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J. M. Schwarz Theory Group

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Emergent properties of learning in living and nonliving matter

How do humans learn? How does slime mold learn? And how do nonliving, physical systems learn? For the last 20 years or so, with the advent of machine learning, the hope has been that if we can understand how algorithms learn, then we can understand, in principle, how living systems, such as slime mold and humans, learn. With such understanding, we can, therefore, ultimately build life, as learning is one of its fundamental properties. However, much of the machine learning community has focused their efforts on such algorithms as backpropagation that involves computing a gradient to ultimately enable a feedforward neural network to recognize, or learn, patterns. With such focus, the overarching question linking our initial set of questions becomes: Do living systems, such as the brain, perform backpropagation? If yes, fantastic. We have a mechanism that generalizes to both living and nonliving systems. If no, then we need a different approach to find answers.

While the jury is still out as to whether or not the brain performs backpropagation, here, we (Vidyesh, Ananth, Benjamin, and JMS) propose an altogether different strategy. Instead, we propose to study nonliving physical systems, such as flow, or resistor, networks, that can be activated by external signals and ask if we also endow such a system with, for example, feedback chemical signaling that reduces error between a target quantity and observed quantity, can such a system learn by local modifications of its own structure, such as the geometry of the tubes in the flow network? If the answer to our question is in the affirmative, then we can determine how physical systems learn via adaptive computation. We have dubbed this new paradigm to learning via at least two distinguishable physical pathways, an activation pathway and an error feedback pathway, as multi-mechanism learning. Please read our pre-prints on arXiv to learn more about it.

Minimal, multiscale mechanical models of organoids and spheroids

How genes affect tissue scale organization remains a longstanding biological puzzle. As experimental efforts are underway to solve this puzzle via quantification of gene expression, chromatin organization, cellular structure, and tissue structure, computational modeling efforts remain far behind. To help accelerate the computational modeling efforts, we (Tao, Sarthak, Madeline, and JMS) review two recent publications, the first on a cellular-based model for tissues and the second on a model of a cell nucleus that includes a lamina shell and chromatin. We then address how the two models can be combined to ultimately test multiscale hypotheses linking the chromatin scale and the tissue scale. To be concrete, we turn to an in vitro system for the brain known as a brain organoid. We provide a multiscale hypothesis to distinguish structural differences between brain organoids built from induced-pluripotent human stem cells and from induced-pluripotent gorilla and chimpanzee stem cells. Recent experiments discover that a cell fate transition from neuroepithelial cells to radial glial cells includes a new intermediate state that is delayed in human-derived brain organoids as compared to their genetically-close relatives, which significantly narrows and lengthens the cells on the apical side (S. Benito-Kwiecinski, et al. Cell 2021). Additional experiments revealed that the protein ZEB2 plays a major role in the emergence of this new intermediate state with ZEB2 mRNA levels peaking at the onset of the emergence (S. Benito-Kwiecinski, et al. Cell 2021). We postulate that the enhancement of ZEB2 expression driving this intermediate state is potentially due to chromatin reorganization. More precisely, there exists critical strain triggering the reorganization that is higher for human-derived stem cells, thereby resulting in a delay. Such a hypothesis can readily be tested experimentally within individual cells and within brain organoids as well as computationally to help work towards solving the gene-to-tissue organization puzzle. Please read our pre-print, with more to come, on arXiv to learn more about our approach.

Building correlated percolation models inspired by jamming in granular and glassy systems

While we are all very familiar with the transition from water to ice, or liquid to crystalline solid, upon cooling, there also exists transitions, if you will, from liquid to disordered solids. Paint drying, coffee beans stuck in a dispenser, and glass making are several "day-to-day" examples. To mathematically describe the transition from flowing to not-flowing, a.k.a. jammed, has proven to be difficult for various technical reasons resulting in a sea of competing approaches. Our approach is to construct toy models that capture different properties of systems near the onset of glassiness and/or jamming. With these toy models we can isolate and, therefore, identify what properties determine a particular response. To date, such models take into account local properties of mechanical stability, or rigidity, via a technique known as correlated percolation. However, we have introduced a new correlated percolation model that incorporates both local and global properties of mechanical rigidity using local rules, dubbed the jamming graph. This graph-based model should provide a basis for understanding the onset of jamming in spherical particle systems and ultimately in systems with more generic shapes that exhibit somewhat different properties of mechanical rigidity from spheres.

Studying the interplay between morphology and rheology in the actin cytoskeleton via rigidity percolation

The actin cytoskeleton gives the cell shape and support, is crucial for cell locomotion, and participates in cell division. To date, there are basically two approaches to modelling the actin cytoskeleton. The first approach is kinetic and models how the actin cytoskeleton changes its structure (from network-like to bundle-like) to perform its tasks, while the second approach invokes an elasticity theory of disordered, static structures, i.e. rigidity percolation. Our group has used both approaches with the ultimate goal of unifying the two. In the mean time, our latest model of the actin cytoskeleton addresses how mechanically different types of crosslinkers act both redundantly and cooperatively in determining the elasticity of the actin cytoskeleton to help explain the "need" for different types of crosslinkers.

Looking for discontinuous, disorder-driven localization transitions in quantum systems via quantum percolation

In the paradigm of quantum metal-insulator transitions, a discontinous onset of conduction suggests that interactions drive the system from one phase to the other, while a continuous onset of conduction suggests that disorder drives the phase transition. Our group has constructed and analyzed a model called quantum k-core percolation and found a discontinuous onset of conduction even though it is disorder driving the transition. In other words, our discovery does not fit the standard paradigm calling for, perhaps, a paradigm shift. :)

Emergent properties of learning in living and nonliving matter How do humans learn? How does slime mold learn? And how do nonliving, physical systems learn? For the last 20 years or so, with the advent of machine learning, the hope has been that if we can understand how algorithms learn, then we can understand, in principle, how living systems, such as slime mold and humans, learn. With such understanding, we can, therefore, ultimately build life, as learning is one of its fundamental properties. However, much of the machine learning community has focused their efforts on such algorithms as backpropagation that involves computing a gradient to ultimately enable a feedforward neural network to recognize, or learn, patterns. With such focus, the overarching question linking our initial set of questions becomes: Do living systems, such as the brain, perform backpropagation? If yes, fantastic. We have a mechanism that generalizes to both living and nonliving systems. If no, then we need a different approach to find answers. While the jury is still out as to whether or not the brain performs backpropagation, here, we (Vidyesh, Ananth, Benjamin, and JMS) propose an altogether different strategy. Instead, we propose to study nonliving physical systems, such as flow, or resistor, networks, that can be activated by external signals and ask if we also endow such a system with, for example, feedback chemical signaling that reduces error between a target quantity and observed quantity, can such a system learn by local modifications of its own structure, such as the geometry of the tubes in the flow network? If the answer to our question is in the affirmative, then we can determine how physical systems learn via adaptive computation. We have dubbed this new paradigm to learning via at least two distinguishable physical pathways, an activation pathway and an error feedback pathway, as multi-mechanism learning. Please read our pre-prints on arXiv to learn more about it.
Minimal, multiscale mechanical models of organoids and spheroids How genes affect tissue scale organization remains a longstanding biological puzzle. As experimental efforts are underway to solve this puzzle via quantification of gene expression, chromatin organization, cellular structure, and tissue structure, computational modeling efforts remain far behind. To help accelerate the computational modeling efforts, we (Tao, Sarthak, Madeline, and JMS) review two recent publications, the first on a cellular-based model for tissues and the second on a model of a cell nucleus that includes a lamina shell and chromatin. We then address how the two models can be combined to ultimately test multiscale hypotheses linking the chromatin scale and the tissue scale. To be concrete, we turn to an in vitro system for the brain known as a brain organoid. We provide a multiscale hypothesis to distinguish structural differences between brain organoids built from induced-pluripotent human stem cells and from induced-pluripotent gorilla and chimpanzee stem cells. Recent experiments discover that a cell fate transition from neuroepithelial cells to radial glial cells includes a new intermediate state that is delayed in human-derived brain organoids as compared to their genetically-close relatives, which significantly narrows and lengthens the cells on the apical side (S. Benito-Kwiecinski, et al. Cell 2021). Additional experiments revealed that the protein ZEB2 plays a major role in the emergence of this new intermediate state with ZEB2 mRNA levels peaking at the onset of the emergence (S. Benito-Kwiecinski, et al. Cell 2021). We postulate that the enhancement of ZEB2 expression driving this intermediate state is potentially due to chromatin reorganization. More precisely, there exists critical strain triggering the reorganization that is higher for human-derived stem cells, thereby resulting in a delay. Such a hypothesis can readily be tested experimentally within individual cells and within brain organoids as well as computationally to help work towards solving the gene-to-tissue organization puzzle. Please read our pre-print, with more to come, on arXiv to learn more about our approach.
Building correlated percolation models inspired by jamming in granular and glassy systems While we are all very familiar with the transition from water to ice, or liquid to crystalline solid, upon cooling, there also exists transitions, if you will, from liquid to disordered solids. Paint drying, coffee beans stuck in a dispenser, and glass making are several "day-to-day" examples. To mathematically describe the transition from flowing to not-flowing, a.k.a. jammed, has proven to be difficult for various technical reasons resulting in a sea of competing approaches. Our approach is to construct toy models that capture different properties of systems near the onset of glassiness and/or jamming. With these toy models we can isolate and, therefore, identify what properties determine a particular response. To date, such models take into account local properties of mechanical stability, or rigidity, via a technique known as correlated percolation. However, we have introduced a new correlated percolation model that incorporates both local and global properties of mechanical rigidity using local rules, dubbed the jamming graph. This graph-based model should provide a basis for understanding the onset of jamming in spherical particle systems and ultimately in systems with more generic shapes that exhibit somewhat different properties of mechanical rigidity from spheres.
Studying the interplay between morphology and rheology in the actin cytoskeleton via rigidity percolation The actin cytoskeleton gives the cell shape and support, is crucial for cell locomotion, and participates in cell division. To date, there are basically two approaches to modelling the actin cytoskeleton. The first approach is kinetic and models how the actin cytoskeleton changes its structure (from network-like to bundle-like) to perform its tasks, while the second approach invokes an elasticity theory of disordered, static structures, i.e. rigidity percolation. Our group has used both approaches with the ultimate goal of unifying the two. In the mean time, our latest model of the actin cytoskeleton addresses how mechanically different types of crosslinkers act both redundantly and cooperatively in determining the elasticity of the actin cytoskeleton to help explain the "need" for different types of crosslinkers.
Looking for discontinuous, disorder-driven localization transitions in quantum systems via quantum percolation In the paradigm of quantum metal-insulator transitions, a discontinous onset of conduction suggests that interactions drive the system from one phase to the other, while a continuous onset of conduction suggests that disorder drives the phase transition. Our group has constructed and analyzed a model called quantum k-core percolation and found a discontinuous onset of conduction even though it is disorder driving the transition. In other words, our discovery does not fit the standard paradigm calling for, perhaps, a paradigm shift. :)