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Resonance modulation, annihilation and generation of anti-resonance and anti-phasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics

Subthreshold (membrane potential) resonance and phasonance (preferred amplitude and zero-phase responses to oscillatory inputs) in single neurons arise from the interaction between positive and negative feedback effects provided by relatively fast amplifying currents and slower resonant currents. In 2D neuronal systems, amplifying currents are required to be slaved to voltage (instantaneously fast) for these phenomena to occur. In higher dimensional systems, additional currents operating at various effective time scales may modulate and annihilate existing resonances and generate antiresonance (minimum amplitude response) and antiphasonance (zero-phase response with phase monotonic properties opposite to phasonance). We use mathematical modeling, numerical simulations and dynamical systems tools to investigate the mechanisms underlying these phenomena in 3D linear models, which are obtained as the linearization of biophysical (conductance-based) models. We characterize the parameter regimes for which the system exhibits the various types of behavior mentioned above in the rather general case in which the underlying 2D system exhibits resonance. We consider two cases: (i) the interplay of two resonant gating variables, and (ii) the interplay of one resonant and one amplifying gating variables. Increasing levels of an amplifying current cause (i) a response amplification if the amplifying current is faster than the resonant current, (ii) resonance and phasonance attenuation and annihilation if the amplifying and resonant currents have identical dynamics, and (iii) antiresonance and antiphasonance if the amplifying current is slower than the resonant current. We investigate the underlying mechanisms by extending the envelope-plane diagram approach developed in previous work (for 2D systems) to three dimensions to include the additional gating variable, and constructing the corresponding envelope curves in these envelope-space diagrams. We find that antiresonance and antiphasonance emerge as the result of an asymptotic boundary layer problem in the frequency domain created by the different balances between the intrinsic time constants of the cell and the input frequency f as it changes. For large enough values of f the envelope curves are quasi-2D and the impedance profile decrease with the input frequency. In contrast, for f << 1 the dynamics is quasi-1D and the impedance profile increases above the limiting value in the other regime. Antiresonance is created because the continuity of the solution requires the impedance profile to connect the portions belonging to the two regimes. If in doing so the phase profile crosses the zero value, then antiphasonance is also generated.

neuroscience

Precise Quantification of Translation Inhibition by mRNA Structures that Overlap with the Ribosomal Footprint in N-terminal Coding Sequences

A mRNAs translation rate is controlled by several sequence determinants, including the presence of RNA structures within the N-terminal regions of its coding sequences. However, the physical rules that govern when such mRNA structures will inhibit translation remain unclear. Here, we introduced systematically designed RNA hairpins into the N-terminal coding region of a reporter protein with steadily increasing distances from the start codon, followed by characterization of their mRNA and expression levels in E. coli. We found that the mRNAs; translation rates were repressed, by up to 1410-fold, when mRNA structures overlapped with the ribosomes footprint. In contrast, when the mRNA structure was located outside the ribosomes footprint, translation was repressed by less than 2-fold. By combining our measurements with biophysical modeling, we determined that the ribosomal footprint extends 13 nucleotides into the N-terminal coding region and, when a mRNA structure overlaps or partially overlaps with the ribosomal footprint, the free energy to unfold only the overlapping structure controlled the extent of translation repression. Overall, our results provide precise quantification of the rules governing translation initiation at N-terminal coding regions, improving the predictive design of post-transcriptional regulatory elements that regulate translation rate.

genetics

Heterogeneous firing responses predict diverse couplings to presynaptic activity in mice layer V pyramidal neurons

In this study, we present a theoretical framework combining experimental characterizations and analytical calculus to capture the firing rate input-output properties of single neurons in the fluctuation-driven regime. Our framework consists of a two-step procedure to treat independently how the dendritic input translates into somatic fluctuation variables, and how the latter determine action potential firing. We use this framework to investigate the functional impact of the heterogeneity in firing responses found experimentally in young mice layer V pyramidal cells. We first design and calibrate in vitro a simplified morphological model of layer V pyramidal neurons with a dendritic tree following Rall's branching rule. Then, we propose an analytical derivation for the membrane potential fluctuations at the soma as a function of the properties of the synaptic input in dendrites. This mathematical description allows us to easily emulate various forms of synaptic input: either balanced, unbalanced, synchronized, purely proximal or purely distal synaptic activity. We find that those different forms of input activity lead to various impact on the membrane potential fluctuations properties, thus raising the possibility that individual neurons will differentially couple to specific forms of activity as a result of their different firing response. We indeed found such a heterogeneous coupling between synaptic input and firing response for all types of presynaptic activity. This heterogeneity can be explained by different levels of cellular excitability in the case of the balanced, unbalanced, synchronized and purely distal activity. A notable exception appears for proximal dendritic inputs: increasing the input level can either promote firing response in some cells, or suppress it in some other cells whatever their individual excitability. This behavior can be explained by different sensitivities to the speed of the fluctuations, which was previously associated to different levels of sodium channel inactivation and density. Because local network connectivity rather targets proximal dendrites, our results suggest that this aspect of biophysical heterogeneity might be relevant to neocortical processing by controlling how individual neurons couple to local network activity.

neuroscience

Evolutionary variations in the biofilm-associated protein BslA from the genus Bacillus

BslA is a protein secreted by Bacillus subtilis which forms a hydrophobic film that coats the biofilm surface and renders it water-repellent. We have characterised three orthologues of BslA from Bacillus amyloliquefaciens, Bacillus licheniformis and Bacillus pumilus as well as a paralogue from B. subtilis called YweA. We find that the three orthologous proteins can substitute for BslA in B. subtilis and confer a degree of protection, whereas YweA cannot. The degree to which the proteins functionally substitute for native BslA correlates with their in vitro biophysical properties. Our results demonstrate the use of naturally-evolved variants to provide a framework for teasing out the molecular basis of interfacial self-assembly.

microbiology

ISCA1 and CRY4: An improbable proposition

This manuscript was submitted to Nature Materials on December 15th 2015.\n\nIn their recent manuscript Xie and colleagues argue that the pigeon ISCA1/CRY4 complex acts as a magnetic protein biocompass having unambiguously proved that these two proteins interact forming a complex with unique biophysical features (1). We do not think the evidence presented in the manuscript supports this conclusion. Firstly, the authors provide no data (such as a reciprocal co-immunoprecipitation from retinal tissue) that demonstrates that ISCA1 and CRY4 interact in vivo, instead the conclusions are based primarily on overexpression in E.coli and in vitro reconstitution experiments. Secondly, their experiments have not employed the correct full length version of CRY4. The CRY4 protein expressed by Xie and colleagues was only 497 amino acids in length. We extracted mRNA from the pigeon retina (Invitrogen, 610.11), generated cDNA (Clontech, 121311), and performed rap ...

animal behavior and cognition

Familial Mutations and Post-translational Modifications of UCH-L1 in Parkinson’s Disease and Neurodegenerative Disorders

Parkinsons disease (PD) is one of the most common progressive neurodegenerative disorders in modern society. The disease involves many genetic risk factors as well as a sporadic pathogenesis that is age- and environment-dependent. Of particular interest is the formation of intra-neural fibrillar aggregates, namely Lewy bodies (LBs), the histological hallmark of PD, which results from aberrant protein homeostasis or misfolding that results in neurotoxicity. A better understanding of the molecular mechanism and composition of these cellular inclusions will help shed light on the progression of misfolding-associated neurodegenerative disorders. Ubiquitin carbonyl-terminal hydrolase L1 (UCH-L1) is found to co-aggregate with -synuclein (S), the major component of LBs. Several familial mutations of UCH-L1, namely p.Ile93Met (p.I93M), p.Glu7Ala (p.E7A), and p.Ser18Tyr (p.S18Y), are associated with PD and other neurodegenerative disorders. Here, we review recent progress and recapitulate the impact of PD-associated mutations of UCH-L1 in the context of their biological functions gleaned from biochemical and biophysical studies. Finally, we summarize the effect of these genetic mutations and post-translational modifications on the association of UCH-L1 and PD in terms of loss of cellular functions or gain of cellular toxicity.

biochemistry

Fusing tree-ring and forest inventory data to infer influences on tree growth

Better understanding and prediction of tree growth is important because of the many ecosystem services provided by forests and the uncertainty surrounding how forests will respond to anthropogenic climate change. With the ultimate goal of improving models of forest dynamics, here we construct a statistical model that combines complementary data sources - tree-ring and forest inventory data. A Bayesian hierarchical model is used to gain inference on the effects of many factors on tree growth - individual tree size, climate, biophysical conditions, stand-level competitive environment, tree-level canopy status, and forest management treatments - using both diameter at breast height (DBH) and tree-ring data. The model consists of two multiple regression models, one each for the two data sources, linked via a constant of proportionality between coefficients that are found in parallel in the two regressions. The model was applied to a dataset developed at a single, well-studied site in the Jemez Mountains of north-central New Mexico, U. S. A. Inferences from the model included positive effects of seasonal precipitation, wetness index, and height ratio, and negative effects of seasonal temperature, southerly aspect and radiation, and plot basal area. Climatic effects inferred by the model compared well to results from a dendroclimatic analysis. Combining the two data sources did not lead to higher predictive accuracy (using the leave-one-out information criterion, LOOIC), either when there was a large number of increment cores (129) or under a reduced data scenario of 15 increment cores. However, there was a clear advantage, in terms of parameter estimates, to the use of both data sources under the reduced data scenario: DBH remeasurement data for ~500 trees substantially reduced uncertainty about non-climate fixed effects on radial increments. We discuss the kinds of research questions that might be addressed when the high-resolution information on climate effects contained in tree rings are combined with the rich metadata on tree- and stand-level conditions found in forest inventories, including carbon accounting and projection of tree growth and forest dynamics under future climate scenarios.

ecology

In vitro reconstitution of T cell receptor-mediated segregation of the CD45 phosphatase

T cell signaling initiates upon binding of peptide-major histocompatibility complex (pMHC) on an antigen-presenting cell (APC) to the T cell receptor (TCR) on a T cell. TCR phosphorylation in response to pMHC binding is accompanied by segregation of the transmembrane phosphatase CD45 away from TCR-pMHC complexes. The kinetic segregation hypothesis proposes that CD45 exclusion shifts the local kinase-phosphatase balance to favor TCR phosphorylation. Spatial partitioning may arise from the size difference between the large CD45 extracellular domain and the smaller TCR-pMHC complex, although parsing potential contributions of extracellular protein size, actin activity, and lipid domains is difficult in living cells. Here, we reconstitute segregation of CD45 from bound receptor-ligand pairs using purified proteins on model membranes. Using a model receptor-ligand pair (FRB-FKBP), we first test physical and computational predictions for protein organization at membrane interfaces. We then show that the TCR-pMHC interaction causes partial exclusion of CD45. Comparing two developmentally-regulated isoforms of CD45, the larger RABC variant is excluded more rapidly and efficiently (~50%) than the smaller R0 isoform (~20%), suggesting that CD45 isotypes could regulate signaling thresholds in different T cell subtypes. Similar to the sensitivity of T cell signaling, TCR-pMHC interactions with Kds of [&le;]15 M were needed to exclude CD45. We further show that the co-receptor PD-1 with its ligand PD-L1, immunotherapy targets that inhibit T cell signaling, also exclude CD45. These results demonstrate that the binding energies of physiological receptor-ligand pairs on the T cell are sufficient to create spatial organization at membrane-membrane interfaces.\n\nSIGNIFICANCE STATEMENTThe interface between a T cell and an antigen-presenting cell (APC) results in the formation of biochemically distinct plasma membrane domains that initiate signaling cascades. Here, using biochemical reconstitution and microscopy, we show that the binding energies of the TCRpMHC and PD-1-PD-L1 complexes are sufficient to create spatial organization at a model membrane-membrane interface. We show that spatial organization depends upon receptor-ligand binding affinity and the relative sizes of the extracellular domains. These biophysical parameters may be used to fine-tune signaling cascades in T cells.

immunology

Encoding variable cortical states with short-term spikepatterns

Neurons in the primary somatosensory cortex (S1) respond to peripheral stimulation with synchronised bursts of spikes, which lock to the macroscopic 600 Hz EEG waves. The mechanism of burst generation and synchronisation in S1 is not yet understood. Using models of single-neuron responses fitted to unit recordings from macaque monkeys, we show that these synchronised bursts are the consequence of correlated synaptic inputs combined with a refractory mechanism. In the presence of noise these models reproduce also the observed trial-to-trial response variability, where individual bursts represent one of many stereotypical temporal spike patterns. When additional slower and global excitability fluctuations are introduced the single-neuron spike patterns are correlated with the population activity, as demonstrated in experimental data. The underlying biophysical mechanism of S1 responses involves thalamic inputs arriving through depressing synapses to cortical neurons in a high-conductance state. Our findings show that a simple feedforward processing of peripheral inputs could give rise to neuronal responses with non-trivial temporal and population statistics. We conclude that neural systems could use refractoriness to encode variable cortical states into stereotypical short-term spike patterns amenable to processing at neuronal time scales (tens of milliseconds).\n\nSignificance statementNeurons in the hand area of the primary somatosensory cortex respond to repeated presentation of the same stimulus with variable sequences of spikes, which can be grouped into distinct temporal spike patterns. In a simplified model, we show that such spike patterns are product of synaptic inputs and intrinsic neural properties. This model can reproduce both single-neuron and population responses only when a private variability in each neuron is combined with a multiplicative gain shared over whole population, which fluctuates over trials and might represent the dynamical state of the early stages of sensory processing. This phenomenon exemplifies a general mechanism of transforming the ensemble cortical states into precise temporal spike patterns at the level of single neurons.

neuroscience

Effects of altered excitation-inhibition balance on decision making in a cortical circuit model

BackgroundDisruption of the synaptic balance between excitation and inhibition (E/I balance) in cortical circuits is a leading hypothesis for pathophysiologies of neuropsychiatric disorders, such as schizophrenia. However, it is poorly understood how synaptic E/I disruptions propagate upward to induce cognitive deficits, including impaired decision making (DM).\n\nMethodsWe investigated how E/I perturbations may impair temporal integration of evidence during perceptual DM in a biophysically-based model of association cortical microcircuits. Using multiple psychophysical task paradigms, we characterized effects of NMDA receptor hypofunction at two key synaptic sites: inhibitory interneurons (elevating E/I ratio, via disinhibition), versus excitatory pyramidal neurons (lowering E/I ratio).\n\nResultsDisruption of E/I balance in either direction can similarly impair DM as assessed by psychometric performance, following inverted-U dependence. Nonetheless, these regimes make dissociable predictions for task paradigms that characterize the time course of evidence accumulation. Under elevated E/I ratio, DM is impulsive: evidence early in time is weighted much more than late evidence. In contrast, under lowered E/I ratio, DM is indecisive: evidence integration and winner-take-all competition between options are weakened. These effects are well captured by an extended drift-diffusion model with self-coupling.\n\nConclusionsOur findings characterize critical roles of cortical E/I balance in cognitive functions, the utility of timing-sensitive psychophysical paradigms, and relationships between circuit and psychological models. The model makes specific predictions for behavior and neural activity that are testable in humans or animals under causal manipulations of E/I balance and in disease states.

neuroscience

Tuning of recombinant protein expression in Escherichia coli by manipulating transcription, translation initiation rates and incorporation of non-canonical amino acids

Protein synthesis in cells has been thoroughly investigated and characterized over the past 60 years. However, some fundamental issues remain unresolved, including the reasons for genetic code redundancy and codon bias. In this study, we changed the kinetics of the E. coli transcription and translation processes by mutating the promoter and ribosome binding domains and by using genetic code expansion. The results expose a counterintuitive phenomenon, whereby an increase in the initiation rates of transcription and translation lead to a decrease in protein expression. This effect can be rescued by introducing slow translating codons into the beginning of the gene, by shortening gene length or by reducing initiation rates. Based on the results, we developed a biophysical model, which suggests that the density of co-transcriptional translation plays a role in bacterial protein synthesis. These findings indicate how cells use codon bias to tune translation speed and protein synthesis.

synthetic biology

Ultrasound elicits behavioral responses through mechanical effects on neurons and ion channels in a simple nervous system

Focused ultrasound has been shown to stimulate excitable cells, but the biophysical mechanisms behind this phenomenon remain poorly understood. To provide additional insight, we devised a behavioral-genetic assay applied to the well-characterized nervous system of C. elegans nematodes. We found that pulsed ultrasound elicits robust reversal behavior in wild-type animals in a pressure-, duration-, and pulse protocol-dependent manner. Responses were preserved in mutants unable to sense thermal fluctuations and absent in mutants lacking neurons required for mechanosensation. Additionally, we found that the worm s response to ultrasound pulses rests on the expression of MEC-4, a DEG/ENaC/ASIC ion channel required for touch sensation. Consistent with prior studies of MEC-4-dependent currents in vivo, the worms response was optimal for pulses repeated 300 to 1000 times per second. Based on these findings, we conclude that mechanical, rather than thermal stimulation accounts for behavioral responses. Further, we propose that acoustic radiation force governs the response to ultrasound in a manner that depends on the touch receptor neurons and MEC-4-dependent ion channels. Our findings illuminate a complete pathway of ultrasound action, from the forces generated by propagating ultrasound to an activation of a specific ion channel. The findings further highlight the importance of optimizing ultrasound pulsing protocols when stimulating neurons via ion channels with mechanosensitive properties.\n\nSignificance StatementHow ultrasound influences neurons and other excitable cells has remained a mystery for decades. Although it is widely understood that ultrasound can heat tissues and induce mechanical strain, whether or not neuronal activation depends on heat, mechanical force, or both physical factors is not known. We harnessed C. elegans nematodes and their extraordinary sensitivity to thermal and mechanical stimuli to address this question. Whereas thermosensory mutants respond to ultrasound similar to wild-type animals, mechanosensory mutants were insensitive to ultrasound stimulation. Additionally, stimulus parameters that accentuate mechanical effects were more effective than those producing more heat. These findings highlight a mechanical nature of the effect of ultrasound on neurons and suggest specific ways to optimize stimulation protocols in specific tissues.

neuroscience

Working memory and decision making in a fronto-parietal circuit model

Working memory (WM) and decision making (DM) are fundamental cognitive functions involving a distributed interacting network of brain areas, with the posterior parietal and prefrontal cortices (PPC and PFC) at the core. However, the shared and distinct roles of these areas and the nature of their coordination in cognitive function remain poorly understood. Biophysically-based computational models of cortical circuits have provided insights into the mechanisms supporting these functions, yet they have primarily focused on the local microcircuit level, raising questions about the principles for distributed cognitive computation in multi-regional networks. To examine these issues, we developed a distributed circuit model of two reciprocally interacting modules representing PPC and PFC circuits. The circuit architecture includes hierarchical differences in local recurrent structure and implements reciprocal long-range projections. This parsimonious model captures a range of behavioral and neuronal features of fronto-parietal circuits across multiple WM and DM paradigms. In the context of WM, both areas exhibit persistent activity, but in response to intervening distractors, PPC transiently encodes distractors, while PFC filters distractors and supports WM robustness. With regards to DM, the PPC module generates graded representations of accumulated evidence supporting target selection, while the PFC module generates more categorical responses related to action or choice. These findings suggest computational principles for distributed, hierarchical processing in cortex during cognitive function, and provide a framework for extension to multi-regional models.

neuroscience

The Dense-Core Vesicle Maturation Protein CCCP-1 Binds both RAB-2 and Membranes through a Conserved C-terminal Coiled-coil Domain

Dense-core vesicles (DCVs) are secretory organelles that store and release modulatory neurotransmitters from neurons and endocrine cells. Recently, the conserved coiled-coil protein CCCP-1 was identified as a component of the DCV biogenesis pathway in the nematode C. elegans. CCCP-1 binds the small GTPase RAB-2 and colocalizes with it at the trans-Golgi. Here we report a structure-function analysis of CCCP-1 to identify domains of the protein important for its localization, binding to RAB-2, and function in DCV biogenesis. We find that the CCCP-1 C-terminal domain (CC3) has multiple activities. CC3 is necessary and sufficient for CCCP-1 localization and for binding to RAB-2, and is required for the function of CCCP-1 in DCV biogenesis. Additionally, CCCP-1 binds membranes directly through its CC3 domain, indicating that CC3 may comprise a previously uncharacterized lipid-binding motif. We conclude that CCCP-1 is a coiled-coil protein that binds an activated Rab and localizes to the Golgi via its C-terminus, properties similar to members of the golgin family of proteins. CCCP-1 also shares biophysical features with golgins; it has an elongated shape and forms oligomers.\n\nSynopsis statementCCCP-1 is a coiled-coil protein important for dense-core vesicle (DCV) biogenesis. A structure-function analysis of CCCP-1 shows that its C-terminal domain is required for (1) localization to membrane compartments near the trans-Golgi, (2) binding to activated RAB-2, (3) function in DCV biogenesis, and (4) direct binding to membranes. CCCP-1 has an elongated shape and forms oligomers. These findings suggest that CCCP-1 resembles members of the golgin family of proteins that act as membrane tethers.

biochemistry

Plaques formed by mutagenized viral populations have elevated co-infection frequencies

The plaque assay is a common technique used to measure virus concentrations and is based upon the principle that each plaque represents a single infectious unit. As such, plaque number is expected to correlate linearly with the virus dilution plated and each plaque should be formed by a single founder virus. Here, we examined whether more than one virus can contribute to plaque formation. By using genetic and phenotypic assays with genetically marked polioviruses, we found that multiple parental viruses are present in 5-7% of plaques, even at an extremely low multiplicity of infection. We demonstrated through visual and biophysical assays that, like many viral stocks, our viral stocks contain both single particles and aggregates. These data suggest that aggregated virions are capable of inducing co-infection and chimeric plaque formation. In fact, inducing virion aggregation via exposure to low pH increased co-infection in a flow cytometry-based assay. We hypothesized that plaques generated by viruses with high mutation loads may have higher co-infection frequencies due to fitness restoring processes such as complementation and recombination. Indeed, we found that co-infection frequency correlated with mutation load, with 17% chimeric plaque formation for heavily mutagenized viruses. Importantly, the frequency of chimeric plaques may be underestimated by up to three-fold, since co-infection with the same parental virus cannot be scored in our assay. This work indicates that more than one virus can contribute to plaque formation and that co-infection may assist plaque formation in situations where the amount of genome damage is high.

microbiology

Intracellular production of hydrogels and synthetic RNA granules by multivalent enhancers

Non-membrane bound, hydrogel-like entities, such as RNA granules, nucleate essential cellular functions through their unique physico-chemical properties. However, these intracellular hydrogels have not been as extensively studied as their extracellular counterparts, primarily due to technical challenges in probing these materials in situ. Here, by taking advantage of a chemically inducible dimerization paradigm, we developed iPOLYMER, a strategy for rapid induction of protein-based hydrogels inside living cells. A series of biochemical and biophysical characterizations, in conjunction with computational modeling, revealed that the polymer network formed in the cytosol resembles a physiological hydrogel-like entity that behaves as a size-dependent molecular sieve. We studied several properties of the gel and functionalized it with RNA binding motifs that sequester polyadenine-containing nucleotides to synthetically mimic RNA granules. Therefore, we here demonstrate that iPOLYMER presents a unique and powerful approach to synthetically reconstitute hydrogel-like structures including RNA granules in intact cells.

synthetic biology

Estimating The Contribution Of Folding Stability To Non-Specific Epistasis In Protein Evolution

The extent of non-additive interaction among mutations or epistasis reflects the ruggedness of the fitness landscape, the mapping of genotype to reproductive fitness. In protein evolution, there is strong support for the importance and prevalence of epistasis, but whether there is a universal mechanism behind epistasis remains unknown. It is also unclear which of the biophysical properties of proteins--folding stability, activity, binding affinity, and dynamics--have the strongest contribution to epistasis. Here, we determine the contribution of selection for folding stability to epistasis in protein evolution. By combining theoretical estimates of the rates of molecular evolution and protein folding thermodynamics, we show that simple selection for folding stability implies that at least ~30% to ~60% of among amino acid substitutions would have experienced epistasis. Additionally, our model predicts substantial epistasis at marginal stabilities therefore linking epistasis to the strength of selection. Estimating the contribution of governing factors in molecular evolution such as protein folding stability to epistasis will provide a better understanding of epistasis that could improve methods in molecular evolution.

genetics

Pairwise Hybrid Incompatibilities Dominate During Allopatric Speciation For A Simple Genotype-Phenotype Map Of Embryonic Spatial Patterning

Developmental system drift is a likely mechanism for the origin of hybrid incompatibilities between closely related species. We examine here the detailed mechanistic basis of hybrid incompatibilities for a genotype-phenotype map for developmental system drift under stabilising selection, where the organismal phenotype is conserved, but the underlying molecular phenotypes and genotype can drift. This leads to number of emergent phenomenon not obtainable by modelling genotype or phenotype alone. Our results show that: 1) speciation is more rapid at smaller population sizes with a characteristic, Orr-like, power law, but at large population sizes slow, characterised by a sub-diffusive growth law; 2) the molecular phenotypes under weakest selection contribute to the earliest incompatibilities; and 3) pairwise incompatibilities dominate over higher order, contrary to previous predictions that the latter should dominate. Our results indicate that biophysics and population size provide a much stronger constraint to speciation than suggested by previous models.

evolutionary biology