Molecular mechanisms of precise timing in cell lysis.

Many biological systems exhibit precise timing of events, and one of the most known examples is cell lysis, which is a process of breaking bacterial host cells in the virus infection cycle. However, the underlying microscopic picture of precise timing remains not well understood. We present a novel theoretical approach to explain the molecular mechanisms of effectively deterministic dynamics in biological systems. Our hypothesis is based on the idea of stochastic coupling between relevant underlying biophysical and biochemical processes that lead to noise cancellation. To test this hypothesis, we introduced a minimal discrete-state stochastic model to investigate how holin proteins produced by bacteriophages break the inner membranes of gram-negative bacteria. By explicitly solving this model, the dynamic properties of cell lysis are fully evaluated, and theoretical predictions quantitatively agree with available experimental data for both wild-type and holin mutants. It is found that the observed threshold-like behavior is a result of the balance between holin proteins entering the membrane and leaving the membrane during the lysis. Theoretical analysis suggests that the cell lysis achieves precise timing for wild-type species by maximizing the number of holins in the membrane and narrowing their spatial distribution. In contrast, for mutated species, these conditions are not satisfied. Our theoretical approach presents a possible molecular picture of precise dynamic regulation in intrinsically random biological processes.

Chemoinformatics Insights on Molecular Jackhammers and Cancer Cells.

One of the most challenging tasks in modern medicine is to find novel efficient cancer therapeutic methods with minimal side effects. The recent discovery of several classes of organic molecules known as "molecular jackhammers" is a promising development in this direction. It is known that these molecules can directly target and eliminate cancer cells with no impact on healthy tissues. However, the underlying microscopic picture remains poorly understood. We present a study that utilizes theoretical analysis together with experimental measurements to clarify the microscopic aspects of jackhammers' anticancer activities. Our physical-chemical approach combines statistical analysis with chemoinformatics methods to design and optimize molecular jackhammers. By correlating specific physical-chemical properties of these molecules with their abilities to kill cancer cells, several important structural features are identified and discussed. Although our theoretical analysis enhances understanding of the molecular interactions of jackhammers, it also highlights the need for further research to comprehensively elucidate their mechanisms and to develop a robust physical-chemical framework for the rational design of targeted anticancer drugs.

Unraveling the role of physicochemical differences in predicting protein-protein interactions.

The ability to accurately predict protein-protein interactions is critically important for understanding major cellular processes. However, current experimental and computational approaches for identifying them are technically very challenging and still have limited success. We propose a new computational method for predicting protein-protein interactions using only primary sequence information. It utilizes the concept of physicochemical similarity to determine which interactions will most likely occur. In our approach, the physicochemical features of proteins are extracted using bioinformatics tools for different organisms. Then they are utilized in a machine-learning method to identify successful protein-protein interactions via correlation analysis. It was found that the most important property that correlates most with the protein-protein interactions for all studied organisms is dipeptide amino acid composition (the frequency of specific amino acid pairs in a protein sequence). While current approaches often overlook the specificity of protein-protein interactions with different organisms, our method yields context-specific features that determine protein-protein interactions. The analysis is specifically applied to the bacterial two-component system that includes histidine kinase and transcriptional response regulators, as well as to the barnase-barstar complex, demonstrating the method's versatility across different biological systems. Our approach can be applied to predict protein-protein interactions in any biological system, providing an important tool for investigating complex biological processes' mechanisms.

Theoretical understanding of evolutionary dynamics on inhomogeneous networks.

Evolution is the main feature of all biological systems that allows populations to change their characteristics over successive generations. A powerful approach to understand evolutionary dynamics is to investigate fixation probabilities and fixation times of novel mutations on networks that mimic biological populations. It is now well established that the structure of such networks can have dramatic effects on evolutionary dynamics. In particular, there are population structures that might amplify the fixation probabilities while simultaneously delaying the fixation events. However, the microscopic origins of such complex evolutionary dynamics remain not well understood. We present here a theoretical investigation of the microscopic mechanisms of mutation fixation processes on inhomogeneous networks. It views evolutionary dynamics as a set of stochastic transitions between discrete states specified by different numbers of mutated cells. By specifically considering star networks, we obtain a comprehensive description of evolutionary dynamics. Our approach allows us to employ physics-inspired free-energy landscape arguments to explain the observed trends in fixation times and fixation probabilities, providing a better microscopic understanding of evolutionary dynamics in complex systems.

Predicting Antimicrobial Activity for Untested Peptide-Based Drugs Using Collaborative Filtering and Link Prediction.

The increase of bacterial resistance to currently available antibiotics has underlined the urgent need to develop new antibiotic drugs. Antimicrobial peptides (AMPs), alone or in combination with other peptides and/or existing antibiotics, have emerged as promising candidates for this task. However, given that there are thousands of known AMPs and an even larger number can be synthesized, it is impossible to comprehensively test all of them using standard wet lab experimental methods. These observations stimulated an application of machine-learning methods to identify promising AMPs. Currently, machine learning studies combine very different bacteria without considering bacteria-specific features or interactions with AMPs. In addition, the sparsity of current AMP data sets disqualifies the application of traditional machine-learning methods or makes the results unreliable. Here, we present a new approach, featuring neighborhood-based collaborative filtering, to predict with high accuracy a given bacteria's response to untested AMPs based on similarities between bacterial responses. Furthermore, we also developed a complementary bacteria-specific link prediction approach that can be used to visualize networks of AMP-antibiotic combinations, enabling us to propose new combinations that are likely to be effective.

Bacteria-Specific Feature Selection for Enhanced Antimicrobial Peptide Activity Predictions Using Machine-Learning Methods.

There are several classes of short peptide molecules, known as antimicrobial peptides (AMPs), which are produced during the immune responses of living organisms against various infections. In recent years, substantial progress has been achieved in applying machine-learning methods to predict the activities of AMPs against bacteria. In most investigated cases, however, the outcome is not bacterium-specific since the specific features of bacteria, such as chemical composition and structure of membranes, are not considered. To overcome this problem, we developed a new computational approach that allowed us to train several supervised machine-learning models using a specific set of data associated with peptides targeting E. coli bacteria. LASSO regression and Support Vector Machine techniques have been utilized to select, among more than 1500 physicochemical descriptors, the most important features that can be used to classify a peptide as antimicrobial or ineffective against E. coli. We then performed the classification of active versus inactive AMPs using the Support Vector classifiers, Logistic Regression, and Random Forest methods. This computational study allows us to make recommendations of how to design more efficient antibacterial drug therapies.

Optimal pathways control fixation of multiple mutations during cancer initiation.

Cancer starts after initially healthy tissue cells accumulate several specific mutations or other genetic alterations. The dynamics of tumor formation is a very complex phenomenon due to multiple involved biochemical and biophysical processes. It leads to a very large number of possible pathways on the road to final fixation of all mutations that marks the beginning of the cancer, complicating the understanding of microscopic mechanisms of tumor formation. We present a new theoretical framework of analyzing the cancer initiation dynamics by exploring the properties of effective free-energy landscape of the process. It is argued that although there are many possible pathways for the fixation of all mutations in the system, there are only a few dominating pathways on the road to tumor formation. The theoretical approach is explicitly tested in the system with only two mutations using analytical calculations and Monte Carlo computer simulations. Excellent agreement with theoretical predictions is found for a large range of parameters, supporting our hypothesis and allowing us to better understand the mechanisms of cancer initiation. Our theoretical approach clarifies some important aspects of microscopic processes that lead to tumor formation.

The role of spatial structures of tissues in cancer initiation dynamics.

It is widely believed that biological tissues evolved to lower the risks of cancer development. One of the specific ways to minimize the chances of tumor formation comes from proper spatial organization of tissues. However, the microscopic mechanisms of underlying processes remain not fully understood. We present a theoretical investigation on the role of spatial structures in cancer initiation dynamics. In our approach, the dynamics of single mutation fixations are analyzed using analytical calculations and computer simulations by mapping them to Moran processes on graphs with different connectivity that mimic various spatial structures. It is found that while the fixation probability is not affected by modifying the spatial structures of the tissues, the fixation times can change dramatically. The slowest dynamics is observed in 'quasi-one-dimensional' structures, while the fastest dynamics is observed in 'quasi-three-dimensional' structures. Theoretical calculations also suggest that there is a critical value of the degree of graph connectivity, which mimics the spatial dimension of the tissue structure, above which the spatial structure of the tissue has no effect on the mutation fixation dynamics. An effective discrete-state stochastic model of cancer initiation is utilized to explain our theoretical results and predictions. Our theoretical analysis clarifies some important aspects on the role of the tissue spatial structures in the cancer initiation processes.

Temporal order of mutations influences cancer initiation dynamics.

Cancer is a set of genetic diseases that are driven by mutations. It was recently discovered that the temporal order of genetic mutations affects the cancer evolution and even the nature of the decease itself. The mechanistic origin of these observations, however, remain not well understood. Here we present a theoretical model for cancer initiation dynamics that allows us to quantify the impact of the temporal order of mutations. In our approach, the cancer initiation process is viewed as a set of stochastic transitions between discrete states defined by the different numbers of mutated cells. Using a first-passage analysis, probabilities and times before the cancer initiation are explicitly evaluated for two alternative sequences of two mutations. It is found that the probability of cancer initiation is determined only by the first mutation, while the dynamics depends on both mutations. In addition, it is shown that the acquisition of a mutation with higher fitness before mutation with lower fitness increases the probability of the tumor formation but delays the cancer initiation. Theoretical results are explained using effective free-energy landscapes.

Relaxation Times of Ligand-Receptor Complex Formation Control T Cell Activation.

One of the most important functions of immune T cells is to recognize the presence of the pathogen-derived ligands and to quickly respond to them while at the same time not responding to its own ligands. This is known as absolute discrimination, and it is one of the most challenging phenomena to explain. The effectiveness of pathogen detection by T cell receptor is limited by chemical similarity of foreign and self-peptides and very low concentrations of foreign ligands. We propose a new mechanism of how absolute discrimination by T cells might function. It is suggested that the decision to activate or not to activate the immune response is controlled by the time to reach the stationary concentration of the T-cell-receptor-ligand-activated complex, which transfers the signal to downstream cellular biochemical networks. Our theoretical method models T cell receptor phosphorylation events as a sequence of stochastic transitions between discrete biochemical states, and this allows us to explicitly describe the dynamical properties of the system. It is found that the proposed criterion on the relaxation times is able to explain available experimental observations. In addition, we suggest that the level of stochastic noise might be an additional factor in the activation mechanisms. Furthermore, our theoretical approach explicitly analyzes the relationships between speed, sensitivity, and specificity of T cell functioning, which are the main characteristics of the process. Thus, it clarifies the molecular picture of T cell activation in immune response.

Dynamics of translation can determine the spatial organization of membrane-bound proteins and their mRNA.

Unlike most macromolecules that are homogeneously distributed in the bacterial cell, mRNAs that encode inner-membrane proteins can be concentrated near the inner membrane. Cotranslational insertion of the nascent peptide into the membrane brings the translating ribosome and the mRNA close to the membrane. This suggests that kinetic properties of translation can determine the spatial organization of these mRNAs and proteins, which can be modulated through posttranscriptional regulation. Here we use a simple stochastic model of translation to characterize the effect of mRNA properties on the dynamics and statistics of its spatial distribution. We show that a combination of the rate of translation initiation, the availability of secretory apparatuses, and the composition of the coding region determines the abundance of mRNAs near the membrane, as well as their residence time. We propose that the spatiotemporal dynamics of mRNAs can give rise to protein clusters on the membrane and determine their size distribution.

Physical-chemical mechanisms of pattern formation during gastrulation.

Gastrulation is a fundamental phase during the biological development of most animals when a single layer of identical embryo cells is transformed into a three-layer structure, from which the organs start to develop. Despite a remarkable progress in quantifying the gastrulation processes, molecular mechanisms of these processes remain not well understood. Here we theoretically investigate early spatial patterning in a geometrically confined colony of embryonic stem cells. Using a reaction-diffusion model, a role of Bone-Morphogenetic Protein 4 (BMP4) signaling pathway in gastrulation is specifically analyzed. Our results show that for slow diffusion rates of BMP4 molecules, a new length scale appears, which is independent of the size of the system. This length scale separates the central region of the colony with uniform low concentrations of BMP molecules from the region near the colony edge where the concentration of signaling molecules is elevated. The roles of different components of the signaling pathway are also explained. Theoretical results are consistent with recent in vitro experiments, providing microscopic explanations for some features of early embryonic spatial patterning. Physical-chemical mechanisms of these processes are discussed.

Sub-cellular mRNA localization modulates the regulation of gene expression by small RNAs in bacteria.

Small non-coding RNAs can exert significant regulatory activity on gene expression in bacteria. In recent years, substantial progress has been made in understanding bacterial gene expression by sRNAs. However, recent findings that demonstrate that families of mRNAs show non-trivial sub-cellular distributions raise the question of how localization may affect the regulatory activity of sRNAs. Here we address this question within a simple mathematical model. We show that the non-uniform spatial distributions of mRNA can alter the threshold-linear response that characterizes sRNAs that act stoichiometrically, and modulate the hierarchy among targets co-regulated by the same sRNA. We also identify conditions where the sub-cellular organization of cofactors in the sRNA pathway can induce spatial heterogeneity on sRNA targets. Our results suggest that under certain conditions, interpretation and modeling of natural and synthetic gene regulatory circuits need to take into account the spatial organization of the transcripts of participating genes.

The role of source delocalization in the development of morphogen gradients.

Successful biological development via spatial regulation of cell differentiation relies on the action of multiple signaling molecules that are known as morphogens. It is now well-established that signaling molecules create non-uniform concentration profiles, morphogen gradients, that activate different genes, leading to patterning in the developing embryos. The current view of the formation of morphogen gradients is that it is a result of complex reaction-diffusion processes that include the strongly localized production, diffusion and uniform degradation of signaling molecules. However, multiple experimental studies also suggest that the production of morphogen in many cases is delocalized. We develop a theoretical method that allows us to investigate the role of the delocalization in the formation of morphogen gradients. The approach is based on discrete-state stochastic models that can be solved exactly for arbitrary production lengths and production rates of morphogen molecules. Our analysis shows that the delocalization might have a strong effect on mechanisms of the morphogen gradient formation. The physical origin of this effect is discussed.

Theoretical analysis of degradation mechanisms in the formation of morphogen gradients.

Fundamental biological processes of development of tissues and organs in multicellular organisms are governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in the concentration profiles of signaling molecules, which are frequently referred as morphogen gradients, lead to a cell differentiation via activating specific genes in a concentration-dependent manner. It is widely accepted that the establishment of the morphogen gradients involves multiple biochemical reactions and diffusion processes. One of the critical elements in the formation of morphogen gradients is a degradation of signaling molecules. We develop a new theoretical approach that provides a comprehensive description of the degradation mechanisms. It is based on the idea that the degradation works as an effective potential that drives the signaling molecules away from the source region. Utilizing the method of first-passage processes, the dynamics of the formation of morphogen gradients for various degradation mechanisms is explicitly evaluated. It is found that linear degradation processes lead to a dynamic behavior specified by times to form the morphogen gradients that depend linearly on the distance from the source. This is because the effective potential due to the degradation is quite strong. At the same time, nonlinear degradation mechanisms yield a quadratic scaling in the morphogen gradients formation times since the effective potentials are much weaker. Physical-chemical explanations of these phenomena are presented.

Development of morphogen gradient: the role of dimension and discreteness.

The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances, and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuum descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.

Physical-Chemical Features Selection Reveals That Differences in Dipeptide Compositions Correlate Most with Protein-Protein Interactions.

The ability to accurately predict protein-protein interactions is critically important for our understanding of major cellular processes. However, current experimental and computational approaches for identifying them are technically very challenging and still have limited success. We propose a new computational method for predicting protein-protein interactions using only primary sequence information. It utilizes a concept of physical-chemical similarity to determine which interactions will most probably occur. In our approach, the physical-chemical features of protein are extracted using bioinformatics tools for different organisms, and then they are utilized in a machine-learning method to identify successful protein-protein interactions via correlation analysis. It is found that the most important property that correlates most with the protein-protein interactions for all studied organisms is dipeptide amino acid compositions. The analysis is specifically applied to the bacterial two-component system that includes histidine kinase and transcriptional response regulators. Our theoretical approach provides a simple and robust method for quantifying the important details of complex mechanisms of biological processes.

Differences in Relevant Physicochemical Properties Correlate with Synergistic Activity of Antimicrobial Peptides.

With the urgent need for new medical approaches due to increased bacterial resistance to antibiotics, antimicrobial peptides (AMPs) have been considered as potential treatments for infections. Experiments indicate that combinations of several types of AMPs might be even more effective at inhibiting bacterial growth with reduced toxicity and a lower likelihood of inducing bacterial resistance. The molecular mechanisms of AMP-AMP synergistic antimicrobial activity, however, remain not well understood. Here, we present a theoretical approach that allows us to relate the physicochemical properties of AMPs and their antimicrobial cooperativity. It utilizes correlation and bioinformatics analysis. A concept of physicochemical similarity is introduced, and it is found that less similar AMPs with respect to certain physicochemical properties lead to greater synergy because of their complementary antibacterial actions. The analysis of correlations between the similarity and the antimicrobial properties allows us to effectively separate synergistic from nonsynergistic AMP pairs. Our theoretical approach can be used for the rational design of more effective AMP combinations for specific bacterial targets, for clarifying the mechanisms of bacterial elimination, and for a better understanding of cooperativity phenomena in biological systems.

Elucidating Physicochemical Features of Holin Proteins Responsible for Bacterial Cell Lysis.

Bacterial resistance to conventional antibiotics stimulated the development of so-called "phage therapies" that rely on cell lysis, which is a process of destroying bacterial cells due to their infections by bacterial viruses. For λ bacteriophages, it is known that the critical role in this process is played by holin proteins that aggregate in cellular membranes before breaking them apart. While multiple experimental studies probed various aspects of cell lysis, the underlying molecular mechanisms remain not well understood. Here we investigate what physicochemical properties of holin proteins are the most relevant for these processes by employing statistical correlation analysis of cell lysis dynamics for different experimentally observed mutant species. Our findings reveal significant correlations between various physicochemical features and cell lysis dynamics. Notably, we uncover a strong inverse correlation between local hydrophobicity and cell lysis times, underscoring the crucial role of hydrophobic interactions in membrane disruption. Stimulated by these observations, a predictive model capable of explicitly estimating cell lysis times for any holin protein mutants based on their mean hydrophobicity values is developed. Our study not only provides important microscopic insights into cell lysis phenomena but also proposes specific routes to optimize medical and biotechnological applications of bacteriophages.

All-time dynamics of continuous-time random walks on complex networks.

The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social, and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallel-chain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.