Beware the tail that wags the dog: informal and formal models in biology

Exploring undiscovered public knowledge in neuroscience

In this essay, I argue that the combination of research synthesis and philosophical methods can fill an important methodological gap in neuroscience. While experimental research and formal modelling have seen their methods progressively increase in rigour and sophistication over the years, the task of analysing and synthesizing the vast literature reporting new results and models has lagged behind. The problem is aggravated because neuroscience has grown and expanded into a vast mosaic of related but partially independent subfields, each with their own literatures. This fragmentation not only makes it difficult to see the full picture emerging from neuroscience research but also limits progress in individual subfields. The current neuroscience literature has the perfect conditions to create what the information scientist Don Swanson called "undiscovered public knowledge"-knowledge that exists in the mutual implications of different published pieces of information but that is nonetheless undiscovered because those pieces have not been explicitly connected. Current methods for rigorous research synthesis, such as systematic reviews and meta-analyses, mostly focus on combining similar studies and are not suited for exploring undiscovered public knowledge. To that aim, they need to be adapted and supplemented. I argue that successful exploration of the hidden implications in the neuroscience literature will require the combination of these adapted research synthesis methods with philosophical methods for rigorous (and creative) analysis and synthesis.

Kinetics of antigen cross-presentation assessed experimentally and by a model of the complete endomembrane system

Dendritic cells (DCs) have a specialized endomembrane system capable of presenting exogenous antigens in the context of MHC class I (MHC-I) molecules. This process, named cross-presentation, is crucial to activate CD8+ T lymphocytes and initiate cytotoxic immune responses. In this report, we present an Agent-Based Model in combination with Ordinary Differential Equations with enough complexity to reproduce cross-presentation. The model embraces the secretory and endocytic pathways, in connection with the plasma membrane, the endoplasmic reticulum, and the cytosol. Key molecules required for cross-presentation were included as cargoes. In the simulations, the kinetics of MHC-I uptake and recycling, and cross-presentation accurately reproduced experimental values. The model proved to be a suitable tool to elaborate hypotheses and design experiments. In particular, the model predictions and the experimental results obtained indicate that the rate-limiting step in cross-presentation of soluble ovalbumin is MHC-I loading after proteasomal processing of the antigenic protein.

From cartoons to quantitative models in Golgi transport

BACKGROUND

Cell biology is evolving to become a more formal and quantitative science. In particular, several mathematical models have been proposed to address Golgi self-organisation and protein and lipid transport. However, most scientific articles about the Golgi apparatus are still using static cartoons that miss the dynamism of this organelle.

RESULTS

In this report, we show that schematic drawings of Golgi trafficking can be easily translated into an agent-based model using the Repast platform. The simulations generate an active interplay among cisternae and vesicles rendering quantitative predictions about Golgi stability and transport of soluble and membrane-associated cargoes. The models can incorporate complex networks of molecular interactions and chemical reactions by association with COPASI, a software that handles ordinary differential equations.

CONCLUSIONS

The strategy described provides a simple, flexible and multiscale support to analyse Golgi transport. The simulations can be used to address issues directly linked to the mechanism of transport or as a way to incorporate the complexity of trafficking to other cellular processes that occur in dynamic organelles.

SIGNIFICANCE

We show that the rules implicitly present in most schematic representations of intracellular trafficking can be used to build dynamic models with quantitative outputs that can be compared with experimental results.

Reconstruction of endosomal organization and function by a combination of ODE and agent-based modeling strategies

BACKGROUND

Reproducing cell processes using an in silico system is an essential tool for understanding the underlying mechanisms and emergent properties of this extraordinary complex biological machine. However, computational models are seldom applied in the field of intracellular trafficking. In a cell, numerous molecular interactions occur on the surface or in the interior of membrane-bound compartments that continually change position and undergo dynamic processes of fusion and fission. At present, the available simulation tools are not suitable to develop models that incorporate the dynamic evolution of the cell organelles.

RESULTS

We developed a modeling platform combining Repast (Agent-Based Modeling, ABM) and COPASI (Differential Equations, ODE) that can be used to reproduce complex networks of molecular interactions. These interactions occur in dynamic cell organelles that change position and composition over the course of time. These two modeling strategies are fundamentally different and comprise of complementary capabilities. The ODEs can easily model the networks of molecular interactions, signaling cascades, and complex metabolic reactions. On the other hand, ABM software is especially suited to simulate the movement, interaction, fusion, and fission of dynamic organelles. We used the combined ABM-ODE platform to simulate the transport of soluble and membrane-associated cargoes that move along an endocytic route composed of early, sorting, recycling and late endosomes. We showed that complex processes that strongly depend on transport can be modeled. As an example, the hydrolysis of a GM2-like glycolipid was programmed by adding a trans-Golgi network compartment, lysosomal enzyme trafficking, endosomal acidification, and cholesterol processing to the simulation model.

CONCLUSIONS

The model captures the highly dynamic nature of cell compartments that fuse and divide, creating different conditions for each organelle. We expect that this modeling strategy will be useful to understand the logic underlying the organization and function of the endomembrane system.

REVIEWERS

This article was reviewed by Drs. Rafael Fernández-Chacón, James Faeder, and Thomas Simmen.

Achilles and the tortoise: Some caveats to mathematical modeling in biology

Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations.

Agents and networks to model the dynamic interactions of intracellular transport

Cell biology is increasingly evolving to become a more formal and quantitative science. The field of intracellular transport is no exception. However, it is extremely challenging to formulate mathematical and computational models for processes that involve dynamic structures that continuously change their shape, position and composition, leading to information transfer and functional outcomes. The two major strategies employed to represent intracellular trafficking are based on "ordinary differential equations" and "agent-" based modeling. Both approaches have advantages and drawbacks. Combinations of both modeling strategies have promising characteristics to generate meaningful simulations for intracellular transport and allow the formulation of new hypotheses and provide new insights. In the near future, cell biologists will encounter and hopefully overcome the challenge of translating descriptive cartoon representations of biological systems into mathematical network models.

Transcriptional precision and accuracy in development: from measurements to models and mechanisms

During development, genes are transcribed at specific times, locations and levels. In recent years, the emergence of quantitative tools has significantly advanced our ability to measure transcription with high spatiotemporal resolution in vivo. Here, we highlight recent studies that have used these tools to characterize transcription during development, and discuss the mechanisms that contribute to the precision and accuracy of the timing, location and level of transcription. We attempt to disentangle the discrepancies in how physicists and biologists use the term ‘precision' to facilitate interactions using a common language. We also highlight selected examples in which the coupling of mathematical modeling with experimental approaches has provided important mechanistic insights, and call for a more expansive use of mathematical modeling to exploit the wealth of quantitative data and advance our understanding of animal transcription.

Summary: This Review highlights how high-resolution quantitative tools and theoretical models have formed our current view of the mechanisms determining precision and accuracy in the timing, location and level of transcription in the Drosophila embryo.