The Phenomenon of Adaptation Across The Biological Scales

Introduction

From archaea thriving in hydrothermal vents on the ocean floor to aspen trees dominating a Coloradan mountainside, all forms of life are unified in their obedience to (and influence on) their environment. Whether it be the stochastic events that can trigger mass extinctions (Jablonski 2001) or the rapid “terraforming” of environments by their inhabitants (such as the rusting of the oceans (Luo et al. 2018)), organisms and their environments are continually engaged in a dialogue that demands the ability to adapt. Over the past 3.5 billion years of evolution, life has evolved myriad clever ways to combat (and exploit) environmental fluctuations to amplify reproductive success. The mechanisms behind this adaptation are diverse and traverse the biological scales, ranging from nanosecond-scale conformational switching of proteins (Fig. 1 (A)), to reconfiguration of metabolic networks to consume different sugars (Fig. 1 (B)), to evolutionary trajectories that only become visible over many generations (Fig. 1 (C)). While “adaptation” is typically only associated with organisms (at least colloquially), one can use the same language to describe the microscopic operations of molecules.

     The idea of molecular adaption is not novel and demands a brief foray into the history of bacterial growth and the dawn of regulatory biology. In the late 1890s, Emilé Duclaux and his graduate student Frédéric Diénert performed a series of experiments illustrating that the common yeast could only consume galactose after an incubation period with the sugar. This led to a general conclusion that “the production of diastases [enzymes] depends on the manner of nutrition” in which the cultures were grown (Loison 2013), a phenomenon later coined enzymatic adaptation. This is one of the first observations of the fact that, while an organism may be able to digest a certain sugar, it may not always be able to do so. Rather, there seemed to be certain conditions in which the production or formation of these enzymes could occur. In his doctoral thesis in 1900, Diénert proposed two mechanisms for the origin of enzymatic adaptation observed for galactozymase in S. cerevisiae (Loison 2013). Either (a) the presence of galactose directly transformed enzymes already present in the cell into galactozymase or (b) that the galactose activated the production of galactozymase de novo (Diénert 1900; Loison 2013).

     Nearly half a century later, Jacques Monod would rediscover the phenomenon of enzymatic adaptation, this time in the context of bacterial growth. In his 1941 work, Monod for the first time reported on the phenomenon of diauxic or biphasic growth, shown in Fig. 2 (A). He noted that for some mixtures of carbon sources, the culture grew “kinetically normal” meaning they grew exponentially to saturation (blue points, Fig. 2 (A)). However, some mixtures (such as sucrose and arabinose) led to biphasic growth where the culture would grow exponentially, undergo a period where growth had ceased (lasting typically 20 - 60 minutes), followed again by another round of exponential growth (green points, Fig. 2 (A)). Additionally, Monod showed that the onset of this diauxic shift could be tuned by varying the relative concentrations of the carbon sources, revealing a controllable chemical basis for the adaptation (Fig. 2 (B)).

     Monod immediately made the connection between diauxic growth and enzymatic adaptation (Loison 2013). Despite his work appearing 40 years after the pioneering work of Ducleaux and Diénért, there had been little progress towards a mechanistic, needless to say quantitative, explanation for the phenomenon. In fact, Monod was particularly disappointed by the teleological explanations where the cells simply changed their behavior to perform only the chemical reactions that were “needed” (Loison 2013). The teleological approach to much of biology during this time period, especially in the French scientific community, severely bothered Monod. To him, this kind of approach belonged to a pre-scientific era and lacked the “postulate of objectivity” that other fields of science (particularly physics) had adopted (Loison 2013). Near the middle of the 20th century, Monod published a 60-page treatise on the phenomenon of enzymatic adaptation with the level of quantitative rigor he thought it deserved (Monod 1947). In this work, he set out to progressively deconstruct and invalidate a series of hypotheses for the phenomenon of enzymatic adaptation. In doing so, he laid the groundwork for what would become (in his opinion) his greatest contribution to science, the nature of allosteric transitions (Loison 2013; Monod, Changeux, and Jacob 1963; Monod, Wyman, and Changeux 1965), a topic that will feature prominently in the remainder of this thesis.

     The diauxic growth transitions shown in Fig. 2 illustrate adaptive processes across the biological scales, as were schematized in Fig. 1. While it was not known to Monod at the time, we now know that many cases of enzymatic adaptation are driven by the regulation of gene expression. As the bacterial culture approaches the auxic shift, the presence or absence of the substrate is sensed by regulatory molecules that control whether the genes encoding the enzymes for metabolism of the substrate are expressed. This represents the level of molecular adaptation where, given binding or unbinding of the substrate molecule, the activity of the regulatory protein is modulated. The amino acid sequence of these proteinaceous regulators are the product of billions of years of evolution with regions of the protein (such as the DNA-binding and inducer-binding domains) undergoing evolutionary adaptation that define how the regulatory molecule senses and responds to these signals. Finally, the precision with which these genes are regulated is determined by their sensitivity to physiological states, capturing the level of physiological adaptation.

     The central aim of this dissertation is to explore the biophysical mechanisms by which these levels of adaptation – molecular, physiological, and evolutionary – are interconnected. Furthermore, in the spirit of Monod, we seek to make our exploration quantitative and leverage the tools of statistical physics to provide precise predictions from pen-and-paper theory that can be rigorously tested through experiment. The remaining sections of this chapter will outline the major topics of this thesis and place them in a historical context alongside the work of Monod. This thesis is structured such that Chapters 1 – 5 present a self-contained summary of how quantitative methods can be used to interrogate and understand the molecular biophysics of adaptation. The remainder, Chapters 6 – 9, are detailed supplements to Chapters 1 – 5,s and are targeted to readers who want to dig into the weeds of statistical inference, error estimation, and analytic properties of the theoretical models.

On The Janus Face of Molecules

Monod is perhaps most famous for his discovery of allostery which he famously referred to as “the second secret of life” (Ullmann 2011; Monod, Wyman, and Changeux 1965). It is fair to say that this “secret” has now been declassified. Allosteric regulation is present in all domains of life across various types of biological processes. Allostery can be found governing the behavior of ion channels (Einav and Phillips 2017; Auerbach 2012), enzymatic reactions (Einav, Mazutis, and Phillips 2016), chemotaxis (Keymer et al. 2006), G-protein coupled receptors (Canals et al. 2012), quorum sensing (Swem et al. 2008), and transcriptional regulation (Huang et al. 2018; Lindsley and Rutter 2006), to name a few of many examples. Despite the objective complexity in the molecular structures of all of these allosteric molecules, they can frequently be reduced to simple cartoons where the details of conformational changes, substrate-binding affinities, and more can be massaged into a small set of key details. Fig. 3 (A) shows the molecular structures of a variety of allosteric transcriptional repressors (top). While each has its own fascinating structure and continuum of conformational states, all can be coarse grained into a simple cartoon representation (bottom) with an active (red) and inactive (purple) state, both of which possess binding pockets (semicircular notches) for an inducer molecule (orange).

     Much as we can reduce the complexity of allosteric molecules schematically, we can enumerate simple mathematical models that describe their behavior. Thermodynamic models built on an assumption of quasi-equilibrium are routinely used to describe complex biological phenomena despite the reality that being in thermodynamic equilibrium is synonymous with being dead. Even with this glaring assumption, such models have been shown to be exceptionally predictive for a variety of complex systems, especially in modeling molecular binding reactions (Dill and Bromberg 2010) and allostery in general (Swem et al. 2008; Keymer et al. 2006; Einav and Phillips 2017; Einav, Mazutis, and Phillips 2016; Phillips 2015). As the timescales of binding and unbinding reactions are orders of magnitude smaller than that of many other processes in the cell, it is fair to make the approximation that molecular binding is in equilibrium. Under this assumption, we are granted the powerful mathematical privilege to say that the probability of a given state of the system P_state follows a Boltzmann distribution,
$$ P_\text{state} = \frac{e^{-\frac{\epsilon_\text{state}}{k_BT}}}{\mathcal{Z}}, \qquad(1)$$
where ϵ_state is the energy of that state, k_B is the Boltzmann constant, and T is the system temperature. The denominator 𝒵 is the partition function of the system and is the sum
$$ \mathcal{Z} = \sum\limits_{i \in \text{states}} e^{-\frac{\epsilon_i}{k_BT}}, \qquad(2)$$
ensuring that the distribution is normalized. Therefore, if we are interested in computing the probability of a given allosteric protein being in the active state, we merely have to enumerate all of the Boltzmann weights (given by the numerator in Eq. 1) and compute
$$ P_\text{active} = \frac{\text{sum over all possible active states}}{\text{sum over all possible states}}. \qquad(3)$$
This probability, defined as a function of the inducer concentration, is shown schematically in Fig. 3 (B). While we have passed over some of the more subtle details of this calculation, the plot in Fig. 3 (B) presents a quantitative prediction of how the activity of an allosteric molecule should scale as a function of the inducer, in this case becoming less active as more inducer molecules are present.

     In Chapter 2 and the associated supplementary Chapter 6 of this dissertation, we use the Monod-Wyman-Changeux model of allostery (Monod, Wyman, and Changeux 1965) to build a predictive model of transcriptional regulation where the level of gene expression changes in response to changing activity of an allosteric transcriptional repressor. Using the same tricks given by Eq. 1 and Eq. 3, we expand upon a previously characterized thermodynamic model of the simple repression motif. This motif, schematized in Fig. 4 (A), is not just a convenient abstraction of a regulatory architecture. Rather, this motif is the most ubiquitous regulatory scheme in E. coli (Gama-Castro et al. 2016; Ireland et al. 2020) and has been the target of much theoretical and experimental dissection (Vilar and Leibler 2003; Buchler, Gerland, and Hwa 2003; Bintu et al. 2005; Garcia and Phillips 2011; Brewster et al. 2014; Phillips et al. 2019). However, inclusion of allostery in a mathematical sense had yet to be explored experimentally.

     At the beginning of 2016, Manuel Razo-Mejia, Stephanie Barnes, Nathan Belliveau, Tal Einav, and I joined forces and set out to build a complete theoretical model for allosteric transcriptional regulation coupled with a thorough experimental dissection. This was no small task and would have likely taken a full Ph.D.’s worth of effort for a single person to do. Yet, within a year of project inception we had submitted a manuscript to preprint servers where all of us were annotated as equal contributors. This experience defined how I view collaboration in scientific research and serves as a shining example of scientific socialism.

     Together, we enumerated a complete thermodynamic model for the inducible simple repression motif and defined a succinct input-output function for the fold-change in gene expression (schematized in Fig. 4 (B)). Here, we define the fold-change in gene expression as the level of gene expression in the presence of a transcriptional repressor relative to the level of expression when the repressor is absent from the system. Therefore, the value of the fold-change is restricted from 0 to 1, corresponding to high and low levels of regulation respectively.

      This model, which is explored in depth in Chapter 2, is defined by a minimal set of biophysical parameters, many of which can be directly measured using standard tricks of molecular biology and biochemistry. With a model in hand, we turned to a collection of 17 unique E. coli strains, each with different copy numbers of the repressor protein and different regulatory DNA sequences. Using our theoretical model, we inferred the lone two biophysical parameters, which we did not know a priori, from a single experimental strain (white points in middle panel of Fig. 4 (C)). We then applied these inferred parameters to our model and drew predictions for all other experimental strains. We found the model to be remarkably predictive, suggesting that our “toy” model of an allosteric repressor captured the underlying physics of the system.

     A key feature of this work is the derivation of thermodynamic state variable termed the free energy (Keymer et al. 2006; Swem et al. 2008). This parameter provides an intuition for the effective free energy difference between states of the promoter in which the repressor is bound and those states in which the repressor is not bound. This parameter accounts for all of the ways in which one can tune the variables and still achieve the same fold-change in gene expression, as is diagrammed in Fig. 5 (A). While we leave the details of this derivation to Chapter 2, we emphasize that this formalism provides a means by which all of the experimental measurements plotted in Fig. 4 (C) can be collapsed onto a master curve defined solely by the free energy, which is illustrated in Fig. 5 (B). This scaling, often referred to as “data collapse” in physics, concretely shows that one has identified the natural variable of the system. With this scaling function in hand, we are able to make a measurement of the biophysical parameters, compute the free energy, and make a concrete prediction of what the fold-change in gene expression will be. Or, as we will see in the following section, details of the biophysical parameters can be determined directly from an empirical measurement of the free energy.

On Using Free Energy to Examine Evolutionary Adaptation

     Allow us to briefly return to Monod and his biphasic growth curves in the mid 1940s. At this point in scientific history, the French vision of biology had taken a strongly finalistic and vitalistic turn (Loison 2013). In particular, a neo-Lamarckian view had been employed to explain the phenomenon of enzymatic adaptation where the enzymes appropriate for digesting the substrate could be spontaneously formed out of the bacterial cytoplasm and inherited by the cell’s descendants, completely independent of genes. In general, this approach to biology deeply frustrated Monod and strongly influenced his desire to “physicalize” the science (Loison 2013). One tool he knew was critical to this mission was the burgeoning field of genetics. In the mid 1930s Monod undertook a short retreat to Thomas Hunt Morgan’s lab at Caltech where he was introduced to genetics which he later remarked as “biology’s first discipline” (Loison 2013). This visit had a profound impact on Monod, who reflected upon it some three decades later:

“Upon my return to France, I had again taken up the study of bacterial growth. But my mind remained full of the concepts of genetics and I was confident of its ability to analyze and convinced that one day these ideas would be applied to bacteria.” (Monod 1966)

     Once he returned to his study of bacterial growth and enzymatic adaptation, he was confronted with incorporating the role of genetic inheritance into his mechanistic explanations. In the mid 1940s, Monod and his coworkers had begun experimenting with a strain of E. coli which was unable to digest lactose, termed L−. When grown on a mixture of glucose and lactose, this strain would not display a diauxic shift and would only be able to consume the glucose in the medium (Fig. 6, black). However, Monod and his coworker Alice Audureau discovered a mutation in this strain which enabled the digestion of lactose, termed L+ (Monod 1947). The growth curve of this strain had the striking feature of diauxic growth. Rather than this mutation merely enabling the digestion of lactose, it did so in a non-constitutive manner and preserved the phenomenon of adaptation. This was an important step forward in Monod’s understanding of enzymatic adaptation (Loison 2013), revealing that it was a “truly genetic property” (Monod 1966).

     This finding illustrates the level of evolutionary adaptation operating at the level of molecules. While it is difficult to find any literature dissecting this particular L+ mutation, it is not difficult to imagine several different mechanisms by which it could be manifest. One such explanation is that this L+ mutation is within a transcriptional regulator itself where a deficiency in the ability to respond to the presence of lactose (and decreasing glucose concentration) had been restored. Such mutations are the crux of Chapter 3 and the corresponding supplemental Chapter 7 of this dissertation.

     As summarized in the previous section and discussed in depth in Chapter 2, Chapter 3 and the associated supplemental Chapter 7 of this dissertation focus on the influence of mutation within the allosteric transcription factor. Furthermore, Chapter 3 presents a generic mechanism by which shifts in the free energy can be mapped directly to changes in values of the biophysical parameters. This chapter, much like Chapter 2, was borne out of a wonderful collaboration with Manuel Razo-Mejia, Stephanie Barnes, Nathan Belliveau, Tal Einav, and Zofii Kaczmarek. Being able to launch another collaborative effort afforded us the opportunity to both develop a new theoretical interpretation for how mutations influence the free energy and acquire enough experimental data to thoroughly test it.

     The primary conceptual development of Chapter 3 is illustrated in Fig. 7. Theoretically, we consider a bacterial strain with an allosteric repressor (which we term the “wild-type” repressor) that has been characterized well enough to have sufficient parametric knowledge of the system. We can use these known parameters of the mutant to easily compute both its predicted average fold-change in gene expression along with the corresponding free energy. However, once a mutation has been introduced into the repressor protein (resulting in a non-synonymous amino acid change), we are once again ignorant a priori of what changes, if any, that mutation may have imparted on the system. In Fig. 7, we examine two separate hypothetical mutations, shown in purple and orange, which significantly change the character of the system by either increasing or decreasing the fold-change in gene expression, respectively. If we assume that these mutations do not change the underlying physics of the system, we are permitted to use the theoretical framework outlined in Fig. 4 and elaborated on in Chapter 2 to characterize each mutation and determine what biophysical parameters have been changed. This framework allows us to calculate the new free energy of the system (F_{mutation 1}) as well as the shift in free energy from the wild-type value,
ΔF_{mutation 1} = F_{mutation 1} − F_wt.   (4)
As will be described in detail in Chapter 3 and the supplemental Chapter 7, the precise value of this free energy shift ΔF can be directly computed given sufficient parametric knowledge.

     This formalism provides a mathematical hypothesis for how double mutants may behave. Given known values for ΔF of each mutation in isolation, can we compute the shift in free energy of the pairwise double mutant ΔF_{mutations 1 &2}? Eq. 4 allows us to make a mathematical null hypothesis that, assuming there are no interactions between the mutants, the net shift in the free energy is simply the sum of the individual shifts in free energy,
ΔF_{mutations 1 &2} = ΔF_{mutation 1} + ΔF_{mutation 2}.   (5)

Given the fact that we can compute the fold-change in gene expression with knowledge of the free energy, we can therefore predict the double mutant phenotype a priori, a prediction not possible prior to this work.

     Over the course of two years (while this theory was in the works), the experimental cast of characters (Stephanie Barnes, Nathan Belliveau, Manuel Razo-Mejia, and Zofii Kaczmarek) and I made a series of mutations in the LacI repressor that we had characterized in the work presented in Chapter 2. These mutations included three point mutations in the DNA binding domain of the repressor, four mutations in the inducer-binding domain, nine double mutants (one inducer binding and one DNA binding each), across four repressor copy numbers and three operator sequences. While this process of strain generation and data collection is not the primary focus of the work, it took  ≈ 80% of the effort. Without them, this work would have remained an untested theoretical novelty. While we leave many of the rich details of this prediction to the reader in Chapter 3, we showcase our experimental success in Fig. 8 (B) where the predicted induction profiles of nine double mutants (light blue shaded regions) are overlaid with their experimental measurements (points). The intimate agreement between theory and experiment illustrates the utility of using free energy shifts as a means to predict new phenotypes.

On The Physiological Adaptability of Transient Molecular Interactions

In Chapers 4 and 5 (and the associated supplementary Chapters 8 and 9), we explore the final level of adaptation in Fig. 1 – physiological adaptation. We do so in two distinctly different systems. The first (discussed in Chapter 4) builds upon our discussion of transcriptional regulation, but now examines how robust the biophysical parameters of the thermodynamic model are to changes in physiology, either by changing the available carbon source or by changing the temperature. Secondly, in Chapter 5, we examine physiological adaptation in the context of osmoregulation – a true matter of life and death in the single-celled world.

     Up to this point in our travels through scientific history, we have examined Monod’s growth curves in various pairwise combinations of sugars. A feature of note is that the presence of diauxic shifts can be seen in various organisms and for many different types of sugars such as sucrose/arabinose, glucose/sorbitol, and glucose/lactose pairings (Monod 1947). These combinations reveal that cells are able to juggle dual-input logic systems where the “decision” to digest one carbon source or another relies on monitoring changes in concentrations of either sugar. In his 1947 treatise, Monod showed that this phenomenon was not limited to dual-carbon mixtures and presented a “triauxic” growth curve of E. coli grown on a glucose/sorbitol/glycerol mixture, shown in Fig. 9. This result illustrated to Monod that the mechanisms underlying enzymatic adaptation “have the character of competitive interactions between different specific enzyme forming systems” (Monod 1947).

     These competing interactions must be resilient to a variety of physiological states. Despite the fact that the carbon atoms in glucose, sorbitol, and glycerol are all ultimately incorporated into the same biomolecules, their pathways to utilization are all distinct and include a variety of different metabolic intermediates. Furthermore, the exponential growth phases in Fig. 9 for each carbon source have different growth rates which itself results in large changes in cell volume (Taheri-Araghi et al. 2015; Jun et al. 2018), genome copy number (Nordström and Dasgupta 2006), and global gene expression patterns (Li et al. 2014; Schmidt et al. 2016; Hui et al. 2015). Despite these changes in cellular physiology, the regulatory systems underlying enzymatic adaptation still function with binding of transcription factors being ignorant of the majority of possible metabolic states of the cell.

     Despite this empirical observation, it has been commonly assumed that the utility of thermodynamic models of gene expression are limited and that the precise values of the biophysical parameters are directly tied to the physiological state in which they were determined. It has even been said that thermodynamic models of gene expression have been a “tactical success, yet strategic failure” in building an understanding of how genomes operate (Phillips et al. 2019).

     In Chapter 4 of this dissertation, we quantitatively assess these assumptions in the context of gene expression by considering the theoretical models built in Chapters 2 and 3 and directly measuring the adaptability of the inducible simple repression regulatory architecture across different physiological states. Namely, we explore how predictive our thermodynamic model can be when modulating either the quality of the carbon source (glucose, glycerol, or acetate, Fig. 10 (A)) or by changing the temperature of the growth medium (32^∘ C, 37^∘ C, or 42^∘ C, Fig. 10 (B)). The culture doubling time varies by nearly a factor of four across the different conditions, illustrating the diversity in physiological states.

      How could this variation in cellular physiology be incorporated into our thermodynamic model? Up to this point in this thesis, all experiments have been conducted in a growth medium supplemented with glucose held at a balmy 37^∘ C. However, nowhere in the thermodynamic model schematized in Fig. 4 (B) is it specified which carbon source must be present whereas the temperature of the system is explicitly included as a multiplicative factor β = (k_BT)^− 1 in front of the exponentiated terms. These features of the model allow us to make explicit predictions of how these perturbations should influence the observed fold-change in gene expression, if at all.

     The parameter that we can say a priori is very likely to change is the repressor copy number R. In Chapters 2 and 3, we had a priori knowledge of the total repressor copy number as previous work directly measured their values in a particular physiological state via quantitative Western blotting (Garcia and Phillips 2011). However, it has been known for nearly three-quarters of a century that the total protein content of the cell scales linearly with the growth rate (Schaechter, Maaløe, and Kjeldgaard 1958; Jun et al. 2018), a phenomenon that has recently been queried at the single-protein level through proteomic methods (Schmidt et al. 2016; Li et al. 2014; Valgepea et al. 2013a; Peebo et al. 2015). Thus, we cannot assume that the protein copy number of the strains used in Chapters 2 and 3 can be left unperturbed. To account for this fact, we used a fluorescence-based method to directly count the number of LacI repressors per cell in each growth condition, a method which is discussed in extensive detail in Chapter 9. This experimental approach, while necessary, is extremely laborious. I am indebted to the work of Zofii A. Kaczmarek for her heroic efforts in conducting a large number of the experiments presented in Chapter 4.

     Our work revealed two key features of this thermodynamic model of gene expression. First, we found that the values of the biophysical parameters inferred from a single physiological state were remarkably predictive when the quality of the carbon source was decreased (Fig. 11 (A, left)). This indicates that this genetic circuit is largely insulated from the metabolic state of the cell. This is exemplified in our ability to yet again collapse the measurements, this time across different carbon sources as a function of the free energy, shown in Fig. 11 (A, right). For the carbon sources studied in this chapter, we conclude that this simple thermodynamic model can be considered both tactically and strategically successful.

     Yet when it comes to temperature, we find that a simple rescaling of the thermal energy of the system is not sufficient to predict the output of this genetic circuit when the temperature is varied (dashed lines in left-hand side of Fig. 11, (B)). This is not necessarily a surprising result as binding of transcription factors is not strictly an enthalpic process. Temperature is known to have a strong influence on many material properties of DNA, such as persistence length and salt release (Goethe, Fita, and Rubi 2015), excluded volume effects (Driessen et al. 2014), and repressor-DNA solubility (Elf, Li, and Xie 2007), to name a few of many effects. To phenomenologically characterize the influence of temperature on the fold-change in gene expression, we considered that there was a constant entropic penalty (though inclusion of a temperature-dependent entropic cost is discussed in Chapter 9). We found that inclusion of this parameter markedly improved the description of the data (solid lines in left-hand side of Fig. 11 (B)) and permitted data collapse within experimental noise of data collected at 37^∘ C (right-hand side of Fig. 11 (B)).

      The inclusion of a phenomenological entropic parameter is not by any means meant to shut the book on temperature effects in this model. Rather, it serves as a representation of what may help explain these effects and demands more focused theoretical and experimental work. To say that the current disagreement between theory and experiment embodies the “strategic failure” of thermodynamic models is, in my view, disingenuous. To say so would be to deem the initial failures of elasticity theory to properly predict the influence of impurities and temperature on the elastic constants of materials as a “strategic failure” in material science. Initial phenomenological models of the effects of impurities and temperature on elastic properties of solids (Friedel 1974) led to several decades of focused theoretical and experimental work that resulted in a complete predictive and mechanistic description (Phillips 2001). Now is the time for a similar approach to biology in the context of temperature and the regulation of gene expression.

On Facing the Elements

The first four chapters of this work encompass myriad perspectives of adaptive processes at the level of transcription regulation. However, just as important as the regulation is the action of the gene that is ultimately expressed. While Monod’s work described in the preceding sections was focused on the expression of enzymes, we now turn to yet another level of physiological adaptation in bacteria – the regulation of turgor pressure.

     In the wild, microbes are constantly faced with an array of environmental insults ranging from changes in temperature, availability of oxygen for aerobic respiration, and even chemical warfare from neighboring microbial communities (Czaran, Hoekstra, and Pagie 2002). One such environmental challenge microbes often face is the variation in the osmolarity of their surroundings. Changes in ion concentrations can result in large volumes of water rushing through the cell membrane, leading to rupture of the membrane and ultimately cell death (Fig. 12 (A)). Unsurprisingly, all domains of life have evolved clever mechanisms to combat these osmotic shocks and regulate their internal turgor pressure.

     One such mechanism for osmoregulation in E. coli is through the action of mechanosensitive ion channels – large, transmembrane structures which sense tension in the cell membrane. Exposure to a hypo-osmotic shock (where water rushes across the cell membrane into the cell), a change in membrane tension is sensed by these mechanosensitive channels, triggering a conformational change which opens a pore in the membrane without rupture (Fig. 12 (B)). This acts as a pressure release valve, providing a means for turgor pressure to be relieved without a potentially fatal burst. This phenomenon represents yet another system in which adaptation can be found at the molecular, evolutionary, and physiological levels. In Chapters 5 and 9 of this dissertation, we explore a fundamental question – how many mechanosensitive channels does a cell need to have an appreciable chance at surviving an osmotic shock?

     To approach this question, Heun Jin Lee and I collaborated on the experimental and data analysis components, respectively. This is a project that had been in preparation for several years before I had the privilege of joining the team in the summer of 2017. While the experimental techniques used to probe transcriptional regulation were far from simple, they pale in comparison to those employed by Heun Jin. This project required an enormous amount of molecular biology to generate the necessary strains in which the number of mechanosensitive channels could be tuned across three orders of magnitude and measured with precision. This process involved reworking classic techniques in molecular biology to remove the presence of osmotic shocks which would prove fatal for strains with few or no mechanosensitive channels. On top of the complex biochemistry, Heun Jin developed a clever microfluidic system where osmotic shocks could be imaged in real time at the single cell level. While the majority of Chapter 5 focuses on the analysis and interpretation of the data, none of it would have been possible without Heun Jin’s Herculean efforts.

     While we leave the details of the inference to Chapter 5 and the supplemental Chapter 9, the survival probability as a function of the total mechanosensitive channel number is given for “slow” and “fast” osmotic shocks in Fig. 12 (C) and (D), respectively. The credible regions in this plot illustrate that for an  ≈ 80% chance of surviving either a slow or a fast osmotic shock, at least  ≈ 500 channels are needed. This number is in agreement with recent proteomic measurements in E. coli (Li et al. 2014; Schmidt et al. 2016; Soufi et al. 2015), but are at odds with current theoretical models. While it is difficult to theoretically define a survival/death criterion, current physical models predict that only a few mechanosensitive channels (specifically MscL) are needed to relieve even large increases in membrane tension. These findings illustrate another avenue in which the disagreement between theory and careful, quantitative experiments reveal gaps in our understanding of fundamental biological phenomena.

On Molecular Biophysics and Evolutionary Dynamics

This thesis as a whole presents an attempt to understand how adaptive processes operate in biological systems at a mechanistic level beyond qualitative description. The thermodynamic model derived and explored in Chapter 2 presents a concrete theoretical framework through which we can understand how mutations and environmental perturbations influence the output of a simple genetic circuit with quantitative precision. While the work here specifically explores the mean level of gene expression of a population, I have had the privilege to be involved in several projects which explore the complete distribution of gene expression of various regulatory motifs using non-equilibrium models (Razo-Mejia et al. 2020; Laxhuber et al. 2020). Both equilibrium and non-equilibrium approaches, while differing in their fundamental assumptions of the system, can be used to understand how the regulation of gene expression occurs in vivo and should be viewed as complimentary rather than adversarial approaches.

     A combination of these types of approaches will be necessary to attack what I believe is the next great frontier of biological physics – predicting evolution. While this thesis is primarily focused on a single type of regulatory architecture regulating a single promoter via a single species of transcription factor, it is worth remembering that systems-level phenotypes are often complex and result from the concerted action of an array of biological processes. As was mentioned in our discussion on physiological adaptation, it has been known for nearly a century that the bacterial growth rate is directly correlated to the total protein content of the cell, with recent works illustrating rich phenomenology in the structure of the bacterial proteome as a whole (Li et al. 2014; Schmidt et al. 2016; Hui et al. 2015; Scott et al. 2010; Klumpp and Hwa 2014).

     In collaboration again with Nathan M. Belliveau, we have begun to explore how the composition of the bacterial proteome is structured at the single-protein level. Fig. 13 (A) shows data compiled from several independent proteomic data sets (using either quantitative mass spectrometry (Schmidt et al. 2016; Peebo et al. 2015; Valgepea et al. 2013a) or ribosomal profiling (Li et al. 2014)) where the abundance of different molecular constituents of the bacterial proteome is plotted as a function of the growth rate. These components, broken down by their functional designation according to their Cluster of Orthologous Groups (COG) annotation (Galperin et al. 2015), reveal varied dependencies on the growth rate. Of note are the COG classes “cellular processes and signaling,” “metabolism,” and “information storage and processing” which all appear to have a correlation between the cellular growth rate and the total mass of that proteome sector. However, when plotted as the total mass fraction of the proteome instead of the total mass, a striking result is observed. Fig. 13 (B) reveals a very strong, negative correlation between the mass fraction of the proteome dedicated to information storage and processing (including ribosomal and transcriptional machinery) and the proteome fraction dedicated to metabolism. This direct competition for resources between the proteins involved in translation (ribosomes, elongation factors, etc.) and metabolic networks has been shown previously (Klumpp and Hwa 2008; Scott et al. 2010; Hui et al. 2015) and suggests a strong evolutionary constraint on how resources can be optimally partitioned.

      As of this writing, our understanding of the cellular resource allocation visible in Fig. 13 remains largely phenomenological (Scott et al. 2014). This is in part due to the tremendously high-dimensional nature of systems-level organization. Our understanding of systems with such huge numbers of degrees-of-freedom have classically benefited enormously from the application of statistical mechanics as this thesis shows in the context of transcriptional regulation. The quantitative framework derived and carefully dissected in this thesis, I believe, lays the groundwork to understand how phenomena such as that shown in Fig. 13 (B) arise, and perhaps more importantly, evolve. A recent work from Michael Lässig, Ville Mustonen, and Aleksandra Walczak entitled Predicting evolution (Lässig, Mustonen, and Walczak 2017) describes what the future of evolutionary theory may look like given these types of models. Recent technological advancements in sequencing, microscopy, and computation coupled with theoretical advancements in the biophysics of gene regulation present an opportunity for a rich theoretical dialogue between molecular biophysics and evolutionary dynamics coupled with experimental dissection (Fig. 14).

     The first 20 years of the 21^st century brought a paradigm shift in our understanding of noise in biological networks, illustrating how cross-disciplinary approaches to scientific discovery can solve and even create new fields of biological inquiry (Ciechonska, Grob, and Isalan 2016; Eldar and Elowitz 2010). I hope that some of the material described in the coming chapters can help contribute to a systems-biology approach to evolution.

References