Roadmap on biology in time varying environments

Abstract

Biological organisms experience constantly changing environments, from sudden changes in physiology brought about by feeding, to the regular rising and setting of the Sun, to ecological changes over evolutionary timescales. Living organisms have evolved to thrive in this changing world but the general principles by which organisms shape and are shaped by time varying environments remain elusive. Our understanding is particularly poor in the intermediate regime with no separation of timescales, where the environment changes on the same timescale as the physiological or evolutionary response. Experiments to systematically characterize the response to dynamic environments are challenging since such environments are inherently high dimensional. This roadmap deals with the unique role played by time varying environments in biological phenomena across scales, from physiology to evolution, seeking to emphasize the commonalities and the challenges faced in this emerging area of research.

Keywords: allostery; cellular signaling; environmental dynamics; evolution; signaling dynamics; time varying environments.

Figure 1.

Signal processing by spiral node dynamics. (A) Cartoon of day–night cycles in irradiance (top) and temperature (bottom). (B) Phase plane dynamics of a symmetric spiral node. ω characterizes the angular frequency, μ characterizes the rate of decay. (C) Signal amplification by linear oscillator as a function of the relative mismatch between the natural frequency ω and the signal frequency Ω. (D) Simulated example of a regular rhythm heavily contaminated by noise at many different frequencies proposed by a spiral node network. (E) Environmental and internal factors predicted to favor increasing or decreasing the damping biological oscillators.

Figure 2.

Some cellular responses are only revealed by dynamic inputs. In steady-state experiments, the blue but not the red molecule appears to respond to the input. A dynamic input, however, shows that the red molecule responds as strongly as the blue molecule, but to the input’s time-derivative not its absolute value.

Figure 3.

Developmental and homeostatic signaling. Throughout development (A), signaling pathways (activity shown in purple) can potentiate cell fate decisions, and do so in a very deterministic and stereotyped manner. However, during homeostasis (B) and throughout the organism’s life, events such as wounding, immune responses, and programmed apoptosis in response to stressors can activate the same pathway in a nondeterministic fashion.

Figure 4.

Decoding signals into appropriate genetic outcomes. Environmental signals sensed by receptors (in blue, red, and yellow) can feed into the same pathway and cause distinct gene expression outcomes (blue, red, yellow genes). One hypothesis for how this occurs is that the conserved pathway (green) can be repurposed in its dynamics to deliver constant linear activation, oscillations of activation and inactivation, or a single transient pulse of activation, all of which are read out in distinct ways.

Figure 5.

Evolution of bnAbs. Vaccination with a single antigen produces only strain-specific Abs, whereas more complex, conflicting selection forces are required to evolve bNAbs (see main text). These conflicting selection forces frustrate the normal process of AM, and can lead to B cell death in GCs. Hence, bnAb evolution walks a fine line, requiring selection forces that are optimally imposed during vaccination.

Figure 6.

Principles gleaned from studies of AM. (A) Cocktail immunization with four antigens (solid lines; dotted lines = control), leads to high variability in binding of the produced Abs for those antigens. (B) Sequential immunization of the same antigens results in high Ab binding to all antigens. (C) Optimal frustration conditions exist for cocktail administration, including the number of antigens and mutational distance between them. Figures were adapted from references [3] (plots A, B) and [4] (plot C).

Figure 7.

(A) Illustration of Kelly’s formalism in a simple case where the environment fluctuates between two states, representing for instance the absence (x = 1, in gray) or presence (x = 2, in blue) of a pathogen. This environment is experienced by a population of reproducing individuals that can themselves be in two states, e.g., resistant (σ = 1, in gray) or not (σ = 2, in blue). At each generation t, the environment has probability p(x∣x′) to change from state x′ to state x. Each individual of the population has also a probability π(σ∣σ′) to change its state from σ′ to σ. An individual that has switched to state σ then contribute an average of f(σ, x) individuals in state σ to the next generation. The dynamics is described by equations (1) and (2). (B) The strategy π(σ∣σ′) optimizing the long-term growth rate Λ depends on the nature of the environmental fluctuations, here the frequency of the pathogen p(x = 2) and a characteristic time of environmental change t_c that we define by e^−1/t_c = 1 − p(1∣2) − p(2∣1). Taking f(σ = 1, x = 1) = 1, f(σ = 1, x = 2) = 0.3, f(σ = 2, x = 1) = 0.4, f(σ = 2, x = 2) = 1 to capture the relative costs of immunity and infection, the results show that switching between the two states σ = 1 and σ = 2 is favored only in some intermediate regime of environmental fluctuations (adapted from [58]).

Figure 8.

Scenarios of co-evolution between host and viral populations. (A) Kelly’s formalism (figure 7) is able to describe the long-time scale evolution of a population (e.g. immune receptors, black line) in response to the known albeit stochastic dynamics of a driving population (e.g. virus, red line). (B) More realistically, other environmental sources (e.g. other viral or bacterial populations, nutrient sources, the emergence of new mutants, orange line) can influence the dynamics of the driving population. (C) Additionally, the evolution of the immune system influences the evolution of the viral population, exerting feedback on its dynamics. This feedback, which is at the heart of the co-evolution problem, makes the dynamics particularly challenging to describe on long timescales.

Figure 9.

Evolve and maintain generalists via time-varying environments. (a) Generalist Abs recognize the conserved epitope of variant antigens (Ags) while specialist Abs bind well to a particular variable epitope. (b) An illustration of our approach to constructing fitness landscapes that encode how specialists and generalists are organized in Ab sequence space. Each Ag defines a distinct landscape with a distinct set of fitness islands around specialist peaks (blue and orange regions); the generalist peak remains in almost the same location across Ags (overlapping shades). (c) Cycling of sufficiently dissimilar Ags at intermediate timescales can evolve (s → g) and maintain (g → g) generalist Abs unobtainable under very fast or very slow cycling (effectively static environments). Adapted from references [48, 69].

Figure 10.

Time-varying drug sequences for slowing the evolution of resistance. (A) Drugs A and B induce reciprocal CS: adaptation to A increases sensitivity to B, and adaptation to B increases sensitivity to A. Right panel: schematic showing resistance to each drug (A, black; B, red) over time during the cyclic application of drugs A and B (see [71, 72]). (B) Left panel: an optimal drug policy uses stochastic control algorithms to assign each CS profile (i.e. a set of values that define the resistance of the population to each of N testing drugs) to a single applied drug. Policies designed to minimize long-term resistance generate aperiodic drug sequences (top right). These optimized sequences correspond to frequent periods of low resistance interspersed with rare periods of high resistance (red dots). The drugs corresponding to periods of high resistance (in this case, drug B) provide little instantaneous inhibition but steer the population to a more vulnerable future state (see [73]).

Figure 11.

(a) The chemoflux microfluidic device, in which growth of a population of cells contained in 10 μm wide chambers is continuously monitored. By flowing different media through a main flow channel, the environment inside the chambers can be quickly exchanged from one nutrient type to another, or from a condition of stress to growth. Data represents a typical response to fluctuating sugars glucose (G) and lactose (L). In the first fluctuation, cells go through a lag phase, followed by recovery to exponential growth. During the lag phase cells produce and accumulate metabolic proteins. Upon repeated fluctuations the lag phase disappears. This effect has been explained through inheritance of very long-lived lac proteins, which provide the physiological memory of the cell. (Adapted from [86]). (b) The phase diagram of optimal response strategies in fluctuating environments. Strategies are separated by solid (dashed) curves corresponding to first order (continuous) evolutionary phase transitions, with their intersections shown at the triple point and a critical point. A finite memory response is optimal exclusively under random fluctuations. (Adapted from [88]).

Figure 12.

The agn43 promoter driving the T7 RNA polymerase stochastically generates tetracycline-resistant cells, switching epigenetically between transcriptional ON and OFF states, with rate 0.1%–1% per cell division (panel a), which is visualized by a GFP reporter (panel b) [87, 89]. Single cell measurements of elongation rate dynamics (panel c) show dependence of killing efficiency on physiological stress response. (Adapted from [87].)

Figure 13.

(a) Examples of pairwise coevolving amino acids (blue) in the S1A family of serine proteases, comprising direct contacts in the tertiary structure. Data are shown on the structure of rat trypsin (PDB 3TGI). (b) Three sectors (red, green, and blue) in the S1A family, demonstrating physically connected coevolving networks within the structure. (c) A sector (blue spheres) in DHFR (PDB 1RX2), connecting the active site (marked by bound substrate, yellow stick bonds) to several distant surface sites (marked in red).

Figure 14.

(a) The spatial distribution of adaptive mutations in the PDZ domain in response to a class-switching T–2F mutation in the ligand (shown as stick bonds); green spheres mark positions harboring CN mutations. Two views of the domain (PDB 1BE9) are shown, demonstrating that CN mutations exclusively occur along allosteric networks extending through the protein structure. (b) A two-dimensional spin lattice model for a protein, with the ‘ligand’ represented by an external field acting at a single boundary node (the ‘binding site’). (c) Evolving the parameters of the spin model under conditions where the lattice must discriminate a right ligand from a wrong ligand produces a final model in which the right ligand specifically triggers an allosteric conformational change through the model protein (red nodes, with the size of the node indicating the strength of the conformational change). Data in (b) and (c) are from reference [101].

Figure 15.

Rapid evolution individual-level simulations capture the eco-evolutionary dynamics characterized by anomalous phase relationship in the experiments, e.g. (a) a transition from the conventional π/2 phase difference to the out-of-phase oscillations between predator (red) and total prey (green) densities and (b) a case with a constant total prey density [117].

Figure 16.

Illustration of collective coevolution between bacteria and viruses via HGT: (1) phages acquire beneficial (+) and inferior (−) genes from bacteria. (2) Phages have high mutation rate and create a rapidly evolving reservoir of genes for the host bacteria. (3) Bacteria create a slowly evolving, stable repository of beneficial genes for phages by filtering out inferior genes. The collective state results in emergent mutualism despite of individual antagonism.