Session S30: Scaling and Phase Transitions in the Life Sciences - From Proteins to Tropical Forests

Measuring the multiscale and multi-mass heterogeneity of complex spatial patterns in synthetic and real datasets

Spatial patterns may exhibit scale-dependent changes in structure and are often difficult to characterize. Lacunarity measures how data fill space enabling the parsimonious analyses of patterns. The lacunarity index (monolacunarity) averages the behavior of variable size structures in a binary image. The generalized lacunarity concept (multilacunarity) on the basis of generalized distribution moments is an appealing model that can account for differences in the mass content at different scales. The method was proposed in Physica A 388, 4305 (2009). Here, the aim is to provide validation on synthetic images (lacking in the original paper) and to quantify the mesostructural changes in the intercellular air spaces of pome and stone fruit parenchymatous tissue after storage and ripening, respectively. These generalized moments can yield an enhanced measure of the spatial organization of intercellular air spaces which is complementary to the monolacunarity model. Essentially, the multilacunarity morphometric is a multiscale multi-mass measure of spatial heterogeneity that offers insights regarding modifications upon the arrangement of cells and voids. This can further stimulate research interest in analyzing tissue (plant, human) under various metabolic and physiological changes.   

Percolation in protein cores: a novel approach to protein decoy detection

Protein cores are regions of densely packed, solvent-excluded residues, and void space inside of cores can often destabilize the structure. Here, we measure the void space in protein cores and find that the void structure is equivalent to that in jammed packings of repulsive residue-shaped particles. A continuum void percolation transition can be defined as when the characteristic void length scale approaches the system size. Using finite-size scaling, we show that the percolation of void space in protein cores belongs to same universality class as voids in static packings of residue-shaped particles. This result provides a novel approach for evaluating whether computationally designed protein structures will take a desired fold in experiments. Molecular dynamics simulations often generate “decoy” protein structures that have low potential energy, but are not observed experimentally. We argue that decoy protein structures will have a fundamentally different void distribution, i.e. belong to a different universality class than the void distribution in real protein structures. Therefore, by analyzing the universal aspects of connected voids in computationally generated protein structures, we will be able to differentiate experimentally observed structures from protein decoys.
  

Scaling and phase transitions – from proteins to ecology

The nature of a phase of matter transcends the microscopic material properties. For example, materials in the liquid phase have certain common properties independent of the chemistry of the constituents: liquids take the shape of the container; they flow; and they can be poured -- alcohol, oil and water as well as a Lennard-Jones computer model exhibit similar behaviour when poised in the liquid phase. I will introduce a simple model of a chain molecule with no spurious symmetries and present the results of computer simulations of its ground state phase diagram. Our calculations on relatively short chains (recall proteins are also much shorter than conventional polymers) reveals a hitherto unstudied “phase” that may have a relationship to proteins, the workhorse molecules of living cells. Our findings may be relevant for understanding proteins as well as for the creation of novel bio-inspired nano-machines.

Scaling ideas are most useful, when one is unable to deal with the full complexity of a problem or more importantly, when many of the details are not essential for the type of information that one is seeking. An important example of scaling arises in the field of ecology, when one wishes to understand the threats of losing bio-diversity. I will describe some recent results on the metabolic scaling of individual trees and a forest comprised of many trees. Our scaling framework unifies seemingly distinct trends in a forest and provides a simple yet promising approach to begin to quantitatively understand a bewilderingly complex many-body system with imperfectly known interactions.

Collaborators: Amos Maritan, Tomasso Anfodillo, Marek Cieplak, Achille Giacometti, Trinh Hoang, Andrea Rinaldo, Tatjana Skrbic, Igor Volkov   

RG-inspired analyses of activity in networks of real neurons

The renormalization group (RG) allows us to understand how theories of macroscopic dynamics can be simpler and more universal than the underlying microscopic mechanisms. Inspired by these ideas, we develop an approach to coarse-graining complex biological systems in which highly correlated groups of variables play the role of spatial neighborhoods or block spins. We apply this to experiments on the activity of 1000+ neurons in mouse hippocampus, recorded as the animal navigates a virtual environment. We find power-law dependences of several static and dynamic quantities on the coarse-graining scale, over two decades, with exponents that are strikingly reproducible across experiments. In addition, the probability distribution of coarse-grained variables seems to converge on a non-trivial fixed form. We explore how different coarse-graining schemes affect the scaling behaviors, and construct minimal models for the coarse-grained variables. Finally, we investigate how the coding properties of the neurons change as we move along the RG flow.   

Hierarchy Near a Critical Point: From the Ising Model to Gene Networks

The renormalization group approach involves locally averaging over microscopic variables to obtain coarse-grained variables that describe the macroscopic behavior of the system. We propose that hierarchical clustering corresponds to the same approach. We used the cophenetic correlation coefficient (CCC) to quantify how well the relationships between the components in a system are approximated by a hierarchical construct that captures the macroscopic behavior. Since the behavior of a system near a critical point is dominated by macroscopic variables, we expected the CCC to be higher near such a point. This was verified for the 2D Ising model. We then applied this approach to gene networks with distinct behaviors in different regions of the parameter space, separated by critical surfaces. The CCC was higher near the critical surface for the two gene networks investigated. Further, a higher CCC correlated with higher susceptibility of the networks to perturbations, mirroring the higher susceptibility of physical systems near a critical point. We suggest that the CCC can be a useful quantitative signature of criticality in biological systems.   

Collective sensing by cell populations with feedback-induced long-range correlations

Cells sense their environment with remarkable precision, and recent experiments have shown that this precision can be enhanced by cell-cell communication. However, most theoretical investigations of this effect have assumed linear sensing and communication, whereas it is well known that cells use nonlinear feedback to internally amplify sensed signals. Here, using a minimal stochastic model we investigate the interplay of feedback and communication in determining sensory precision. We find that feedback can induce a critical transition and long-range correlations among cells. We investigate the associated sensing tradeoff: on the one hand, we expect long-range order to enhance communication; on the other hand, fluctuations become large at the critical point, so order may come at the cost of precision. We find that depending on the parameters the system can exist in one of two universal regimes, one which permits an ordered phase and one which does not.   

Chemotaxis: A New Mechanism for Molecular Transport

In aqueous environments, molecules bounce around through random Brownian walk. However, the environment is often not uniform and there might be a gradient of an interacting solute. In that case, the probe molecules can show directional motion known as chemotaxis. In contrast to diffusion, the chemotactic motion is directional and can be toward or away from high solute concentration which constitutes positive or negative chemotaxis. We have found that enzyme undergoes directional movement towards high concentration of substrate under different conditions, even when the enzyme is not catalyzing the corresponding reaction [1]. In addition to enzymes, we have shown that chemotaxis can happen in a simpler system comprised of dye and interacting polymer molecules [2].
Despite the very different chemistries of the two chemotaxing species (enzyme and dye), the driving force for molecular chemotaxis appears to be similar: the lowering of chemical potential due to a thermodynamically favorable interaction or binding. Based on this thermodynamic insight, we have proposed a general expression to model the observed molecular chemotaxis.

[1] F. Mohajerani, et al. Biochemistry, 2018
[2] R. Guha, et al. J. Am. Chem. Soc., 2017   

Ising model with memory: results and applications to synchronization in population ecology

Synchronized oscillations in spatially extended populations can be modeled by coupled noisy, quadratic maps in the two-cycle regime. These dynamical systems exhibit a phase transition from incoherence to synchrony that is in the equilibrium Ising universality class. However individuals in real populations have phase memory that is not contained in the standard Ising model. In this work we analyze a dynamical Ising model with an additional memory term and investigate the phase transition using analytical and numerical approaches. The effective equilibrium model of this dynamical system undergoes a phase transition in the equilibrium Ising universality class with a critical temperature that increases with the strength of the memory. We present results for this system and discuss connections to coupled map systems and also to agricultural data describing oscillations in pistachio production (masting) where tree level data from an orchard in California reveals Ising critical behavior.