PLOP - Polymer Length Optimization Program

Introduction

We have developed a unique software tool in the form of a web app that supports the choice of polymer length in biological systems. Examples of polymers are protein linkers and DNA segments. The app uses a novel modeling method that was developed for optimizing protein linker lengths in our systems, which you can read more about here. To make it easier for others to use our modeling we developed PLOP - Polymer Length Optimization Program. You can use PLOP online here. The source code can be found here.

At the time of writing protein linker design is normally done by analyzing previous work and elaborating on published results. However, often previous results on protein linkers are unlikely to be transferable to new systems due to the new systems being too different. Therefore PLOP was developed. PLOP can be used to simulate the contact probability between two different proteins based on the linker length that separates them. The probability results can be used to choose a polymer length that optimizes the probability, has probability close to zero, or attains any probability in between. The contact probability is related to reaction rates between the proteins. In other words it is possible to use PLOP for getting the highest possible reaction rate for protein-protein interactions, set the reaction rate to zero, or try to attain a specific reaction rate. PLOP is also general enough that it can be applied for other polymers than protein linkers, such as DNA. As an example the iGEM team UTokyo used the model for simulating DNA connected to recombinases. You can read more about the modeling collaboration between our teams here.

Usage Instructions

In this section, a complete PLOP user guide is described. Before proceeding with the app, preliminary knowledge about the modeled system is recommended. The guide also provides information on optimal parameter tuning to take full advantage of PLOP. See below for a more detailed description on the app features and implementation.

Research before use

Research stiffness of polymers. The parameter for stiffness is called persistence length, which is needed to run PLOP.

Research size of proteins connected to your polymers.

Optional: look at similar systems for a first guess of optimal linker length.

Advice for running PLOP

Range: Choose a wide range of polymer lengths. After each run of PLOP, it is recommended to reduce the range according to the new information.

Number of segments: The number of segments in PLOP is not related to the number of monomers in a polymer. The accuracy increases according to the number of segments, and so does the run time. Choose a low number of segments (20-30) for lower accuracy but shorter run time. Choose a high number of segments (50-100) for higher accuracy.

Polymer lengths: If possible, choose a low number (1-5) of polymer lengths to model. This dramatically reduces the run time. It is possible to run PLOP with many polymer lengths, but the run time could increase on the orders of hours.

Protein radiuses: Enter average radius for proteins. Approximations are often adequate. For modeling polymers not connected to proteins, set protein radiuses to zero.

Persistence length: A lower persistence length results in the polymer bending more. PLOP is not made for optimizing persistence length, but it is possible to use it for testing how persistence length affects the system. This can be used for analyzing an amino acid sequence in protein linkers.

Number of simulations: Choose a low number of simulations (10³-10⁴) for approximate results. Choose a high number of simulations (10⁵ - 10⁶) for more exact results.

Description and possible applications

General

PLOP has been developed in order to support others facing the problem of polymer length optimization, as we did in our project. It is possible to use PLOP to model any polymer as long as you know the polymer’s persistence length. PLOP uses a variant of worm-like chain (WLC) modeling that can be applied for example for modeling DNA, RNA and intrinsically disordered proteins. PLOP can currently model polymers at a time. The function of modeling two polymers at a time is under development.

The accuracy of PLOP is dependent on the simulated systems. The accuracy would be lower if PLOP is used to model long and flexible polymers as it becomes a problem that the polymers are modeled as lines without volume. This results in that polymers can go through themselves. See examples of simulations below for clarification. If a polymer would be plotted with accurate thickness, its volume would overlap itself.

One polymer

The main application of one polymer modeling is to simulate how proteins at the ends of the polymer will interact depending on polymer length. If the proteins bind together, the system will have formed a loop. For example PLOP can model recombinase interaction depending on the length of the DNA segment between the recombinase binding sites. UTokyo simulated the latter by using the same modeling programs that PLOP is based on (more info here).

Besides calculating protein contact probability, PLOP shows examples of simulations as shown in the figure below. There is one example for each polymer length.

Lastly PLOP also returns an estimation of the probability density for surface distances. As shown below, it generates a probability density for each polymer length.

Two polymers

When modeling two polymers with PLOP, the relative starting positions for the two polymers must be known. This is often the case for systems where the system’s behavior is dependent on polymer length. One example application is modeling a Fluorescence Resonance Energy Transfer (FRET) biosensor system. FRET is often used for analyzing protein-protein interactions, a signal is generated if two proteins bind. The image below shows an example.

Assuming that Protein A and Protein B bind, you could use a protein database for estimating the distance between the points where the two linkers are connected to Protein A and B. Those points are the starting points of the linkers. Then PLOP can be used for choosing linker lengths that results in the highest possible probability of the donor and acceptor coming in contact, to get a fast response showing that the proteins have come in contact.
Unfortunately, the function of modeling two polymers is at the moment of writing still under development.

Future Development

The results generated by PLOP have not been extensively compared with data from experiments. There is a high need of evaluating PLOP’s performance, and implementing changes if major flaws are found. The accuracy of the model that PLOP is based on is discussed on our Model page. There is a need of performing further testing on how performance is affected by the number of segments in polymers, accuracy of protein radiuses, accuracy of persistence length, and number of simulations. Both validity and robustness of PLOP, depending on these parameters, have not been evaluated enough.

The assumptions done for the modeling could also be further examined. The model assumes that there is no force at the end of the polymers, an assumption that is not likely true in actual systems. This is one of the assumptions that could bias PLOP’s results. However, any improvements of the model could be implemented in PLOP. For example, one extension of the model would be to include protein orientation regarding protein-protein interactions.

In our project, the highest possible reaction rates were the goal for systems with protein linkers. Therefore, interpreting the model results were straightforward, the goal was to find polymer lengths that gave the highest possible probability of proteins coming in contact. In other situations there might be a need for a more specific reaction rate. A non-linear relationship between protein contact probability and reaction rate could also generate results that are difficult to interpret. Another future development opportunity is therefore to relate PLOP’s results to reaction rate.