Lawrence Livermore National Laboratory, California’s scientists have developed a theoretical model based on Dynamic Density Functional Theory (DDFT) for modeling multicomponent cellular membranes as a continuum. The cellular membranes considered are composed of an arbitrary number of lipid types, and the continuum model for the cellular membranes is trained on molecular dynamics (MD) simulations. Within this framework, simulations can access length scales of the order of microns and timescales of the order of seconds, with a relatively low sacrifice to the accuracy of the underlying MD simulations. The authors explore the lipid interaction and aggregation of RAS proteins linked with cancer growth as an application of the developed model system. The results shed light on valuable insights on this often labeled undruggable target.

Cell membranes and why do we need a multicomponent model framework?

Cell membranes are crucial to cells for maintaining structure and permeability. Membrane proteins present on the cell membrane enable cell adhesion, ion conductivity as well as cellular signaling. Researchers have been greatly invested in modeling cellular membranes and their interactions with these membrane proteins, as such dynamics scales are often beyond the scope of experiments. However, a significant gap exists between experimental scales and the atomic resolutions of simulations. Consequently, a plethora of biological processes, including the migration and signaling of membrane proteins, remain poorly addressed as they fall within this elusive range.

Cellular membrane modeling primarily involves molecular dynamics and Monte Carlo (MC) simulations. These simulations typically implement individual atoms or biologically relevant clusters of atoms evolving under an effective force field. MD simulations are limited by the accessibility of time and length scales, thereby rendering MD unable to explore several biological mechanisms. 

Continuum models are a better choice for achieving larger time and length scales but with trade-offs of accuracy and generality. Phase field models are a suitable continuum approach in this regard. However, they have their share of limitations. These continuum models heavily depend on the phenomenological construction of free energy, which must be fit to MD data or experimental data. In addition, cell membranes house different types of lipids, which complicate the generation of a detailed description resolving common species. However, phase models are restricted by the number of species, often two or three, due to problems with parameter fitting. 

Classical density functional theory (DFT) connects macroscopic quantities with microscopic degrees of freedom. The theory naturally generalizes to multicomponent systems with an arbitrary number of species and does not require empirical parameters. Dynamic DFT, a non-equilibrium extension of DFT, is the best choice for modeling cellular membranes- a multicomponent dynamic system. Thus, the authors present a theoretical framework involving DDFT for modeling cellular membrane dynamics, which has already been successful in the machine learning-driven multiscale approach, MuMMI.

A brief overview of the theoretical modeling framework

The theoretical model framework involves two major steps :

  • Constructing an appropriate free energy function of the system. This is achieved by decomposing the total free energy of the system into free energy of lipid-lipid, lipid-protein, and protein-protein interactions. DDFT incorporates the microscopic statistics of the system in capturing these interactions using correlation expansion.
  • From this fee energy functional, the evolution equations for the lipid density fields and protein beads can be determined.

It is noteworthy that the theoretical framework allows for membrane deformations.

MuMMI: Mutliscale Machine-learned Modelling infrastructure

The authors have previously published an article on MuMMI, which employs a macro model for exploring lipid-protein interactions over large lengths and time scales. The macro model represents a lipid bilayer and explores the RAS protein interactions therein. The underlying theory of the simulation framework is what is described in the current article. The MuMMI model also describes RAS-RAF protein interactions amongst themselves as well as with the lipids of the membrane. Given the significance of RAS signaling in cancer biology, the aim was to gain deeper insights into RAS signaling-mediated cancer growth using simulations and predictive models.

Lipid interaction and aggregation of RAS proteins on plasma membrane: an application

RAS proteins are signaling proteins and are found to be greatly involved in 30%of cancers. Probing the RAS protein interactions with lipid bilayers has been challenging, given the gap in timescales and length scales between experiments and simulations. Such challenges rendered RAS the undruggable target for cancer treatment until the authors developed the MuMMI framework and explored the lipid-protein interactions involved in the RAS signaling pathway at large.

In the current article, as an application of the theoretical framework, the authors illustrate the model validity and efficacy using the RAS protein interactions. Owing to the computational efficiency of the DDFT model framework, the authors were able to explore the parameter space associated with the empirical protein interactions with ease. The authors observed a phase transition associated with the strength of the PAPS-RAS interaction.

The video illustrates the MuMMI simulation framework for the RAS protein interactions. 

Video Source: https://www.llnl.gov/news/llnl-scientists-develop-model-more-efficient-simulations-protein-interactions-linked-cancer

Conclusion

The authors have developed the DDFT theoretical framework for modeling cellular membranes and their interactions with lipids and proteins therein. The multicomponent architecture and the arbitrary number of molecule species of the cellular membrane required a theoretical framework that incorporates these aspects as well as enables efficient simulations with a resolution of micron-level length scales and timescales of the order of seconds. The model is truly remarkable in combining continuum dynamics with particle dynamics. The RAS protein interactions reveal deeper insights into cancer biology and point to potential targets for drug discovery and therapeutics. The authors envision future iterations to include feedback loops between the continuum and molecular scales as well as include more accurate protein interactions, thereby unraveling unexplored biological mechanisms and processes.

Article Source: Reference Paper | Reference Article

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Banhita is a consulting scientific writing intern at CBIRT. She's a mathematician turned bioinformatician. She has gained valuable experience in this field of bioinformatics while working at esteemed institutions like KTH, Sweden, and NCBS, Bangalore. Banhita holds a Master's degree in Mathematics from the prestigious IIT Madras, as well as the University of Western Ontario in Canada. She's is deeply passionate about scientific writing, making her an invaluable asset to any research team.

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