The Mathematical Modeling of Living Systems (MMLS) program at the Simons Foundation held its third annual all-day Conference on Theory and Biology. The meeting was an occasion for scientists in the greater New York area to come together to meet, discuss and hear talks highlighting a few of the many areas where theoretical ideas are having an impact on topics in the life sciences.
Jan Skotheim, Stanford University
How biosynthesis scales (or not) with cell size
While cells of a given type span a large range of sizes, most proteins and mRNA molecules are maintained at constant concentrations independent of cell size. This ensures that biochemical reactions can proceed regardless of the size of the cell, but it raises the question of how cells can achieve size-dependent signals when needed, such as those coordinating cell size and cell cycle. Recently, we showed that one way to achieve size-dependent reaction rates is to decouple specific protein synthesis rates from the cell growth rate. Specifically, budding yeast size control results from size-independent synthesis of the cell cycle inhibitor Whi5 and size-proportional synthesis of the cell cycle activator CLN3. As a consequence, larger cells have a higher ratio of cell-cycle activator to inhibitor. Thus, at its most fundamental level, size control results from differential size-dependence in protein synthesis. This raises two key questions: (1) To what extent does expression of individual genes deviate from constant concentration? (2) What are the molecular mechanisms that determine whether gene expression depends on cell size?
To address these questions, we examined flow cytometry data collected using the yeast GFP-fusion library. We identified approximately 200 proteins whose abundance does not scale with cell size. Next, we validated a representative fraction of these candidates using quantitative single-cell microscopy. Gene ontology analysis revealed that the non-scaling genes are enriched for membrane transport and DNA-templated processes such as replication. Since neither DNA content nor membrane area is proportional to cell size, our result suggests that cells employ differential protein synthesis to coordinate gene product requirements with cell size. Moreover, a targeted analysis of Whi5 and histone genes suggests that cells employ both transcriptional control and protein degradation to coordinate gene expression with size. Specifically, transcriptional reporters based on the 1,000 base pairs upstream of the Whi5 coding sequence exhibit size-independent synthesis; in contrast, similar histone transcriptional reporters show size-dependent synthesis. So far, our work demonstrates a functional role for differential size dependency of protein synthesis and offers insights into the underlying molecular mechanisms.
Ken Irvine, Rutgers University
Normal health and physiology is dependent upon formation of organs of appropriate size. Cells in a developing organ are exposed to multiple growth factors, which provide information about their location, developmental stage, and nutritional status. In addition to this biochemical environment, cells in a developing organ also experience a mechanical environment, in which they are subject to forces through their contact with neighboring cells and the extracellular matrix. The mechanical environment has also been proposed to modulate organ growth, yet how this occurs and what it contributes to in vivo growth regulation remains largely unknown. We recently discovered a biomechanical signaling pathway, which we refer to as the Jub biomechanical pathway, that regulates organ growth through modulation of the conserved Hippo signaling network. I will discuss evidence that this pathway carries out a mechanical feedback response that modulates growth rates in developing organs.
Sue Brown, Kansas State University
An Insect segmentation mechanism discovered in Tribolium castaneum
The evolution of insect segmentation has intrigued developmental biologists for more than a century and has inspired many theories to explain the differences in embryonic development discovered in short- and long-germ insects. For several years we have compared segmentation in the red ﬂour beetle to that of the fruit fly. Expression of the segment polarity gene engrailed provided the ﬁrst molecular evidence of sequential segmentation in the short-germ insect, Tribolium, in comparison to the paradigm of simultaneous segmentation in the long-germ insect, Drosophila. Expression of pair-rule gene homologs in complementary double-segment periodicity indicated the involvement of a negative feedback loop in a previously unknown insect segmentation clock in short-germ insects. A posterior gradient of the homeotic gene caudal regulates kinematic waves of pair-rule genes during blastoderm and germ-band elongation. Our most recent studies highlight the regulation of the caudal gradient by the Wnt signaling pathway. Altogether, our studies describe an insect segmentation mechanism that incorporates pair-rule gene homologs as oscillators in a gradient-dependent insect segmentation mechanism that is in many ways similar to the vertebrate segmentation mechanism.
Michael Akam, University of Cambridge
Time and space in arthropod segmentation
Vivek Jayaraman, Janelia Research Campus
Towards a Mechanistic Understanding of Elements of Cognition
The fruit fly, Drosophila melanogaster, has long been a favored model organism for geneticists and developmental biologists. In the past decade, however, its powerful genetic tools have made the fly an attractive choice for systems neuroscientists seeking a mechanistic understanding of neural circuit function. Early studies focused on sensory processing, but in my lab we have focused on using the fly as a model in order to gain general insights into higher brain functions. Like many other animals, fruit flies display a range of sophisticated behaviors including visual navigation and place learning. Behavioral genetics studies strongly suggest that a central brain region called the central complex is closely involved in the experience- and context-dependent integration of the sensory and motor information needed for navigation. My lab uses a combination of novel physiological and optogenetic techniques to study the behavior of head-fixed flies in order to identify and understand circuit computations carried out by this intriguing brain region. I will discuss recent results from two-photon calcium imaging experiments in which we observed the flies’ behavior during tethered walking in virtual reality. Our experiments reveal neural activity patterns in the central complex that resemble the dynamics that are theorized to underlie the computation of head direction in mammals. We are now attempting to harness the power of fly genetics in combination with modeling, physiology and selective neural perturbation to understand how these circuit dynamics arise and how they relate to the fly’s behavioral decisions.
Larry Abbott, Columbia University
Sense from Randomness in Neural Circuits
Many neural circuits are interconnected with remarkable precision, but others appear to be wired randomly. How extensive is this randomness, and how can randomly connected circuits perform useful functions? I will address these questions using experimental data and models.
Mukund Thattai, National Centre for Biological sciences
Possible and Impossible Cells
This work was done in collaboration with Arnab Bhattacharya, Department of Computer Science and Automation, Indian Institute of Science, Bangalore.
Biology is molecules plus mechanisms. Theory allows us to extrapolate mechanisms far beyond the regimes where they were originally observed, but also places bounds on the capabilities of living systems given assumptions about their molecular constituents. We study the logistics system of eukaryotic cells, whose warehouses are micron-scale “organelles” and whose trucks are 10-nanometer-scale “vesicles”. Organelles form the nodes and vesicle fluxes form the edges of a transport graph. Unlike traditional logistics systems, this graph is self-organized: vesicles are regulated by the very molecular cargo they carry, and organelle chemical identities arise as a balance of molecular gain and loss. James Rothman, Randy Schekman and Thomas Südhof shared the Nobel Prize in 2013 “for their discoveries of machinery regulating vesicle traffic.” We ask: given this molecular machinery, what is the set of possible and impossible transport graphs? Surprisingly, the answer can be framed purely in terms of the graph theoretic concept of “k-edge-connectedness,” where a minimum of k edges must be removed in order to disconnect a graph. Traditional logistics systems are at least 2-connected, all vesicle traffic systems are at least 3-connected, and Rothman-Schekman-Südhof vesicle traffic systems are at least 4-connected. Our constructive proof of this result explains many puzzling properties of vesicle traffic molecules and makes testable predictions about how they must move about inside cells.
Luca Cardelli, Microsoft Research
Noise reduction in complex biological switches
Complex regulatory networks allow cells to operate in noisy molecular environments. It is possible to understand how the number of molecules is related to noise in specific networks, but it is less clear how noise relates to network complexity, because different levels of complexity also imply different overall numbers of molecules. For a fixed function, does increased network complexity reduce noise, beyond the mere increase of overall molecular counts? If so, complexity could provide an advantage that counteracts the costs involved in maintaining larger networks.
For that purpose, we investigate how noise affects multistable systems, where a small amount of noise could lead to very different outcomes; thus we turn to biochemical switches like the G2/M cell cycle transition switch. To compare networks with different structures and levels of complexity, we place them in conditions in which they will produce exactly the same deterministic function. We are then in a good position to compare their noise characteristics relative to their identical deterministic traces.
We show that more complex networks are better at coping with both intrinsic and extrinsic noise. Intrinsic noise tends to decrease with complexity, and extrinsic noise tends to have less impact. Our findings suggest a new role for increased complexity in biological networks, at parity of function.