE on Solution mol/molMust be calculated by user given amount and composition of desired medium to be filtered
\begin{equation} \dot{V}_{in} \end{equation}Volumetric Flow Rate of Solution into Tray ~1200~1500L/hBased on the pump we used
\begin{equation} M_S \end{equation}Molecular Weight of Filtered Liquid ~15~30g/molEstimates from bioleaching
\begin{equation} \rho_S \end{equation}Density of Filtered Liquid ~0.9~1.2g/cm^3Estimates from bioleaching
\begin{equation} M_D \end{equation}Molecular Weight of Dissolution Fluid ~15~30g/molEstimate, to be examined further
\begin{equation} \rho_D \end{equation}Density of Dissolution Fluid ~0.9~1.2g/m^3Estimate, to be examined further
\begin{equation} V_{ad} \end{equation}Amount of Treated Solution0~25LStandard capacity of MycoFlux (without continuous drain)
\begin{equation} V_{de} \end{equation}Desired Amount of Concentrated Solution0~25LStandard capacity of MycoFlux (without continuous drain)
\begin{equation} V_{Tray} \end{equation}Volume of Extraction Space in MycoFlux 25~100LMycoFlux geometry can vary between single tray and multi tray operation mode
\begin{equation} \epsilon_{Tray} \end{equation}Average Porosity of Extraction Space ~20~50%The trays are about half filled with substrate and mycelium, assumed to be constant
\begin{equation} k_{ad} \end{equation}Adsorption Kinetic m^3/s/molFurther research needed, however the kinetic seems to be very fast
\begin{equation} k_{de} \end{equation}Desorption Kinetic 1/sFurther research needed, however the kinetic seems to be very fast
\begin{equation} n_{REE,bound} \end{equation}Bound Target Component at the Beginning of Desorption Phase molDetermined by previous adsorption step
\begin{equation} \theta_{\infty} \end{equation}Relationship between Biomass and Binding Capacity0.443~0.7mmol/gExperimental result from wetlab, estimated to be a lower bound from experimental design
\begin{equation} \mu_{max} \end{equation}Maximum Biomass Growth Rate~0.02~0.061/hRough estimate from literature, further research necessary
\begin{equation} K \end{equation}Monod Constant~0.3~0.5g/LRough estimate from literature, further research necessary
\begin{equation} d_{ad} \end{equation}Biomass Death Rate during Adsorption Phase~50~1000g/hEstimated based on hardware observations
\begin{equation} d_{de} \end{equation}Biomass Death Rate during Desorption Phase~50~1000g/hEstimated based on hardware observations
\begin{equation} \rho_{Sub} \end{equation}Density of Substrate~95~150kg/m^3Literature values for straw
\begin{equation} Y_{XS} \end{equation}Biomass from Substrate Yield~0.3~0.6g/gRough estimate from literature, further research necessary

With the described model equations and parameters, we arrive at the full model description that we can now implement in software.

Full Model Descriptions

1. Adsorption Phase

Balances: \begin{align*} \frac{dn_{REE}}{dt} &= \dot{N}_{in} \: X_{REE,in} - \dot{N}_{out} \: X_{REE} - R_{ad} \\ \frac{dn_{B}}{dt} &= R_{ad} \\ n_{BS} &= B_{\infty} - n_{B} \\ 0 &= \dot{N}_{in} - \dot{N}_{out} \\ \\ \frac{dV_{prod}}{dt} &= \dot{N}_{out} \: \frac{M_S}{\rho_S} \\ \frac{dn_{prod}}{dt} &= \dot{N}_{out} \: X_{REE} \end{align*}

Kinetics: \begin{align*} R_{ad} &= k_{ad} \: c_{REE} \: n_{BS} \end{align*} Constitutive Equations: \begin{align*} c_{REE} &= \frac{n_{REE}}{V_S} \\ X_{REE} &= \frac{n_{REE}}{n_S} \\ V_S &= n_S \: \frac{M_S}{\rho_S} \\ V_S &= \epsilon_{Tray} \: V_{Tray} \\ \dot{V}_{in} &= \dot{N}_{in} \: \frac{M_S}{\rho_S} \\ B_{\infty} &= \theta_{\infty} \: X_{bio}^{pre} \\ \end{align*} 2. Desorption / Concentration Phase

Balances: \begin{align*} \frac{dn_{REE}}{dt} &= - \dot{N}_{out} \: X_{REE} + R_{de} \\ \frac{dn_{B}}{dt} &= - R_{de} \\ n_{BS} &= B_{\infty} - n_{B} \\ 0 &= \dot{N}_{in} - \dot{N}_{out} \\ \\ \frac{dV_{prod}}{dt} &= \dot{N}_{out} \: \frac{M_D}{\rho_D} \\ \frac{dn_{prod}}{dt} &= \dot{N}_{out} \: X_{REE} \end{align*}

Kinetics: \begin{align*} R_{de} &= k_{de} \: n_{B} \\ \\ \end{align*} Constitutive Equations: \begin{align*} X_{REE} &= \frac{n_{REE}}{n_D} \\ V_D &= n_D \: \frac{M_D}{\rho_D} \\ V_D &= \epsilon_{Tray} \: V_{Tray} \\ \dot{V}_{in} &= \dot{N}_{in} \: \frac{M_D}{\rho_D} \\ B_{\infty} &= \theta_{\infty} \: X_{bio}^{pre} \\ \end{align*} Initial Conditions: \begin{align*} n_B(t=0) &= n_{REE,bound} \\ \end{align*}

3. Mycelial Growth Phase

Balances: \begin{align*} \frac{dX_{bio}}{dt} &= \mu \: X_{bio} \\ \frac{dS}{dt} &= - \frac{1}{Y_{XS}} \: \mu \: X_{bio} \\ \end{align*}

Kinetics: \begin{align*} \mu &= \mu_{max} \: \frac{S}{S+(1-\epsilon_{Tray}) \: V_{Tray} \: K} \end{align*}

Initial Conditions: \begin{align*} X_{bio}(t=0) &= X_{bio}^{pre}(t_{end}) - d_{ad} \: t_{end}^{ad} - d_{de} \: t_{end}^{de} \\ S(t=0) &= (1-\epsilon_{Tray}) \: V_{Tray} \: \rho_{Sub} \end{align*}

Software and Simulation

The resulting model is a differential-algebraic system of equations, consisting both of differential quantities (e.g. the time differential of the amount of the target component) and algebraic relations (e.g. the limitation on the number of binding sites). To solve this model, we use an easily accessible DAE solver in the free-to-use Python package Pyomo. A wrapping script pre-processes the linkage of the different phases and keeps track of everything. Additionally, we have programmed a dashboard interface using the Python package streamlit that automatically visualizes simulation results based on user given inputs. This way, we enable the user to run the simulation with different parameters choices, e.g., dependent on laboratory measurements or geometric adaptations of hardware. We used this simulation in the design and construction phase of our hardware project by examining different biological and process characteristics and changing, e.g., the amount of substrate with respect to them.

Download the scripts to run this model here!

Expand Dashboard Preview 1

After starting the streamlit dashboard, the user is given various choices to parametrize the model to his given application and goal. First, the mycelium growth is simulated. Through interactive plots, the user can explore the solution space of their simulation as well as manually fit parameters to expected outcomes.

Expand Dashboard Preview 2

In the spirit of the MycoFlux, the simulated biomass is directly inserted into the simulation for the adsorption process that uses that biomass as a filter medium to recover target components like Rare-Earth elements.

Expand Dashboard Preview 3

Again, the simulation is dynamically visualized and the amount of bound target component is transfered to the following desorption simulation.

Expand Dashboard Preview 4

After the desorption simulation, all three phases of the MycoFlux extraction process are completed. What remains is calculating the destruction of biomass through the extraction phases and initializing the next extraction cycle with that data.

Expand Dashboard Preview 5

With this dashboard, the user of the MycoFlux can dynamically explore the capabilities and expected outcomes of their operation. This model will also be an extremely useful companion for further research and experiments for the engineered biomaterial and hardware, e.g., to automatically fit kinetic data or to extend it with economic data to estimate costs and profit. However, the main goal of this simulation environment is to support the adaption of the MycoFlux in communities everywhere on earth. We want to empower communities to recycle and profit from their own e-waste using our sustainable synthetic biology. By using our open source companion code, these communities can gain better insights into the workings of the MycoFlux and optimize the design and process execution to their respective circumstances.

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